Lecture
Modern Hydrogen Bonding TheoryModern Hydrogen Bonding Theory
By Gastone GilliDepartment of Chemistry
andCentre for Structural Diffractometry
University of Ferrara Italy
23rd EuropeanCrystallographicMeeting
6-11 August 2006Leuven Belgium
The Tale of the Princess of the Hydrogen Bond TheoryThe Tale of the Princess of the Hydrogen Bond Theory
The HB story begins in 1920 It has not been a season of peaceful advancement of sciences but rather a perpetual and sometimes bitter dispute among partisan groups of spectroscopists thermodynamics crystallographers and theoreticians
I find more elegant to look at it as a fairy tale the tale of the beautiful and gifted Princess of the HB Theory who was born in a wonderful palace of white marbles over the Great Sea full of great savants who dedicated themselves to enlighten the life of men making light where before there was darkness
In her first years of life she enlightened the world with the treasures of her wisdom disclosing the secrets of ice and water and of the molecules of life
When she was twenty however a terrible war devastated the world and after it nothing was longer the same The business people took the place of the enlightened people new discoveries became to be sold for money as Patents The white palace was deserted and abandoned and finally occupied by the merciless tribe of the Advanced Technologists
The princess fled with a small group of Physicochemical Followers to the Highlands of Crystallography where all was dazzling white and frozen and everything transformed into beautiful crystals There they remained more than twenty years pursuing their aims in the bright light of the high mountains
This lecture is a kind of Return Tale telling us how the princess came back to the plain and rebuilt her white palace among the people loosing however the clear light of the heights
The Birth of the HBThe Birth of the HB
The idea of HB was firstly conceived in the laboratory of Gilbert Newton Lewis at the end of the lsquo20ties while he was writing his famous book Valence and the structure of atoms and molecules (1923)
The final assessment of the HB concept is accredited to ML Huggins and
independently to WM Latimer and WH Rodebush three young men working there The first paper published on the HB was WM Latimer and WH Rodebush
Polarity and ionization from the standpoint of the Lewis theory of valence J Am Chem Soc 42 1419-1433 1920
The first book on the HB was written by Pauling who made eventually known the
HB to the wider chemical community Pauling L The Nature of the chemical bond and the structure of molecules and crystals An introduction to modern structural chemistry Cornell University Press Ithaca NY 1939 1940 1960 Chapter 12 55 pages
The definition of HB has remained substantially unchanged from then on I prefer
that proposed by Vinogradov SN and Linnel RH Hydrogen bonding Van Nostrand-Reinhold New York 1971
The Hydrogen Bond DefinitionThe Hydrogen Bond Definition Three-Center-Four-Electron Interaction
RDmiddotmiddotH ARrsquowhere D is the HB Donor An electronegative atom such as F O N C S Cl Br I
and A the HB Acceptor or Lone Pair Carrier A second electronegative atom or a multiple bond that is -bond
Alternatively a proton sharing two lone electron pairs from
two adjacent electronegative atoms
RD H+ ARrsquo
Two Very Important HB PropertiesTwo Very Important HB Properties The HB acceptor is not an atom but a lone electron pair located on that atom
Being both D and A electronegative the HB must have a fixed polarity
RDHARrsquo
Electrostatic and Covalent HBs The Paulingrsquos ModelElectrostatic and Covalent HBs The Paulingrsquos Model
Linus Pauling (The Nature of the Chemical Bond 1939 1940 1960) describes two distinct classes of HBs
Weak and dissymmetric HBs of electrostatic nature It is recognized that the hydrogen atom with only one stable orbital (the 1s orbital) can form only one covalent bond that the hydrogen bond is largely ionic in character and that it is formed only between the most electronegative atoms (HB Chapter - Page 1)
Strong and symmetric HBs of covalent nature These ldquoare exceptionsrdquo described as ldquo the hydrogen bond in the [HF2]
ion lies midway the two fluorine atoms and
may be considered to form a half-bond with eachrdquo (HB Chapter - Page 49)
[FHF] [OHO][OHO]+ [OHO]+
Coulsonrsquos VB Treatment (The Standard HB Model)Coulsonrsquos VB Treatment (The Standard HB Model)
Paulingrsquos ideas acquired theoretical dignity with the VB treatment of Coulson and Danielsson in 1954 where the O-HO bond is described as a mixture of three main VB forms two covalent and one ionic
This line of thought was embraced by
Pimentel and McClellan in their famous book The Hydrogen Bond (1960)
They write ldquoAt the 1957 Ljubljana Conference one of the important points of fairly general accord was that the electro-static model does not account for all of the phenomena associated with H bond formationrdquo
E E
NCT
CT
CTNCT
COV2
IONIC
COV1
IONIC
COV1 COV2
NCT
NCT
(a) Electrostatic HB (b) Covalent HB
The Birth of the Simple Electrostatic ParadigmThe Birth of the Simple Electrostatic Paradigm For reasons difficult to understand the Standard HB Model was abandoned
in the mid-lsquo60ies and the HB became the weak electrostatic interaction of some 4-6 kcal mol-1 everyone has heard of while strong HBs just disappeared from the chemical horizon
From there on the HB was divided between a small group of specialists (who still believed in the Standard Model) and the great majority of other scientists (who trusted more the much simpler Electrostatic Paradigm)
The effect on HB studies was disastrous and it took more than twenty years to put it right
Why Paulingrsquos Thought was AbandonedWhy Paulingrsquos Thought was Abandoned Weak electrostatic HBs are quoted on page 1 and strong covalent ones at
page 49 Since most people read only the first few pages helliphellip On page 50 strong HBs are defined ldquoexceptionsrdquo Most readers may have
thought Why to bother about exceptions when there are already so many regular HBs to bother about These are things for specialists
In VB terms ldquothe hydrogen atom can form only one covalent bondhelliprdquo does not mean that there is only one bond but that there may be any combination of two bonds whose bond orders sum up to one from 1+0 to 0+1 through frac12+ frac12 Probably very few people understood that correctly
Another Unsolved Problem The HB PuzzleAnother Unsolved Problem The HB Puzzle
Bond lengths and energies of normal chemical bonds are found to depend on the nature of the interacting atoms
and are weakly perturbed by their external environment
Conversely binding energies (EHB) and DmiddotmiddotmiddotA distances (dDmiddotmiddotmiddotA) of DHmiddotmiddotmiddotA bonds
do not simply depend on the donor (D) and acceptor (A) nature but show very large variations even for the same donor-acceptor couple
This is what we have called for the sake of brevity
the HB Puzzlethe HB PuzzleAn extreme example of this behavior comes from the effects produced on
the OHmiddotmiddotmiddotO bond by the changing acid-base properties of its environment The weak HOHmiddotmiddotmiddotOH2 bond in water [EHB5 kcal mol-1 dOmiddotmiddotmiddotO270-275 Aring]
is switched in acidic or basic medium to the very strong [H2OmiddotmiddotmiddotHmiddotmiddotmiddotOH2]+ or
[HOmiddotmiddotmiddotHmiddotmiddotmiddotOH] bonds with EHB up to 30-31 kcal mol-1 and dOmiddotmiddotmiddotO down to 238-242 Aring
How to Solve the HB Puzzle How to Solve the HB Puzzle the Problem of the Driving Variablethe Problem of the Driving Variable
The Electrostatic Paradigm cannot explain the HB Puzzle
Neither the Standard Model provides a full interpretation of it because while it can explain what covalent and electrostatic HBs are
it cannot suggest which circumstances can produce them
To put the problem in more general terms there are dozens of physicochemical variables commonly measured in connection with the HB (energies geometries IR frequencies NMR chemical shifts NQR couplings and isotopic effects of the HB itself and in addiction a large number of other properties of the interacting molecules) and most if not all appear to be strongly inter-correlated But
whatrsquos the driving variablewhatrsquos the driving variable
whatrsquos the variable which among the many intercorrelated ones drives the transformation from weak and electrostatic
to strong and covalent HB
A Proposal The PApA Proposal The PApKKaa Equalization Principle Equalization Principle
Two very similar proposals come from early thermodynamic or spectroscopic investigations and are both centered on the
matching of the acid-base properties of the HB donor and acceptors moieties what we like too call for the sake of brevity the
PApPApKKaa Equalization Principle Equalization Principle
With reference to any generic DHmiddotmiddotmiddotA bond this principle states that the HB becomes the stronger the smaller is the difference of the donor-acceptor
proton affinities proton affinities PA = PA(DPA = PA(D) ) PA(A) PA(A)or
acidic constants acidic constants ppKKa a = p= pKKAHAH(D(DH) H) p pKKBH+BH+(A(AHH++))
------------------------------------------------------------------------------------------------------------------------- Ault BS and Pimentel GG (1975) J Phys Chem 79 615 Huyskens PL and Zeegers-Huyskens Th (1964) J Chim Phys Phys- Chim Biol
61 81
Our First Steps in the HB FieldOur First Steps in the HB Field As usual we entered the field by chance In 1985 we were studying the ligands
of the benzadiazepine membrane receptor One of these ligands was CGS8216 where we noticed something strange a rather short N-HhellipO bond of 2694 Aring associated with an interleaving β-enaminone hellipO=C-C=C-NHhellip fragment which was almost completely π-delocalized
It was the first indication of a possible correlation between -delocalization and H-bond strength what was called a few years later the
Resonance-Assisted H-Bond (RAHB)Resonance-Assisted H-Bond (RAHB) (Gilli Bellucci Ferretti amp Bertolasi JACS 1989 Bertolasi Gilli Ferretti amp Gilli JACS 1991) Since at the time few -enaminones were known the work started on the analogous class of -enolones (or -diketone enols) which were already known to give strong O-HO bonds through the equally resonant O=C-C=C-OH fragment
The Development of the OThe Development of the OHO RAHBHO RAHB
The OThe OHO RAHBsHO RAHBs
Very interesting Class of Strong HBs Different lengths of the resonant spacer Rn
(n = 1 3 5 7) The HBs formed were all much stronger than normal (non-resonant) OHO bonds withd(OO)INTRA =
239-255 Aringd(OO)INTER =
246-265 Aring
R1-RAHBR5-RAHB
24256 Aring
N
N
O M e
N
N
OM e
M eM e
H
lt 257 gt1 Aring
P
O H
OO
O H
H P
O H
OO
O H
H
R3-RAHB
O OH
237-255 Aring
262-267 Aring
O
O H O
OH
262-270 Aring
O
O
H
O
O H
R7-RAHB
24462 Aring
NOO
OO
M eM e
H
OOH
O
O
H
CARBOXYLIC ACIDS
DIBENZOYLMETHANE ENOLS
CYCLOHEXANEDIONE ENOLS
PHOPHORIC ACID
A Model for RAHB Electrostatic or CovalentA Model for RAHB Electrostatic or Covalent
At first (JACS 1989) we suggested a RAHB Electrostatic Model but it became rapidly evident that an efficient RAHB treatment would require a Covalent Model
All hell broke loose because as we discovered with surprise the concept itself of covalent HB had been banned some twenty years before and substituted by the acritical but more comfortable Simple Electrostatic Paradigm RAHB seriously risked to became a kind of bizarre covalent hypothesis
I must thank George A Jeffrey with his inimitable unbiased and skeptical style if RAHB was not immediately cast aside by the scientific establishment but started to be quoted in important books and reviews during the lsquo90ties
A RAHB Electrostatic ModelA RAHB Electrostatic Model A RAHB Covalent ModelA RAHB Covalent Model
Starting Again The Purely Empirical ApproachStarting Again The Purely Empirical Approach Fortunately we were realistic enough not to try to confute the Electrostatic
Paradigm On the other hand it was perfectly useless because too deeply rooted in the Weltanschaung of so many important and self-confident scientists
I have already given a short critical account of the very nature of these scientific paradigms at the ECM-2000 of Nancy based on the ideas of Thomas S Kuhn (The Structure of Scientific Revolutions The University of Chicago 1962 and 1970)
Anyway to get out of this impasse at the beginning of 1993 we decided to change approach and to restart to investigate the O-HO bond problem from the very beginning by adopting a purely empirical strategy
(i) suspend any previous ideas on the electrostatic or covalent nature of the HB (ii) define the OHmiddotmiddotmiddotO bond as a simple topological structure where a H atom is connected to two or more oxygen atoms(iii) collect all crystal structures having OHmiddotmiddotmiddotO bonds with d(OmiddotmiddotmiddotO) 270 Aring(iv) collect all available IR (O-H) and NMR (H) data of H-bonded protons(v) collect all available HB energy data from thermodynamic measurements in gas phase and non-polar solvents(vi) try to infer a conclusion on the very nature of the OHmiddotmiddotmiddotO bond from the ensemble of the data collected
A Full Classification of Strong HBsA Full Classification of Strong HBs
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs)CHARGE - ASSISTED HBs
PENTACHLOROPHENOL - p-TOLUIDINE
pKa = -070
12
12
N
CH3
O
ClCl
Cl
Cl
Cl
H25062 AringCL 1 (+ndash)CAHB SHB VSHB
Double Charge-Assisted HBDirect Acid-Base PApKa Matching
CL 2 (ndash)CAHB SHB VSHBNegative Charge-Assisted HB
Acid-Base PApKa Matching by Proton Loss R
OOH
R
O O24371 Aring
CARBOXYLIC ACID - CARBOXYLATE
CL 3 (+)CAHB SHB VSHBPositive Charge-Assisted HB
Acid-Base PApKa Matching by Proton Gain
O
HH H
O
HH
24303 Aring
WATER - HYDRONIUM
-BOND POLARIZATION - ASSISTED HBs
237-255 Aring
O OH
ArAr
DIBENZOYLMETHANE ENOLS
CL 4 RAHB SHB VSHB Resonance-Assisted or -Cooperative HB
PApKa Matching by -Conjugated-Bond Polarization
27501 Aring
OO
O
O O
WATER
CL 5 PAHB MHBPolarization-Assisted or -Cooperative HB(Partial) PApKa Matching by -Bond Polarization
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs) The most interesting aspect of a HB classification based on HB strength is that strong HBs belong only to a small number of chemical schemes that we have called Chemical Leitmotifs
The Alchemic Piper plays the Five Magic Tunes that make any Hydrogen Bond stronger The Chemical Leitmotifs
Symmetry and Covalency (1)Symmetry and Covalency (1)The covalent nature of the strong OHmiddotmiddotmiddotO bond was assessed by interpreting the
experimental results in terms of the Coulsonrsquos VB formalismWe cannot measure covalency but can evaluate molecular symmetry the
Coulsonrsquos model being the algorithm able to translate one concept into the other
In fact total symmetry across the HB implies energy equivalence between the two covalent VB forms ie E(ΨCOV1) = E(ΨCOV2) which is just the situation
associated with formation of the covalent HB
E E
NCT
CT
CTNCT
COV2
IONIC
COV1
IONIC
COV1 COV2
NCT
NCT
(a) Electrostatic HB (b) Covalent HB
Symmetry and Covalency (2)Symmetry and Covalency (2)
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 1
(+-)CAHBDouble Charge-Assisted HB
Direct Acid-Base PApKa Matching
R12DH+A12R
The role played by the PApKa equalization in HB strengthening
is self-evident for the (+-)CAHB chemical leitmotif
RDHARrsquo R12DH+A12Rrsquo RDHA+Rrsquo
which collects by definition all strong HBs formed by the acid-base pairs with a pKa matching within say ndash3 divide 3 pKa units
But what about the other leitmotifs Can we prove that
all chemical leitmotifs are simple artificesthat molecules can use to obliterate the normally
very large pKa between HB donor and acceptor atoms
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 2(-)CAHB
Negative Charge-Assisted HBAcid-Base PApKa Matching
by Proton Loss[R-DHA-R]-
Chemical Leitmotif 3(+)CAHB
Positive Charge-Assisted HBAcid-Base PApKa Matching
by Proton Gain[R-DHA-R]+
2II
2III
2IIa
2IIb
2IIIb
2IIIa
2VIa
pKa = pKAH(HO-H)-pKAH(HO-H) = 157 - 157 = 0
pKa = pKBH(H2O-H+)-pKBH(H2O-H
+) = -17 + 17 = 0
pKAH(HO-H) = 157
pKBH(H2O-H+) = -17
H
O H
H
O
H
(ndash)CAHB pKa = 00
VERYSTRONG~ 25-30 kcalmol
(+)CAHB pKa = 00
VERYSTRONG ~ 25-31 kcalmol
pKa = 175
OHB
WEAK ~ 4- 5kcalmol
ndash H+
+ H+
H
O H O
H
H
O H O
H
H
OHO
H
H
O
H
H
H
O
H
H
O
H
H
O
H
H H
O
H
H
H
O
H
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 4RAHB
Resonance-Assisted or -Bond Cooperative HBPApKa Matching by -Conjugated-Bond Polarization
R-D-HA=R R=DH-A-R
pKAH(RO-H) = 1518
pKBH(R2C=O-H+) = -(67)
O OH
O H O
R
R
R
Rn-RAHB pKa = ~ 21-25
WEAK ~ 4- 5kcalmol
EKO O
H
KEOO
H
pKa = 00
STRONG ~ 15-22 kcalmol
2IV
2IVa
2IVb
2VIb
OHB
The HB Empirical RulesThe HB Empirical Rules
The empirical analysis of experimental data joined with homeopathic doses of VB theory leads us to formulate two important HB Empirical Rules which have been called elsewhere ECHBM (Electrostatic-Covalent HB Model Gilli amp Gilli J Mol Struct 2000) and can be summarized as follows
Any given D-HA system may form HBs in a wide range of strengths lengths symmetries and proton locations the two extremes being represented
by the weak long dissymmetric and proton-out-centred HB of electrostatic nature
and by the very strong very short symmetric and proton-centred HB
classifiable as a true 3-center-4-electron covalent bond
The driving variable able to transform strong into weak HBs is dimensionally a free enthalpy corresponding to the difference between the Proton Affinities (PA) or related Acid-Base Dissociation Constants (pKa) of the Donor and Acceptor moieties
These rules have been verified beyond any reasonable doubt for the Conventional HBs of the following classification
Provisional Conclusions and New ControlsProvisional Conclusions and New Controls
We have so far established a sound set of empirical rules which include A full classification of all existing HBs A full classification of all strong HBs (The Chemical Leitmotifs) A plausible correlation between HB strengths and acid-base properties of the interacting molecules (The PApKa Equalization Principle)
To confirm this last point we have undertaken two years ago
a new research program aimed at assessing the Full Validity of the PApKa Equalization Principle
by comparing extended tables of pKa values arranged for chemical classes
withthe corresponding CSD-derived HB geometries
Hundreds of pKa were collected and more than 11000 crystal structures examined
The pThe pKKa Slide Rulea Slide Rule
It is a tool for the graphical evaluation of the difference
pKa = pKAH(DH) - pKBH+(AH+)
HB Acceptors on the left and HB Donors on the right
pKa values given for chemical class
Results expected
ΔpKagtgt0 DHmiddotmiddotmiddotmiddotA weak amp neutral
ΔpKa asymp 0 DmiddotmiddotmiddotHmiddotmiddotmiddotA strong amp
centeredΔpKa ltlt0DmiddotmiddotmiddotmiddotHA+ weak amp charged
pKa ranges of organic compounds
C-H acids -11 ltpKalt 53
Other Donors -1 ltpKalt 40
Acceptors -12 ltpKalt 16
All -15 ltpKalt 53
Water 0 ltpKalt 14
50
-10
0
10
20
30
40
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
ALDEHYDES
ETHERSALCOHOLS
AMIDES
NITRILES
ANILINES
CF3-SO3H
HClO4HI
HBrHCl
H2SO4
HSO4
HNO3
HBF4
H3PO4
H2PO4
HPO42
HF HNO2
HNNN
NH2OHH2CO3
HCO3
H2S
HS-
HCN H3BO3
H2BO3
H4SiO4
H2O2
HO
HSCN
H-H
SULFONICACIDS
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
OXIMES
ALCOHOLS
THIOLES
HB ACCEPTORS (A)pK BH+
HB DONORS (D-H)pK AH
C-H ACIDS pK AH
BE
TT
ER
HB
AC
CE
PT
OR
BE
TT
ER
BA
SE
BE
TT
ER
HB
DO
NO
R
BE
TT
ER
AC
ID
N-OXIDES
AMIDINES
UREA
THIOUREA
BARBITURICURIC ACID
MONO DIPHOSPHINES
TRIPHOSPHINES
TRINITROANILINES
AMINES
ANILINES
MONO DINITROANILINES
AMIDES
CARBOXYLIC ACIDS
HALOGENOANILINES
AZOCOMPS
TRINITROANILINES
PROTONSPONGES
ACIDSESTERS
H2O
H2O
MONODINITROANILINES
KETONES
SULFIDES
HALOGENCARB ACIDS
TRINITROPHENOLS
ENOLS
MONO DINITROPHENOLS
PHENOLSNAPHTHOLS
HALOGENOPHENOLS
HALOGENOALCOHOLS
SULFOXIDES
(NC)5-CYCLO
PENTADIENE
(NC)3CH
(O2N)2=CH2
HCCHNC-CH3
CH3-CO-CH3INDENE
O2N-CH3
(NC)2=CH2
(O2N)3CH
H2C=CH2
C6H6
CH4
CYCLOPENTADIENE
CYCLOPROPENE
Ar3CH
Ar2=CH2
Ar-CH3
NITROCOMPS
SELENOXIDES
AZOLES
AZINESDIAZINES
AMINES
Cl5-PHENOL
CH3-CH3
(CH3)3CH
NH3
NH3
51
53
51
53
Chemical Leitmotifs and PApChemical Leitmotifs and PApKKaa Equalization Rules Equalization Rules RAHB RAHB cannot be treated by pKa equalization methods because π-delocalization
modifies the pKarsquos of the donor and acceptor moieties (+)CAHB is a true proton transfer from an acid (HB donor) to a base (HB acceptor)
RndashDndashHAndashRrsquo Rndash12DH+A12ndashndashRrsquo RndashDHndashA+ndashRrsquoΔpKa = pKAH(RDH) pKBH+(RrsquoA)
()CAHB is a proton sharing between two acids (HB donors)
RndashDndashHDrsquondashRrsquo [RDHDrsquoRrsquo] RDHDrsquoRrsquoΔpKa = pKAH(RDH) pKAH(RDH)
(+)CAHB is a proton sharing between two bases (HB acceptors)
R+AHArsquoRrsquo [RAHArsquoRrsquo]+ RAHArsquo+RrsquoΔpKa = pKBH+(RA) pKBH+(RrsquoArsquo)
Whenever () and (+)CAHBs are both homonuclear (D = Drsquo or A = Arsquo) and
homomolecular (R = Rrsquo) the matching condition ΔpKa= 0 will hold irrespective of the
actual pKarsquos of the two interacting moieties All HBs formed will be strong
Some Famous HBsSome Famous HBs
The NThe NHmiddotmiddotmiddotOOHmiddotmiddotmiddotOOHmiddotmiddotmiddotN System over the Full HmiddotmiddotmiddotN System over the Full ppKKaa Range Range
When evaluated from the pKa slide rule the total pKa range is extremely wide
ndash30 pa 60 So far we have been able to shown that the pKa equalization rule certainly holds in
a restricted interval around zero The problem is now Does this rule hold in the full pKa range
We will try to prove that by a full analysis the N-HmiddotmiddotmiddotOO-HmiddotmiddotmiddotN system
Procedure In a first CSD search functional groups of known pKa value and more frequently
implied in NHmiddotmiddotmiddotOOHmiddotmiddotmiddotN bonds were identified Finally 10 classes of donors and 11 of acceptors were selected and the search restarted for each separate donor-acceptor group Altogether 9078 different bonds were analyzed (4364 NHmiddotmiddotmiddotO 2289 OHmiddotmiddotmiddotN and
2425 OmiddotmiddotmiddotHN+) For each bond the NmiddotmiddotmiddotO distances were evaluated as dNH + dHO to account for the
N-H-O angle and for each group the shortest and average distances [dNmiddotmiddotmiddotO (min)
and dNmiddotmiddotmiddotO (mean)] were registered
These values were compared (see next slide) with the acid-base features of the donors (pKAH range) acceptors (pKBH+ range) and with their combinations
(pKa range)
pKa large amp positive
pKa largeamp negative
Increasing Acidity of the Protonated A H+ Acceptor Increasing Basicity of the A Acceptor
ppKKaa versusversus HB Geometry Correlation - Conclusions HB Geometry Correlation - Conclusions The PApKa Equalization Principle is therefore fully confirmed in its two forms All strong HBs correspond to very small pKa values
pKa values modulate the HB strength over the full pKa range These conclusions are of great practical importance in at least two respects pKa is definitively established as the driving force which controls the HB
strength by modulating the HB covalent contribution It is definitively established that an accurate analysis of structural crystal data
leads to the same conclusions suggested but never proved on a general base by thermodynamic and spectroscopic methods
References Huyskens and Zeegers-Huyskens 1964 Zeegers-Huyskens 1986 1988 Ault and Pimentel 1975 Ratajczak and Sobczyk 1969 Sobczyk et al 1982 Barnes 1983 Kebarle et al 1974-1979 Meot-Ner (Mautner) et al
1984-1988
Towards a General HB TheoryTowards a General HB Theory
The results so far obtained are not a True HB Theory but rather a Set of Empirical Rules (or an Empirical Natural Law) that is a great collection of HB experimental data neatly organized in tables which all together represent a General Taxonomy of the HB Phenomenon exactly as the Carl Linnaeusrsquo classification of plants A scientific theory is something different It is the casting of the empirical natural law into the frame of a theory which is more fundamental down to the reductionistic chain of the scientific disciplines For instance the kinetic gas theory is the casting of the empirical gas laws (the empirical natural law) into Newtonrsquos classical mechanics
How to make a HB TheoryHow to make a HB Theory
HB Properties = FF (HB Driving Variable)where
HB Driving Variable = PApKa and FF = Transition-State Theory
The Transition-State HB TheoryThe Transition-State HB Theory(Gilli et al JACS 2002 2005 Gilli et al J Mol Struct 2006)
Though it has taken us more than 12 years to develop it
the basic idea is very simpleAny DndashHmiddotmiddotmiddotA bond can be considered as a chemical reaction which is
bimolecular in both directions and proceeds via transition-state (TS) formation
AndashB + C AmiddotmiddotmiddotBmiddotmiddotmiddotC A + BndashCDndashHmiddotmiddotmiddotA DmiddotmiddotmiddotHmiddotmiddotmiddotA DmiddotmiddotmiddotHndashA
Changes of nomenclatureReaction Pathway PTPathwayActivation Energy DaggerE PTBarrierReaction Energy Er PApKa Transition State (TS) PTTS
Reaction Coordinate RC=[d(DH)ndashd(AH)] Experimentals Variable-Temperature X-allographyCalculations DFTEmulated PTPathwaysInterpretation Marcus Rate-Equilibrium Theory LefflerHammond Postulate
AcknowledgmentsAcknowledgments I have to thank my direct coworkers without whose help this work could have not been accomplished
Valerio BERTOLASI Paola GILLI
Valeria FERRETTI Loretta PRETTO
and the scientific institutions which made available to us the databases without which this work could not even be started
CCDCCambridge Crystallographic
Data Centrefor the use of the
Cambridge Structural Database
NIST National Institute of Standards and
Technologyfor the use of the
NIST Chemistry WebBook
The Tale of the Princess of the Hydrogen Bond TheoryThe Tale of the Princess of the Hydrogen Bond Theory
The HB story begins in 1920 It has not been a season of peaceful advancement of sciences but rather a perpetual and sometimes bitter dispute among partisan groups of spectroscopists thermodynamics crystallographers and theoreticians
I find more elegant to look at it as a fairy tale the tale of the beautiful and gifted Princess of the HB Theory who was born in a wonderful palace of white marbles over the Great Sea full of great savants who dedicated themselves to enlighten the life of men making light where before there was darkness
In her first years of life she enlightened the world with the treasures of her wisdom disclosing the secrets of ice and water and of the molecules of life
When she was twenty however a terrible war devastated the world and after it nothing was longer the same The business people took the place of the enlightened people new discoveries became to be sold for money as Patents The white palace was deserted and abandoned and finally occupied by the merciless tribe of the Advanced Technologists
The princess fled with a small group of Physicochemical Followers to the Highlands of Crystallography where all was dazzling white and frozen and everything transformed into beautiful crystals There they remained more than twenty years pursuing their aims in the bright light of the high mountains
This lecture is a kind of Return Tale telling us how the princess came back to the plain and rebuilt her white palace among the people loosing however the clear light of the heights
The Birth of the HBThe Birth of the HB
The idea of HB was firstly conceived in the laboratory of Gilbert Newton Lewis at the end of the lsquo20ties while he was writing his famous book Valence and the structure of atoms and molecules (1923)
The final assessment of the HB concept is accredited to ML Huggins and
independently to WM Latimer and WH Rodebush three young men working there The first paper published on the HB was WM Latimer and WH Rodebush
Polarity and ionization from the standpoint of the Lewis theory of valence J Am Chem Soc 42 1419-1433 1920
The first book on the HB was written by Pauling who made eventually known the
HB to the wider chemical community Pauling L The Nature of the chemical bond and the structure of molecules and crystals An introduction to modern structural chemistry Cornell University Press Ithaca NY 1939 1940 1960 Chapter 12 55 pages
The definition of HB has remained substantially unchanged from then on I prefer
that proposed by Vinogradov SN and Linnel RH Hydrogen bonding Van Nostrand-Reinhold New York 1971
The Hydrogen Bond DefinitionThe Hydrogen Bond Definition Three-Center-Four-Electron Interaction
RDmiddotmiddotH ARrsquowhere D is the HB Donor An electronegative atom such as F O N C S Cl Br I
and A the HB Acceptor or Lone Pair Carrier A second electronegative atom or a multiple bond that is -bond
Alternatively a proton sharing two lone electron pairs from
two adjacent electronegative atoms
RD H+ ARrsquo
Two Very Important HB PropertiesTwo Very Important HB Properties The HB acceptor is not an atom but a lone electron pair located on that atom
Being both D and A electronegative the HB must have a fixed polarity
RDHARrsquo
Electrostatic and Covalent HBs The Paulingrsquos ModelElectrostatic and Covalent HBs The Paulingrsquos Model
Linus Pauling (The Nature of the Chemical Bond 1939 1940 1960) describes two distinct classes of HBs
Weak and dissymmetric HBs of electrostatic nature It is recognized that the hydrogen atom with only one stable orbital (the 1s orbital) can form only one covalent bond that the hydrogen bond is largely ionic in character and that it is formed only between the most electronegative atoms (HB Chapter - Page 1)
Strong and symmetric HBs of covalent nature These ldquoare exceptionsrdquo described as ldquo the hydrogen bond in the [HF2]
ion lies midway the two fluorine atoms and
may be considered to form a half-bond with eachrdquo (HB Chapter - Page 49)
[FHF] [OHO][OHO]+ [OHO]+
Coulsonrsquos VB Treatment (The Standard HB Model)Coulsonrsquos VB Treatment (The Standard HB Model)
Paulingrsquos ideas acquired theoretical dignity with the VB treatment of Coulson and Danielsson in 1954 where the O-HO bond is described as a mixture of three main VB forms two covalent and one ionic
This line of thought was embraced by
Pimentel and McClellan in their famous book The Hydrogen Bond (1960)
They write ldquoAt the 1957 Ljubljana Conference one of the important points of fairly general accord was that the electro-static model does not account for all of the phenomena associated with H bond formationrdquo
E E
NCT
CT
CTNCT
COV2
IONIC
COV1
IONIC
COV1 COV2
NCT
NCT
(a) Electrostatic HB (b) Covalent HB
The Birth of the Simple Electrostatic ParadigmThe Birth of the Simple Electrostatic Paradigm For reasons difficult to understand the Standard HB Model was abandoned
in the mid-lsquo60ies and the HB became the weak electrostatic interaction of some 4-6 kcal mol-1 everyone has heard of while strong HBs just disappeared from the chemical horizon
From there on the HB was divided between a small group of specialists (who still believed in the Standard Model) and the great majority of other scientists (who trusted more the much simpler Electrostatic Paradigm)
The effect on HB studies was disastrous and it took more than twenty years to put it right
Why Paulingrsquos Thought was AbandonedWhy Paulingrsquos Thought was Abandoned Weak electrostatic HBs are quoted on page 1 and strong covalent ones at
page 49 Since most people read only the first few pages helliphellip On page 50 strong HBs are defined ldquoexceptionsrdquo Most readers may have
thought Why to bother about exceptions when there are already so many regular HBs to bother about These are things for specialists
In VB terms ldquothe hydrogen atom can form only one covalent bondhelliprdquo does not mean that there is only one bond but that there may be any combination of two bonds whose bond orders sum up to one from 1+0 to 0+1 through frac12+ frac12 Probably very few people understood that correctly
Another Unsolved Problem The HB PuzzleAnother Unsolved Problem The HB Puzzle
Bond lengths and energies of normal chemical bonds are found to depend on the nature of the interacting atoms
and are weakly perturbed by their external environment
Conversely binding energies (EHB) and DmiddotmiddotmiddotA distances (dDmiddotmiddotmiddotA) of DHmiddotmiddotmiddotA bonds
do not simply depend on the donor (D) and acceptor (A) nature but show very large variations even for the same donor-acceptor couple
This is what we have called for the sake of brevity
the HB Puzzlethe HB PuzzleAn extreme example of this behavior comes from the effects produced on
the OHmiddotmiddotmiddotO bond by the changing acid-base properties of its environment The weak HOHmiddotmiddotmiddotOH2 bond in water [EHB5 kcal mol-1 dOmiddotmiddotmiddotO270-275 Aring]
is switched in acidic or basic medium to the very strong [H2OmiddotmiddotmiddotHmiddotmiddotmiddotOH2]+ or
[HOmiddotmiddotmiddotHmiddotmiddotmiddotOH] bonds with EHB up to 30-31 kcal mol-1 and dOmiddotmiddotmiddotO down to 238-242 Aring
How to Solve the HB Puzzle How to Solve the HB Puzzle the Problem of the Driving Variablethe Problem of the Driving Variable
The Electrostatic Paradigm cannot explain the HB Puzzle
Neither the Standard Model provides a full interpretation of it because while it can explain what covalent and electrostatic HBs are
it cannot suggest which circumstances can produce them
To put the problem in more general terms there are dozens of physicochemical variables commonly measured in connection with the HB (energies geometries IR frequencies NMR chemical shifts NQR couplings and isotopic effects of the HB itself and in addiction a large number of other properties of the interacting molecules) and most if not all appear to be strongly inter-correlated But
whatrsquos the driving variablewhatrsquos the driving variable
whatrsquos the variable which among the many intercorrelated ones drives the transformation from weak and electrostatic
to strong and covalent HB
A Proposal The PApA Proposal The PApKKaa Equalization Principle Equalization Principle
Two very similar proposals come from early thermodynamic or spectroscopic investigations and are both centered on the
matching of the acid-base properties of the HB donor and acceptors moieties what we like too call for the sake of brevity the
PApPApKKaa Equalization Principle Equalization Principle
With reference to any generic DHmiddotmiddotmiddotA bond this principle states that the HB becomes the stronger the smaller is the difference of the donor-acceptor
proton affinities proton affinities PA = PA(DPA = PA(D) ) PA(A) PA(A)or
acidic constants acidic constants ppKKa a = p= pKKAHAH(D(DH) H) p pKKBH+BH+(A(AHH++))
------------------------------------------------------------------------------------------------------------------------- Ault BS and Pimentel GG (1975) J Phys Chem 79 615 Huyskens PL and Zeegers-Huyskens Th (1964) J Chim Phys Phys- Chim Biol
61 81
Our First Steps in the HB FieldOur First Steps in the HB Field As usual we entered the field by chance In 1985 we were studying the ligands
of the benzadiazepine membrane receptor One of these ligands was CGS8216 where we noticed something strange a rather short N-HhellipO bond of 2694 Aring associated with an interleaving β-enaminone hellipO=C-C=C-NHhellip fragment which was almost completely π-delocalized
It was the first indication of a possible correlation between -delocalization and H-bond strength what was called a few years later the
Resonance-Assisted H-Bond (RAHB)Resonance-Assisted H-Bond (RAHB) (Gilli Bellucci Ferretti amp Bertolasi JACS 1989 Bertolasi Gilli Ferretti amp Gilli JACS 1991) Since at the time few -enaminones were known the work started on the analogous class of -enolones (or -diketone enols) which were already known to give strong O-HO bonds through the equally resonant O=C-C=C-OH fragment
The Development of the OThe Development of the OHO RAHBHO RAHB
The OThe OHO RAHBsHO RAHBs
Very interesting Class of Strong HBs Different lengths of the resonant spacer Rn
(n = 1 3 5 7) The HBs formed were all much stronger than normal (non-resonant) OHO bonds withd(OO)INTRA =
239-255 Aringd(OO)INTER =
246-265 Aring
R1-RAHBR5-RAHB
24256 Aring
N
N
O M e
N
N
OM e
M eM e
H
lt 257 gt1 Aring
P
O H
OO
O H
H P
O H
OO
O H
H
R3-RAHB
O OH
237-255 Aring
262-267 Aring
O
O H O
OH
262-270 Aring
O
O
H
O
O H
R7-RAHB
24462 Aring
NOO
OO
M eM e
H
OOH
O
O
H
CARBOXYLIC ACIDS
DIBENZOYLMETHANE ENOLS
CYCLOHEXANEDIONE ENOLS
PHOPHORIC ACID
A Model for RAHB Electrostatic or CovalentA Model for RAHB Electrostatic or Covalent
At first (JACS 1989) we suggested a RAHB Electrostatic Model but it became rapidly evident that an efficient RAHB treatment would require a Covalent Model
All hell broke loose because as we discovered with surprise the concept itself of covalent HB had been banned some twenty years before and substituted by the acritical but more comfortable Simple Electrostatic Paradigm RAHB seriously risked to became a kind of bizarre covalent hypothesis
I must thank George A Jeffrey with his inimitable unbiased and skeptical style if RAHB was not immediately cast aside by the scientific establishment but started to be quoted in important books and reviews during the lsquo90ties
A RAHB Electrostatic ModelA RAHB Electrostatic Model A RAHB Covalent ModelA RAHB Covalent Model
Starting Again The Purely Empirical ApproachStarting Again The Purely Empirical Approach Fortunately we were realistic enough not to try to confute the Electrostatic
Paradigm On the other hand it was perfectly useless because too deeply rooted in the Weltanschaung of so many important and self-confident scientists
I have already given a short critical account of the very nature of these scientific paradigms at the ECM-2000 of Nancy based on the ideas of Thomas S Kuhn (The Structure of Scientific Revolutions The University of Chicago 1962 and 1970)
Anyway to get out of this impasse at the beginning of 1993 we decided to change approach and to restart to investigate the O-HO bond problem from the very beginning by adopting a purely empirical strategy
(i) suspend any previous ideas on the electrostatic or covalent nature of the HB (ii) define the OHmiddotmiddotmiddotO bond as a simple topological structure where a H atom is connected to two or more oxygen atoms(iii) collect all crystal structures having OHmiddotmiddotmiddotO bonds with d(OmiddotmiddotmiddotO) 270 Aring(iv) collect all available IR (O-H) and NMR (H) data of H-bonded protons(v) collect all available HB energy data from thermodynamic measurements in gas phase and non-polar solvents(vi) try to infer a conclusion on the very nature of the OHmiddotmiddotmiddotO bond from the ensemble of the data collected
A Full Classification of Strong HBsA Full Classification of Strong HBs
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs)CHARGE - ASSISTED HBs
PENTACHLOROPHENOL - p-TOLUIDINE
pKa = -070
12
12
N
CH3
O
ClCl
Cl
Cl
Cl
H25062 AringCL 1 (+ndash)CAHB SHB VSHB
Double Charge-Assisted HBDirect Acid-Base PApKa Matching
CL 2 (ndash)CAHB SHB VSHBNegative Charge-Assisted HB
Acid-Base PApKa Matching by Proton Loss R
OOH
R
O O24371 Aring
CARBOXYLIC ACID - CARBOXYLATE
CL 3 (+)CAHB SHB VSHBPositive Charge-Assisted HB
Acid-Base PApKa Matching by Proton Gain
O
HH H
O
HH
24303 Aring
WATER - HYDRONIUM
-BOND POLARIZATION - ASSISTED HBs
237-255 Aring
O OH
ArAr
DIBENZOYLMETHANE ENOLS
CL 4 RAHB SHB VSHB Resonance-Assisted or -Cooperative HB
PApKa Matching by -Conjugated-Bond Polarization
27501 Aring
OO
O
O O
WATER
CL 5 PAHB MHBPolarization-Assisted or -Cooperative HB(Partial) PApKa Matching by -Bond Polarization
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs) The most interesting aspect of a HB classification based on HB strength is that strong HBs belong only to a small number of chemical schemes that we have called Chemical Leitmotifs
The Alchemic Piper plays the Five Magic Tunes that make any Hydrogen Bond stronger The Chemical Leitmotifs
Symmetry and Covalency (1)Symmetry and Covalency (1)The covalent nature of the strong OHmiddotmiddotmiddotO bond was assessed by interpreting the
experimental results in terms of the Coulsonrsquos VB formalismWe cannot measure covalency but can evaluate molecular symmetry the
Coulsonrsquos model being the algorithm able to translate one concept into the other
In fact total symmetry across the HB implies energy equivalence between the two covalent VB forms ie E(ΨCOV1) = E(ΨCOV2) which is just the situation
associated with formation of the covalent HB
E E
NCT
CT
CTNCT
COV2
IONIC
COV1
IONIC
COV1 COV2
NCT
NCT
(a) Electrostatic HB (b) Covalent HB
Symmetry and Covalency (2)Symmetry and Covalency (2)
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 1
(+-)CAHBDouble Charge-Assisted HB
Direct Acid-Base PApKa Matching
R12DH+A12R
The role played by the PApKa equalization in HB strengthening
is self-evident for the (+-)CAHB chemical leitmotif
RDHARrsquo R12DH+A12Rrsquo RDHA+Rrsquo
which collects by definition all strong HBs formed by the acid-base pairs with a pKa matching within say ndash3 divide 3 pKa units
But what about the other leitmotifs Can we prove that
all chemical leitmotifs are simple artificesthat molecules can use to obliterate the normally
very large pKa between HB donor and acceptor atoms
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 2(-)CAHB
Negative Charge-Assisted HBAcid-Base PApKa Matching
by Proton Loss[R-DHA-R]-
Chemical Leitmotif 3(+)CAHB
Positive Charge-Assisted HBAcid-Base PApKa Matching
by Proton Gain[R-DHA-R]+
2II
2III
2IIa
2IIb
2IIIb
2IIIa
2VIa
pKa = pKAH(HO-H)-pKAH(HO-H) = 157 - 157 = 0
pKa = pKBH(H2O-H+)-pKBH(H2O-H
+) = -17 + 17 = 0
pKAH(HO-H) = 157
pKBH(H2O-H+) = -17
H
O H
H
O
H
(ndash)CAHB pKa = 00
VERYSTRONG~ 25-30 kcalmol
(+)CAHB pKa = 00
VERYSTRONG ~ 25-31 kcalmol
pKa = 175
OHB
WEAK ~ 4- 5kcalmol
ndash H+
+ H+
H
O H O
H
H
O H O
H
H
OHO
H
H
O
H
H
H
O
H
H
O
H
H
O
H
H H
O
H
H
H
O
H
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 4RAHB
Resonance-Assisted or -Bond Cooperative HBPApKa Matching by -Conjugated-Bond Polarization
R-D-HA=R R=DH-A-R
pKAH(RO-H) = 1518
pKBH(R2C=O-H+) = -(67)
O OH
O H O
R
R
R
Rn-RAHB pKa = ~ 21-25
WEAK ~ 4- 5kcalmol
EKO O
H
KEOO
H
pKa = 00
STRONG ~ 15-22 kcalmol
2IV
2IVa
2IVb
2VIb
OHB
The HB Empirical RulesThe HB Empirical Rules
The empirical analysis of experimental data joined with homeopathic doses of VB theory leads us to formulate two important HB Empirical Rules which have been called elsewhere ECHBM (Electrostatic-Covalent HB Model Gilli amp Gilli J Mol Struct 2000) and can be summarized as follows
Any given D-HA system may form HBs in a wide range of strengths lengths symmetries and proton locations the two extremes being represented
by the weak long dissymmetric and proton-out-centred HB of electrostatic nature
and by the very strong very short symmetric and proton-centred HB
classifiable as a true 3-center-4-electron covalent bond
The driving variable able to transform strong into weak HBs is dimensionally a free enthalpy corresponding to the difference between the Proton Affinities (PA) or related Acid-Base Dissociation Constants (pKa) of the Donor and Acceptor moieties
These rules have been verified beyond any reasonable doubt for the Conventional HBs of the following classification
Provisional Conclusions and New ControlsProvisional Conclusions and New Controls
We have so far established a sound set of empirical rules which include A full classification of all existing HBs A full classification of all strong HBs (The Chemical Leitmotifs) A plausible correlation between HB strengths and acid-base properties of the interacting molecules (The PApKa Equalization Principle)
To confirm this last point we have undertaken two years ago
a new research program aimed at assessing the Full Validity of the PApKa Equalization Principle
by comparing extended tables of pKa values arranged for chemical classes
withthe corresponding CSD-derived HB geometries
Hundreds of pKa were collected and more than 11000 crystal structures examined
The pThe pKKa Slide Rulea Slide Rule
It is a tool for the graphical evaluation of the difference
pKa = pKAH(DH) - pKBH+(AH+)
HB Acceptors on the left and HB Donors on the right
pKa values given for chemical class
Results expected
ΔpKagtgt0 DHmiddotmiddotmiddotmiddotA weak amp neutral
ΔpKa asymp 0 DmiddotmiddotmiddotHmiddotmiddotmiddotA strong amp
centeredΔpKa ltlt0DmiddotmiddotmiddotmiddotHA+ weak amp charged
pKa ranges of organic compounds
C-H acids -11 ltpKalt 53
Other Donors -1 ltpKalt 40
Acceptors -12 ltpKalt 16
All -15 ltpKalt 53
Water 0 ltpKalt 14
50
-10
0
10
20
30
40
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
ALDEHYDES
ETHERSALCOHOLS
AMIDES
NITRILES
ANILINES
CF3-SO3H
HClO4HI
HBrHCl
H2SO4
HSO4
HNO3
HBF4
H3PO4
H2PO4
HPO42
HF HNO2
HNNN
NH2OHH2CO3
HCO3
H2S
HS-
HCN H3BO3
H2BO3
H4SiO4
H2O2
HO
HSCN
H-H
SULFONICACIDS
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
OXIMES
ALCOHOLS
THIOLES
HB ACCEPTORS (A)pK BH+
HB DONORS (D-H)pK AH
C-H ACIDS pK AH
BE
TT
ER
HB
AC
CE
PT
OR
BE
TT
ER
BA
SE
BE
TT
ER
HB
DO
NO
R
BE
TT
ER
AC
ID
N-OXIDES
AMIDINES
UREA
THIOUREA
BARBITURICURIC ACID
MONO DIPHOSPHINES
TRIPHOSPHINES
TRINITROANILINES
AMINES
ANILINES
MONO DINITROANILINES
AMIDES
CARBOXYLIC ACIDS
HALOGENOANILINES
AZOCOMPS
TRINITROANILINES
PROTONSPONGES
ACIDSESTERS
H2O
H2O
MONODINITROANILINES
KETONES
SULFIDES
HALOGENCARB ACIDS
TRINITROPHENOLS
ENOLS
MONO DINITROPHENOLS
PHENOLSNAPHTHOLS
HALOGENOPHENOLS
HALOGENOALCOHOLS
SULFOXIDES
(NC)5-CYCLO
PENTADIENE
(NC)3CH
(O2N)2=CH2
HCCHNC-CH3
CH3-CO-CH3INDENE
O2N-CH3
(NC)2=CH2
(O2N)3CH
H2C=CH2
C6H6
CH4
CYCLOPENTADIENE
CYCLOPROPENE
Ar3CH
Ar2=CH2
Ar-CH3
NITROCOMPS
SELENOXIDES
AZOLES
AZINESDIAZINES
AMINES
Cl5-PHENOL
CH3-CH3
(CH3)3CH
NH3
NH3
51
53
51
53
Chemical Leitmotifs and PApChemical Leitmotifs and PApKKaa Equalization Rules Equalization Rules RAHB RAHB cannot be treated by pKa equalization methods because π-delocalization
modifies the pKarsquos of the donor and acceptor moieties (+)CAHB is a true proton transfer from an acid (HB donor) to a base (HB acceptor)
RndashDndashHAndashRrsquo Rndash12DH+A12ndashndashRrsquo RndashDHndashA+ndashRrsquoΔpKa = pKAH(RDH) pKBH+(RrsquoA)
()CAHB is a proton sharing between two acids (HB donors)
RndashDndashHDrsquondashRrsquo [RDHDrsquoRrsquo] RDHDrsquoRrsquoΔpKa = pKAH(RDH) pKAH(RDH)
(+)CAHB is a proton sharing between two bases (HB acceptors)
R+AHArsquoRrsquo [RAHArsquoRrsquo]+ RAHArsquo+RrsquoΔpKa = pKBH+(RA) pKBH+(RrsquoArsquo)
Whenever () and (+)CAHBs are both homonuclear (D = Drsquo or A = Arsquo) and
homomolecular (R = Rrsquo) the matching condition ΔpKa= 0 will hold irrespective of the
actual pKarsquos of the two interacting moieties All HBs formed will be strong
Some Famous HBsSome Famous HBs
The NThe NHmiddotmiddotmiddotOOHmiddotmiddotmiddotOOHmiddotmiddotmiddotN System over the Full HmiddotmiddotmiddotN System over the Full ppKKaa Range Range
When evaluated from the pKa slide rule the total pKa range is extremely wide
ndash30 pa 60 So far we have been able to shown that the pKa equalization rule certainly holds in
a restricted interval around zero The problem is now Does this rule hold in the full pKa range
We will try to prove that by a full analysis the N-HmiddotmiddotmiddotOO-HmiddotmiddotmiddotN system
Procedure In a first CSD search functional groups of known pKa value and more frequently
implied in NHmiddotmiddotmiddotOOHmiddotmiddotmiddotN bonds were identified Finally 10 classes of donors and 11 of acceptors were selected and the search restarted for each separate donor-acceptor group Altogether 9078 different bonds were analyzed (4364 NHmiddotmiddotmiddotO 2289 OHmiddotmiddotmiddotN and
2425 OmiddotmiddotmiddotHN+) For each bond the NmiddotmiddotmiddotO distances were evaluated as dNH + dHO to account for the
N-H-O angle and for each group the shortest and average distances [dNmiddotmiddotmiddotO (min)
and dNmiddotmiddotmiddotO (mean)] were registered
These values were compared (see next slide) with the acid-base features of the donors (pKAH range) acceptors (pKBH+ range) and with their combinations
(pKa range)
pKa large amp positive
pKa largeamp negative
Increasing Acidity of the Protonated A H+ Acceptor Increasing Basicity of the A Acceptor
ppKKaa versusversus HB Geometry Correlation - Conclusions HB Geometry Correlation - Conclusions The PApKa Equalization Principle is therefore fully confirmed in its two forms All strong HBs correspond to very small pKa values
pKa values modulate the HB strength over the full pKa range These conclusions are of great practical importance in at least two respects pKa is definitively established as the driving force which controls the HB
strength by modulating the HB covalent contribution It is definitively established that an accurate analysis of structural crystal data
leads to the same conclusions suggested but never proved on a general base by thermodynamic and spectroscopic methods
References Huyskens and Zeegers-Huyskens 1964 Zeegers-Huyskens 1986 1988 Ault and Pimentel 1975 Ratajczak and Sobczyk 1969 Sobczyk et al 1982 Barnes 1983 Kebarle et al 1974-1979 Meot-Ner (Mautner) et al
1984-1988
Towards a General HB TheoryTowards a General HB Theory
The results so far obtained are not a True HB Theory but rather a Set of Empirical Rules (or an Empirical Natural Law) that is a great collection of HB experimental data neatly organized in tables which all together represent a General Taxonomy of the HB Phenomenon exactly as the Carl Linnaeusrsquo classification of plants A scientific theory is something different It is the casting of the empirical natural law into the frame of a theory which is more fundamental down to the reductionistic chain of the scientific disciplines For instance the kinetic gas theory is the casting of the empirical gas laws (the empirical natural law) into Newtonrsquos classical mechanics
How to make a HB TheoryHow to make a HB Theory
HB Properties = FF (HB Driving Variable)where
HB Driving Variable = PApKa and FF = Transition-State Theory
The Transition-State HB TheoryThe Transition-State HB Theory(Gilli et al JACS 2002 2005 Gilli et al J Mol Struct 2006)
Though it has taken us more than 12 years to develop it
the basic idea is very simpleAny DndashHmiddotmiddotmiddotA bond can be considered as a chemical reaction which is
bimolecular in both directions and proceeds via transition-state (TS) formation
AndashB + C AmiddotmiddotmiddotBmiddotmiddotmiddotC A + BndashCDndashHmiddotmiddotmiddotA DmiddotmiddotmiddotHmiddotmiddotmiddotA DmiddotmiddotmiddotHndashA
Changes of nomenclatureReaction Pathway PTPathwayActivation Energy DaggerE PTBarrierReaction Energy Er PApKa Transition State (TS) PTTS
Reaction Coordinate RC=[d(DH)ndashd(AH)] Experimentals Variable-Temperature X-allographyCalculations DFTEmulated PTPathwaysInterpretation Marcus Rate-Equilibrium Theory LefflerHammond Postulate
AcknowledgmentsAcknowledgments I have to thank my direct coworkers without whose help this work could have not been accomplished
Valerio BERTOLASI Paola GILLI
Valeria FERRETTI Loretta PRETTO
and the scientific institutions which made available to us the databases without which this work could not even be started
CCDCCambridge Crystallographic
Data Centrefor the use of the
Cambridge Structural Database
NIST National Institute of Standards and
Technologyfor the use of the
NIST Chemistry WebBook
The Birth of the HBThe Birth of the HB
The idea of HB was firstly conceived in the laboratory of Gilbert Newton Lewis at the end of the lsquo20ties while he was writing his famous book Valence and the structure of atoms and molecules (1923)
The final assessment of the HB concept is accredited to ML Huggins and
independently to WM Latimer and WH Rodebush three young men working there The first paper published on the HB was WM Latimer and WH Rodebush
Polarity and ionization from the standpoint of the Lewis theory of valence J Am Chem Soc 42 1419-1433 1920
The first book on the HB was written by Pauling who made eventually known the
HB to the wider chemical community Pauling L The Nature of the chemical bond and the structure of molecules and crystals An introduction to modern structural chemistry Cornell University Press Ithaca NY 1939 1940 1960 Chapter 12 55 pages
The definition of HB has remained substantially unchanged from then on I prefer
that proposed by Vinogradov SN and Linnel RH Hydrogen bonding Van Nostrand-Reinhold New York 1971
The Hydrogen Bond DefinitionThe Hydrogen Bond Definition Three-Center-Four-Electron Interaction
RDmiddotmiddotH ARrsquowhere D is the HB Donor An electronegative atom such as F O N C S Cl Br I
and A the HB Acceptor or Lone Pair Carrier A second electronegative atom or a multiple bond that is -bond
Alternatively a proton sharing two lone electron pairs from
two adjacent electronegative atoms
RD H+ ARrsquo
Two Very Important HB PropertiesTwo Very Important HB Properties The HB acceptor is not an atom but a lone electron pair located on that atom
Being both D and A electronegative the HB must have a fixed polarity
RDHARrsquo
Electrostatic and Covalent HBs The Paulingrsquos ModelElectrostatic and Covalent HBs The Paulingrsquos Model
Linus Pauling (The Nature of the Chemical Bond 1939 1940 1960) describes two distinct classes of HBs
Weak and dissymmetric HBs of electrostatic nature It is recognized that the hydrogen atom with only one stable orbital (the 1s orbital) can form only one covalent bond that the hydrogen bond is largely ionic in character and that it is formed only between the most electronegative atoms (HB Chapter - Page 1)
Strong and symmetric HBs of covalent nature These ldquoare exceptionsrdquo described as ldquo the hydrogen bond in the [HF2]
ion lies midway the two fluorine atoms and
may be considered to form a half-bond with eachrdquo (HB Chapter - Page 49)
[FHF] [OHO][OHO]+ [OHO]+
Coulsonrsquos VB Treatment (The Standard HB Model)Coulsonrsquos VB Treatment (The Standard HB Model)
Paulingrsquos ideas acquired theoretical dignity with the VB treatment of Coulson and Danielsson in 1954 where the O-HO bond is described as a mixture of three main VB forms two covalent and one ionic
This line of thought was embraced by
Pimentel and McClellan in their famous book The Hydrogen Bond (1960)
They write ldquoAt the 1957 Ljubljana Conference one of the important points of fairly general accord was that the electro-static model does not account for all of the phenomena associated with H bond formationrdquo
E E
NCT
CT
CTNCT
COV2
IONIC
COV1
IONIC
COV1 COV2
NCT
NCT
(a) Electrostatic HB (b) Covalent HB
The Birth of the Simple Electrostatic ParadigmThe Birth of the Simple Electrostatic Paradigm For reasons difficult to understand the Standard HB Model was abandoned
in the mid-lsquo60ies and the HB became the weak electrostatic interaction of some 4-6 kcal mol-1 everyone has heard of while strong HBs just disappeared from the chemical horizon
From there on the HB was divided between a small group of specialists (who still believed in the Standard Model) and the great majority of other scientists (who trusted more the much simpler Electrostatic Paradigm)
The effect on HB studies was disastrous and it took more than twenty years to put it right
Why Paulingrsquos Thought was AbandonedWhy Paulingrsquos Thought was Abandoned Weak electrostatic HBs are quoted on page 1 and strong covalent ones at
page 49 Since most people read only the first few pages helliphellip On page 50 strong HBs are defined ldquoexceptionsrdquo Most readers may have
thought Why to bother about exceptions when there are already so many regular HBs to bother about These are things for specialists
In VB terms ldquothe hydrogen atom can form only one covalent bondhelliprdquo does not mean that there is only one bond but that there may be any combination of two bonds whose bond orders sum up to one from 1+0 to 0+1 through frac12+ frac12 Probably very few people understood that correctly
Another Unsolved Problem The HB PuzzleAnother Unsolved Problem The HB Puzzle
Bond lengths and energies of normal chemical bonds are found to depend on the nature of the interacting atoms
and are weakly perturbed by their external environment
Conversely binding energies (EHB) and DmiddotmiddotmiddotA distances (dDmiddotmiddotmiddotA) of DHmiddotmiddotmiddotA bonds
do not simply depend on the donor (D) and acceptor (A) nature but show very large variations even for the same donor-acceptor couple
This is what we have called for the sake of brevity
the HB Puzzlethe HB PuzzleAn extreme example of this behavior comes from the effects produced on
the OHmiddotmiddotmiddotO bond by the changing acid-base properties of its environment The weak HOHmiddotmiddotmiddotOH2 bond in water [EHB5 kcal mol-1 dOmiddotmiddotmiddotO270-275 Aring]
is switched in acidic or basic medium to the very strong [H2OmiddotmiddotmiddotHmiddotmiddotmiddotOH2]+ or
[HOmiddotmiddotmiddotHmiddotmiddotmiddotOH] bonds with EHB up to 30-31 kcal mol-1 and dOmiddotmiddotmiddotO down to 238-242 Aring
How to Solve the HB Puzzle How to Solve the HB Puzzle the Problem of the Driving Variablethe Problem of the Driving Variable
The Electrostatic Paradigm cannot explain the HB Puzzle
Neither the Standard Model provides a full interpretation of it because while it can explain what covalent and electrostatic HBs are
it cannot suggest which circumstances can produce them
To put the problem in more general terms there are dozens of physicochemical variables commonly measured in connection with the HB (energies geometries IR frequencies NMR chemical shifts NQR couplings and isotopic effects of the HB itself and in addiction a large number of other properties of the interacting molecules) and most if not all appear to be strongly inter-correlated But
whatrsquos the driving variablewhatrsquos the driving variable
whatrsquos the variable which among the many intercorrelated ones drives the transformation from weak and electrostatic
to strong and covalent HB
A Proposal The PApA Proposal The PApKKaa Equalization Principle Equalization Principle
Two very similar proposals come from early thermodynamic or spectroscopic investigations and are both centered on the
matching of the acid-base properties of the HB donor and acceptors moieties what we like too call for the sake of brevity the
PApPApKKaa Equalization Principle Equalization Principle
With reference to any generic DHmiddotmiddotmiddotA bond this principle states that the HB becomes the stronger the smaller is the difference of the donor-acceptor
proton affinities proton affinities PA = PA(DPA = PA(D) ) PA(A) PA(A)or
acidic constants acidic constants ppKKa a = p= pKKAHAH(D(DH) H) p pKKBH+BH+(A(AHH++))
------------------------------------------------------------------------------------------------------------------------- Ault BS and Pimentel GG (1975) J Phys Chem 79 615 Huyskens PL and Zeegers-Huyskens Th (1964) J Chim Phys Phys- Chim Biol
61 81
Our First Steps in the HB FieldOur First Steps in the HB Field As usual we entered the field by chance In 1985 we were studying the ligands
of the benzadiazepine membrane receptor One of these ligands was CGS8216 where we noticed something strange a rather short N-HhellipO bond of 2694 Aring associated with an interleaving β-enaminone hellipO=C-C=C-NHhellip fragment which was almost completely π-delocalized
It was the first indication of a possible correlation between -delocalization and H-bond strength what was called a few years later the
Resonance-Assisted H-Bond (RAHB)Resonance-Assisted H-Bond (RAHB) (Gilli Bellucci Ferretti amp Bertolasi JACS 1989 Bertolasi Gilli Ferretti amp Gilli JACS 1991) Since at the time few -enaminones were known the work started on the analogous class of -enolones (or -diketone enols) which were already known to give strong O-HO bonds through the equally resonant O=C-C=C-OH fragment
The Development of the OThe Development of the OHO RAHBHO RAHB
The OThe OHO RAHBsHO RAHBs
Very interesting Class of Strong HBs Different lengths of the resonant spacer Rn
(n = 1 3 5 7) The HBs formed were all much stronger than normal (non-resonant) OHO bonds withd(OO)INTRA =
239-255 Aringd(OO)INTER =
246-265 Aring
R1-RAHBR5-RAHB
24256 Aring
N
N
O M e
N
N
OM e
M eM e
H
lt 257 gt1 Aring
P
O H
OO
O H
H P
O H
OO
O H
H
R3-RAHB
O OH
237-255 Aring
262-267 Aring
O
O H O
OH
262-270 Aring
O
O
H
O
O H
R7-RAHB
24462 Aring
NOO
OO
M eM e
H
OOH
O
O
H
CARBOXYLIC ACIDS
DIBENZOYLMETHANE ENOLS
CYCLOHEXANEDIONE ENOLS
PHOPHORIC ACID
A Model for RAHB Electrostatic or CovalentA Model for RAHB Electrostatic or Covalent
At first (JACS 1989) we suggested a RAHB Electrostatic Model but it became rapidly evident that an efficient RAHB treatment would require a Covalent Model
All hell broke loose because as we discovered with surprise the concept itself of covalent HB had been banned some twenty years before and substituted by the acritical but more comfortable Simple Electrostatic Paradigm RAHB seriously risked to became a kind of bizarre covalent hypothesis
I must thank George A Jeffrey with his inimitable unbiased and skeptical style if RAHB was not immediately cast aside by the scientific establishment but started to be quoted in important books and reviews during the lsquo90ties
A RAHB Electrostatic ModelA RAHB Electrostatic Model A RAHB Covalent ModelA RAHB Covalent Model
Starting Again The Purely Empirical ApproachStarting Again The Purely Empirical Approach Fortunately we were realistic enough not to try to confute the Electrostatic
Paradigm On the other hand it was perfectly useless because too deeply rooted in the Weltanschaung of so many important and self-confident scientists
I have already given a short critical account of the very nature of these scientific paradigms at the ECM-2000 of Nancy based on the ideas of Thomas S Kuhn (The Structure of Scientific Revolutions The University of Chicago 1962 and 1970)
Anyway to get out of this impasse at the beginning of 1993 we decided to change approach and to restart to investigate the O-HO bond problem from the very beginning by adopting a purely empirical strategy
(i) suspend any previous ideas on the electrostatic or covalent nature of the HB (ii) define the OHmiddotmiddotmiddotO bond as a simple topological structure where a H atom is connected to two or more oxygen atoms(iii) collect all crystal structures having OHmiddotmiddotmiddotO bonds with d(OmiddotmiddotmiddotO) 270 Aring(iv) collect all available IR (O-H) and NMR (H) data of H-bonded protons(v) collect all available HB energy data from thermodynamic measurements in gas phase and non-polar solvents(vi) try to infer a conclusion on the very nature of the OHmiddotmiddotmiddotO bond from the ensemble of the data collected
A Full Classification of Strong HBsA Full Classification of Strong HBs
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs)CHARGE - ASSISTED HBs
PENTACHLOROPHENOL - p-TOLUIDINE
pKa = -070
12
12
N
CH3
O
ClCl
Cl
Cl
Cl
H25062 AringCL 1 (+ndash)CAHB SHB VSHB
Double Charge-Assisted HBDirect Acid-Base PApKa Matching
CL 2 (ndash)CAHB SHB VSHBNegative Charge-Assisted HB
Acid-Base PApKa Matching by Proton Loss R
OOH
R
O O24371 Aring
CARBOXYLIC ACID - CARBOXYLATE
CL 3 (+)CAHB SHB VSHBPositive Charge-Assisted HB
Acid-Base PApKa Matching by Proton Gain
O
HH H
O
HH
24303 Aring
WATER - HYDRONIUM
-BOND POLARIZATION - ASSISTED HBs
237-255 Aring
O OH
ArAr
DIBENZOYLMETHANE ENOLS
CL 4 RAHB SHB VSHB Resonance-Assisted or -Cooperative HB
PApKa Matching by -Conjugated-Bond Polarization
27501 Aring
OO
O
O O
WATER
CL 5 PAHB MHBPolarization-Assisted or -Cooperative HB(Partial) PApKa Matching by -Bond Polarization
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs) The most interesting aspect of a HB classification based on HB strength is that strong HBs belong only to a small number of chemical schemes that we have called Chemical Leitmotifs
The Alchemic Piper plays the Five Magic Tunes that make any Hydrogen Bond stronger The Chemical Leitmotifs
Symmetry and Covalency (1)Symmetry and Covalency (1)The covalent nature of the strong OHmiddotmiddotmiddotO bond was assessed by interpreting the
experimental results in terms of the Coulsonrsquos VB formalismWe cannot measure covalency but can evaluate molecular symmetry the
Coulsonrsquos model being the algorithm able to translate one concept into the other
In fact total symmetry across the HB implies energy equivalence between the two covalent VB forms ie E(ΨCOV1) = E(ΨCOV2) which is just the situation
associated with formation of the covalent HB
E E
NCT
CT
CTNCT
COV2
IONIC
COV1
IONIC
COV1 COV2
NCT
NCT
(a) Electrostatic HB (b) Covalent HB
Symmetry and Covalency (2)Symmetry and Covalency (2)
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 1
(+-)CAHBDouble Charge-Assisted HB
Direct Acid-Base PApKa Matching
R12DH+A12R
The role played by the PApKa equalization in HB strengthening
is self-evident for the (+-)CAHB chemical leitmotif
RDHARrsquo R12DH+A12Rrsquo RDHA+Rrsquo
which collects by definition all strong HBs formed by the acid-base pairs with a pKa matching within say ndash3 divide 3 pKa units
But what about the other leitmotifs Can we prove that
all chemical leitmotifs are simple artificesthat molecules can use to obliterate the normally
very large pKa between HB donor and acceptor atoms
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 2(-)CAHB
Negative Charge-Assisted HBAcid-Base PApKa Matching
by Proton Loss[R-DHA-R]-
Chemical Leitmotif 3(+)CAHB
Positive Charge-Assisted HBAcid-Base PApKa Matching
by Proton Gain[R-DHA-R]+
2II
2III
2IIa
2IIb
2IIIb
2IIIa
2VIa
pKa = pKAH(HO-H)-pKAH(HO-H) = 157 - 157 = 0
pKa = pKBH(H2O-H+)-pKBH(H2O-H
+) = -17 + 17 = 0
pKAH(HO-H) = 157
pKBH(H2O-H+) = -17
H
O H
H
O
H
(ndash)CAHB pKa = 00
VERYSTRONG~ 25-30 kcalmol
(+)CAHB pKa = 00
VERYSTRONG ~ 25-31 kcalmol
pKa = 175
OHB
WEAK ~ 4- 5kcalmol
ndash H+
+ H+
H
O H O
H
H
O H O
H
H
OHO
H
H
O
H
H
H
O
H
H
O
H
H
O
H
H H
O
H
H
H
O
H
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 4RAHB
Resonance-Assisted or -Bond Cooperative HBPApKa Matching by -Conjugated-Bond Polarization
R-D-HA=R R=DH-A-R
pKAH(RO-H) = 1518
pKBH(R2C=O-H+) = -(67)
O OH
O H O
R
R
R
Rn-RAHB pKa = ~ 21-25
WEAK ~ 4- 5kcalmol
EKO O
H
KEOO
H
pKa = 00
STRONG ~ 15-22 kcalmol
2IV
2IVa
2IVb
2VIb
OHB
The HB Empirical RulesThe HB Empirical Rules
The empirical analysis of experimental data joined with homeopathic doses of VB theory leads us to formulate two important HB Empirical Rules which have been called elsewhere ECHBM (Electrostatic-Covalent HB Model Gilli amp Gilli J Mol Struct 2000) and can be summarized as follows
Any given D-HA system may form HBs in a wide range of strengths lengths symmetries and proton locations the two extremes being represented
by the weak long dissymmetric and proton-out-centred HB of electrostatic nature
and by the very strong very short symmetric and proton-centred HB
classifiable as a true 3-center-4-electron covalent bond
The driving variable able to transform strong into weak HBs is dimensionally a free enthalpy corresponding to the difference between the Proton Affinities (PA) or related Acid-Base Dissociation Constants (pKa) of the Donor and Acceptor moieties
These rules have been verified beyond any reasonable doubt for the Conventional HBs of the following classification
Provisional Conclusions and New ControlsProvisional Conclusions and New Controls
We have so far established a sound set of empirical rules which include A full classification of all existing HBs A full classification of all strong HBs (The Chemical Leitmotifs) A plausible correlation between HB strengths and acid-base properties of the interacting molecules (The PApKa Equalization Principle)
To confirm this last point we have undertaken two years ago
a new research program aimed at assessing the Full Validity of the PApKa Equalization Principle
by comparing extended tables of pKa values arranged for chemical classes
withthe corresponding CSD-derived HB geometries
Hundreds of pKa were collected and more than 11000 crystal structures examined
The pThe pKKa Slide Rulea Slide Rule
It is a tool for the graphical evaluation of the difference
pKa = pKAH(DH) - pKBH+(AH+)
HB Acceptors on the left and HB Donors on the right
pKa values given for chemical class
Results expected
ΔpKagtgt0 DHmiddotmiddotmiddotmiddotA weak amp neutral
ΔpKa asymp 0 DmiddotmiddotmiddotHmiddotmiddotmiddotA strong amp
centeredΔpKa ltlt0DmiddotmiddotmiddotmiddotHA+ weak amp charged
pKa ranges of organic compounds
C-H acids -11 ltpKalt 53
Other Donors -1 ltpKalt 40
Acceptors -12 ltpKalt 16
All -15 ltpKalt 53
Water 0 ltpKalt 14
50
-10
0
10
20
30
40
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
ALDEHYDES
ETHERSALCOHOLS
AMIDES
NITRILES
ANILINES
CF3-SO3H
HClO4HI
HBrHCl
H2SO4
HSO4
HNO3
HBF4
H3PO4
H2PO4
HPO42
HF HNO2
HNNN
NH2OHH2CO3
HCO3
H2S
HS-
HCN H3BO3
H2BO3
H4SiO4
H2O2
HO
HSCN
H-H
SULFONICACIDS
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
OXIMES
ALCOHOLS
THIOLES
HB ACCEPTORS (A)pK BH+
HB DONORS (D-H)pK AH
C-H ACIDS pK AH
BE
TT
ER
HB
AC
CE
PT
OR
BE
TT
ER
BA
SE
BE
TT
ER
HB
DO
NO
R
BE
TT
ER
AC
ID
N-OXIDES
AMIDINES
UREA
THIOUREA
BARBITURICURIC ACID
MONO DIPHOSPHINES
TRIPHOSPHINES
TRINITROANILINES
AMINES
ANILINES
MONO DINITROANILINES
AMIDES
CARBOXYLIC ACIDS
HALOGENOANILINES
AZOCOMPS
TRINITROANILINES
PROTONSPONGES
ACIDSESTERS
H2O
H2O
MONODINITROANILINES
KETONES
SULFIDES
HALOGENCARB ACIDS
TRINITROPHENOLS
ENOLS
MONO DINITROPHENOLS
PHENOLSNAPHTHOLS
HALOGENOPHENOLS
HALOGENOALCOHOLS
SULFOXIDES
(NC)5-CYCLO
PENTADIENE
(NC)3CH
(O2N)2=CH2
HCCHNC-CH3
CH3-CO-CH3INDENE
O2N-CH3
(NC)2=CH2
(O2N)3CH
H2C=CH2
C6H6
CH4
CYCLOPENTADIENE
CYCLOPROPENE
Ar3CH
Ar2=CH2
Ar-CH3
NITROCOMPS
SELENOXIDES
AZOLES
AZINESDIAZINES
AMINES
Cl5-PHENOL
CH3-CH3
(CH3)3CH
NH3
NH3
51
53
51
53
Chemical Leitmotifs and PApChemical Leitmotifs and PApKKaa Equalization Rules Equalization Rules RAHB RAHB cannot be treated by pKa equalization methods because π-delocalization
modifies the pKarsquos of the donor and acceptor moieties (+)CAHB is a true proton transfer from an acid (HB donor) to a base (HB acceptor)
RndashDndashHAndashRrsquo Rndash12DH+A12ndashndashRrsquo RndashDHndashA+ndashRrsquoΔpKa = pKAH(RDH) pKBH+(RrsquoA)
()CAHB is a proton sharing between two acids (HB donors)
RndashDndashHDrsquondashRrsquo [RDHDrsquoRrsquo] RDHDrsquoRrsquoΔpKa = pKAH(RDH) pKAH(RDH)
(+)CAHB is a proton sharing between two bases (HB acceptors)
R+AHArsquoRrsquo [RAHArsquoRrsquo]+ RAHArsquo+RrsquoΔpKa = pKBH+(RA) pKBH+(RrsquoArsquo)
Whenever () and (+)CAHBs are both homonuclear (D = Drsquo or A = Arsquo) and
homomolecular (R = Rrsquo) the matching condition ΔpKa= 0 will hold irrespective of the
actual pKarsquos of the two interacting moieties All HBs formed will be strong
Some Famous HBsSome Famous HBs
The NThe NHmiddotmiddotmiddotOOHmiddotmiddotmiddotOOHmiddotmiddotmiddotN System over the Full HmiddotmiddotmiddotN System over the Full ppKKaa Range Range
When evaluated from the pKa slide rule the total pKa range is extremely wide
ndash30 pa 60 So far we have been able to shown that the pKa equalization rule certainly holds in
a restricted interval around zero The problem is now Does this rule hold in the full pKa range
We will try to prove that by a full analysis the N-HmiddotmiddotmiddotOO-HmiddotmiddotmiddotN system
Procedure In a first CSD search functional groups of known pKa value and more frequently
implied in NHmiddotmiddotmiddotOOHmiddotmiddotmiddotN bonds were identified Finally 10 classes of donors and 11 of acceptors were selected and the search restarted for each separate donor-acceptor group Altogether 9078 different bonds were analyzed (4364 NHmiddotmiddotmiddotO 2289 OHmiddotmiddotmiddotN and
2425 OmiddotmiddotmiddotHN+) For each bond the NmiddotmiddotmiddotO distances were evaluated as dNH + dHO to account for the
N-H-O angle and for each group the shortest and average distances [dNmiddotmiddotmiddotO (min)
and dNmiddotmiddotmiddotO (mean)] were registered
These values were compared (see next slide) with the acid-base features of the donors (pKAH range) acceptors (pKBH+ range) and with their combinations
(pKa range)
pKa large amp positive
pKa largeamp negative
Increasing Acidity of the Protonated A H+ Acceptor Increasing Basicity of the A Acceptor
ppKKaa versusversus HB Geometry Correlation - Conclusions HB Geometry Correlation - Conclusions The PApKa Equalization Principle is therefore fully confirmed in its two forms All strong HBs correspond to very small pKa values
pKa values modulate the HB strength over the full pKa range These conclusions are of great practical importance in at least two respects pKa is definitively established as the driving force which controls the HB
strength by modulating the HB covalent contribution It is definitively established that an accurate analysis of structural crystal data
leads to the same conclusions suggested but never proved on a general base by thermodynamic and spectroscopic methods
References Huyskens and Zeegers-Huyskens 1964 Zeegers-Huyskens 1986 1988 Ault and Pimentel 1975 Ratajczak and Sobczyk 1969 Sobczyk et al 1982 Barnes 1983 Kebarle et al 1974-1979 Meot-Ner (Mautner) et al
1984-1988
Towards a General HB TheoryTowards a General HB Theory
The results so far obtained are not a True HB Theory but rather a Set of Empirical Rules (or an Empirical Natural Law) that is a great collection of HB experimental data neatly organized in tables which all together represent a General Taxonomy of the HB Phenomenon exactly as the Carl Linnaeusrsquo classification of plants A scientific theory is something different It is the casting of the empirical natural law into the frame of a theory which is more fundamental down to the reductionistic chain of the scientific disciplines For instance the kinetic gas theory is the casting of the empirical gas laws (the empirical natural law) into Newtonrsquos classical mechanics
How to make a HB TheoryHow to make a HB Theory
HB Properties = FF (HB Driving Variable)where
HB Driving Variable = PApKa and FF = Transition-State Theory
The Transition-State HB TheoryThe Transition-State HB Theory(Gilli et al JACS 2002 2005 Gilli et al J Mol Struct 2006)
Though it has taken us more than 12 years to develop it
the basic idea is very simpleAny DndashHmiddotmiddotmiddotA bond can be considered as a chemical reaction which is
bimolecular in both directions and proceeds via transition-state (TS) formation
AndashB + C AmiddotmiddotmiddotBmiddotmiddotmiddotC A + BndashCDndashHmiddotmiddotmiddotA DmiddotmiddotmiddotHmiddotmiddotmiddotA DmiddotmiddotmiddotHndashA
Changes of nomenclatureReaction Pathway PTPathwayActivation Energy DaggerE PTBarrierReaction Energy Er PApKa Transition State (TS) PTTS
Reaction Coordinate RC=[d(DH)ndashd(AH)] Experimentals Variable-Temperature X-allographyCalculations DFTEmulated PTPathwaysInterpretation Marcus Rate-Equilibrium Theory LefflerHammond Postulate
AcknowledgmentsAcknowledgments I have to thank my direct coworkers without whose help this work could have not been accomplished
Valerio BERTOLASI Paola GILLI
Valeria FERRETTI Loretta PRETTO
and the scientific institutions which made available to us the databases without which this work could not even be started
CCDCCambridge Crystallographic
Data Centrefor the use of the
Cambridge Structural Database
NIST National Institute of Standards and
Technologyfor the use of the
NIST Chemistry WebBook
The Hydrogen Bond DefinitionThe Hydrogen Bond Definition Three-Center-Four-Electron Interaction
RDmiddotmiddotH ARrsquowhere D is the HB Donor An electronegative atom such as F O N C S Cl Br I
and A the HB Acceptor or Lone Pair Carrier A second electronegative atom or a multiple bond that is -bond
Alternatively a proton sharing two lone electron pairs from
two adjacent electronegative atoms
RD H+ ARrsquo
Two Very Important HB PropertiesTwo Very Important HB Properties The HB acceptor is not an atom but a lone electron pair located on that atom
Being both D and A electronegative the HB must have a fixed polarity
RDHARrsquo
Electrostatic and Covalent HBs The Paulingrsquos ModelElectrostatic and Covalent HBs The Paulingrsquos Model
Linus Pauling (The Nature of the Chemical Bond 1939 1940 1960) describes two distinct classes of HBs
Weak and dissymmetric HBs of electrostatic nature It is recognized that the hydrogen atom with only one stable orbital (the 1s orbital) can form only one covalent bond that the hydrogen bond is largely ionic in character and that it is formed only between the most electronegative atoms (HB Chapter - Page 1)
Strong and symmetric HBs of covalent nature These ldquoare exceptionsrdquo described as ldquo the hydrogen bond in the [HF2]
ion lies midway the two fluorine atoms and
may be considered to form a half-bond with eachrdquo (HB Chapter - Page 49)
[FHF] [OHO][OHO]+ [OHO]+
Coulsonrsquos VB Treatment (The Standard HB Model)Coulsonrsquos VB Treatment (The Standard HB Model)
Paulingrsquos ideas acquired theoretical dignity with the VB treatment of Coulson and Danielsson in 1954 where the O-HO bond is described as a mixture of three main VB forms two covalent and one ionic
This line of thought was embraced by
Pimentel and McClellan in their famous book The Hydrogen Bond (1960)
They write ldquoAt the 1957 Ljubljana Conference one of the important points of fairly general accord was that the electro-static model does not account for all of the phenomena associated with H bond formationrdquo
E E
NCT
CT
CTNCT
COV2
IONIC
COV1
IONIC
COV1 COV2
NCT
NCT
(a) Electrostatic HB (b) Covalent HB
The Birth of the Simple Electrostatic ParadigmThe Birth of the Simple Electrostatic Paradigm For reasons difficult to understand the Standard HB Model was abandoned
in the mid-lsquo60ies and the HB became the weak electrostatic interaction of some 4-6 kcal mol-1 everyone has heard of while strong HBs just disappeared from the chemical horizon
From there on the HB was divided between a small group of specialists (who still believed in the Standard Model) and the great majority of other scientists (who trusted more the much simpler Electrostatic Paradigm)
The effect on HB studies was disastrous and it took more than twenty years to put it right
Why Paulingrsquos Thought was AbandonedWhy Paulingrsquos Thought was Abandoned Weak electrostatic HBs are quoted on page 1 and strong covalent ones at
page 49 Since most people read only the first few pages helliphellip On page 50 strong HBs are defined ldquoexceptionsrdquo Most readers may have
thought Why to bother about exceptions when there are already so many regular HBs to bother about These are things for specialists
In VB terms ldquothe hydrogen atom can form only one covalent bondhelliprdquo does not mean that there is only one bond but that there may be any combination of two bonds whose bond orders sum up to one from 1+0 to 0+1 through frac12+ frac12 Probably very few people understood that correctly
Another Unsolved Problem The HB PuzzleAnother Unsolved Problem The HB Puzzle
Bond lengths and energies of normal chemical bonds are found to depend on the nature of the interacting atoms
and are weakly perturbed by their external environment
Conversely binding energies (EHB) and DmiddotmiddotmiddotA distances (dDmiddotmiddotmiddotA) of DHmiddotmiddotmiddotA bonds
do not simply depend on the donor (D) and acceptor (A) nature but show very large variations even for the same donor-acceptor couple
This is what we have called for the sake of brevity
the HB Puzzlethe HB PuzzleAn extreme example of this behavior comes from the effects produced on
the OHmiddotmiddotmiddotO bond by the changing acid-base properties of its environment The weak HOHmiddotmiddotmiddotOH2 bond in water [EHB5 kcal mol-1 dOmiddotmiddotmiddotO270-275 Aring]
is switched in acidic or basic medium to the very strong [H2OmiddotmiddotmiddotHmiddotmiddotmiddotOH2]+ or
[HOmiddotmiddotmiddotHmiddotmiddotmiddotOH] bonds with EHB up to 30-31 kcal mol-1 and dOmiddotmiddotmiddotO down to 238-242 Aring
How to Solve the HB Puzzle How to Solve the HB Puzzle the Problem of the Driving Variablethe Problem of the Driving Variable
The Electrostatic Paradigm cannot explain the HB Puzzle
Neither the Standard Model provides a full interpretation of it because while it can explain what covalent and electrostatic HBs are
it cannot suggest which circumstances can produce them
To put the problem in more general terms there are dozens of physicochemical variables commonly measured in connection with the HB (energies geometries IR frequencies NMR chemical shifts NQR couplings and isotopic effects of the HB itself and in addiction a large number of other properties of the interacting molecules) and most if not all appear to be strongly inter-correlated But
whatrsquos the driving variablewhatrsquos the driving variable
whatrsquos the variable which among the many intercorrelated ones drives the transformation from weak and electrostatic
to strong and covalent HB
A Proposal The PApA Proposal The PApKKaa Equalization Principle Equalization Principle
Two very similar proposals come from early thermodynamic or spectroscopic investigations and are both centered on the
matching of the acid-base properties of the HB donor and acceptors moieties what we like too call for the sake of brevity the
PApPApKKaa Equalization Principle Equalization Principle
With reference to any generic DHmiddotmiddotmiddotA bond this principle states that the HB becomes the stronger the smaller is the difference of the donor-acceptor
proton affinities proton affinities PA = PA(DPA = PA(D) ) PA(A) PA(A)or
acidic constants acidic constants ppKKa a = p= pKKAHAH(D(DH) H) p pKKBH+BH+(A(AHH++))
------------------------------------------------------------------------------------------------------------------------- Ault BS and Pimentel GG (1975) J Phys Chem 79 615 Huyskens PL and Zeegers-Huyskens Th (1964) J Chim Phys Phys- Chim Biol
61 81
Our First Steps in the HB FieldOur First Steps in the HB Field As usual we entered the field by chance In 1985 we were studying the ligands
of the benzadiazepine membrane receptor One of these ligands was CGS8216 where we noticed something strange a rather short N-HhellipO bond of 2694 Aring associated with an interleaving β-enaminone hellipO=C-C=C-NHhellip fragment which was almost completely π-delocalized
It was the first indication of a possible correlation between -delocalization and H-bond strength what was called a few years later the
Resonance-Assisted H-Bond (RAHB)Resonance-Assisted H-Bond (RAHB) (Gilli Bellucci Ferretti amp Bertolasi JACS 1989 Bertolasi Gilli Ferretti amp Gilli JACS 1991) Since at the time few -enaminones were known the work started on the analogous class of -enolones (or -diketone enols) which were already known to give strong O-HO bonds through the equally resonant O=C-C=C-OH fragment
The Development of the OThe Development of the OHO RAHBHO RAHB
The OThe OHO RAHBsHO RAHBs
Very interesting Class of Strong HBs Different lengths of the resonant spacer Rn
(n = 1 3 5 7) The HBs formed were all much stronger than normal (non-resonant) OHO bonds withd(OO)INTRA =
239-255 Aringd(OO)INTER =
246-265 Aring
R1-RAHBR5-RAHB
24256 Aring
N
N
O M e
N
N
OM e
M eM e
H
lt 257 gt1 Aring
P
O H
OO
O H
H P
O H
OO
O H
H
R3-RAHB
O OH
237-255 Aring
262-267 Aring
O
O H O
OH
262-270 Aring
O
O
H
O
O H
R7-RAHB
24462 Aring
NOO
OO
M eM e
H
OOH
O
O
H
CARBOXYLIC ACIDS
DIBENZOYLMETHANE ENOLS
CYCLOHEXANEDIONE ENOLS
PHOPHORIC ACID
A Model for RAHB Electrostatic or CovalentA Model for RAHB Electrostatic or Covalent
At first (JACS 1989) we suggested a RAHB Electrostatic Model but it became rapidly evident that an efficient RAHB treatment would require a Covalent Model
All hell broke loose because as we discovered with surprise the concept itself of covalent HB had been banned some twenty years before and substituted by the acritical but more comfortable Simple Electrostatic Paradigm RAHB seriously risked to became a kind of bizarre covalent hypothesis
I must thank George A Jeffrey with his inimitable unbiased and skeptical style if RAHB was not immediately cast aside by the scientific establishment but started to be quoted in important books and reviews during the lsquo90ties
A RAHB Electrostatic ModelA RAHB Electrostatic Model A RAHB Covalent ModelA RAHB Covalent Model
Starting Again The Purely Empirical ApproachStarting Again The Purely Empirical Approach Fortunately we were realistic enough not to try to confute the Electrostatic
Paradigm On the other hand it was perfectly useless because too deeply rooted in the Weltanschaung of so many important and self-confident scientists
I have already given a short critical account of the very nature of these scientific paradigms at the ECM-2000 of Nancy based on the ideas of Thomas S Kuhn (The Structure of Scientific Revolutions The University of Chicago 1962 and 1970)
Anyway to get out of this impasse at the beginning of 1993 we decided to change approach and to restart to investigate the O-HO bond problem from the very beginning by adopting a purely empirical strategy
(i) suspend any previous ideas on the electrostatic or covalent nature of the HB (ii) define the OHmiddotmiddotmiddotO bond as a simple topological structure where a H atom is connected to two or more oxygen atoms(iii) collect all crystal structures having OHmiddotmiddotmiddotO bonds with d(OmiddotmiddotmiddotO) 270 Aring(iv) collect all available IR (O-H) and NMR (H) data of H-bonded protons(v) collect all available HB energy data from thermodynamic measurements in gas phase and non-polar solvents(vi) try to infer a conclusion on the very nature of the OHmiddotmiddotmiddotO bond from the ensemble of the data collected
A Full Classification of Strong HBsA Full Classification of Strong HBs
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs)CHARGE - ASSISTED HBs
PENTACHLOROPHENOL - p-TOLUIDINE
pKa = -070
12
12
N
CH3
O
ClCl
Cl
Cl
Cl
H25062 AringCL 1 (+ndash)CAHB SHB VSHB
Double Charge-Assisted HBDirect Acid-Base PApKa Matching
CL 2 (ndash)CAHB SHB VSHBNegative Charge-Assisted HB
Acid-Base PApKa Matching by Proton Loss R
OOH
R
O O24371 Aring
CARBOXYLIC ACID - CARBOXYLATE
CL 3 (+)CAHB SHB VSHBPositive Charge-Assisted HB
Acid-Base PApKa Matching by Proton Gain
O
HH H
O
HH
24303 Aring
WATER - HYDRONIUM
-BOND POLARIZATION - ASSISTED HBs
237-255 Aring
O OH
ArAr
DIBENZOYLMETHANE ENOLS
CL 4 RAHB SHB VSHB Resonance-Assisted or -Cooperative HB
PApKa Matching by -Conjugated-Bond Polarization
27501 Aring
OO
O
O O
WATER
CL 5 PAHB MHBPolarization-Assisted or -Cooperative HB(Partial) PApKa Matching by -Bond Polarization
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs) The most interesting aspect of a HB classification based on HB strength is that strong HBs belong only to a small number of chemical schemes that we have called Chemical Leitmotifs
The Alchemic Piper plays the Five Magic Tunes that make any Hydrogen Bond stronger The Chemical Leitmotifs
Symmetry and Covalency (1)Symmetry and Covalency (1)The covalent nature of the strong OHmiddotmiddotmiddotO bond was assessed by interpreting the
experimental results in terms of the Coulsonrsquos VB formalismWe cannot measure covalency but can evaluate molecular symmetry the
Coulsonrsquos model being the algorithm able to translate one concept into the other
In fact total symmetry across the HB implies energy equivalence between the two covalent VB forms ie E(ΨCOV1) = E(ΨCOV2) which is just the situation
associated with formation of the covalent HB
E E
NCT
CT
CTNCT
COV2
IONIC
COV1
IONIC
COV1 COV2
NCT
NCT
(a) Electrostatic HB (b) Covalent HB
Symmetry and Covalency (2)Symmetry and Covalency (2)
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 1
(+-)CAHBDouble Charge-Assisted HB
Direct Acid-Base PApKa Matching
R12DH+A12R
The role played by the PApKa equalization in HB strengthening
is self-evident for the (+-)CAHB chemical leitmotif
RDHARrsquo R12DH+A12Rrsquo RDHA+Rrsquo
which collects by definition all strong HBs formed by the acid-base pairs with a pKa matching within say ndash3 divide 3 pKa units
But what about the other leitmotifs Can we prove that
all chemical leitmotifs are simple artificesthat molecules can use to obliterate the normally
very large pKa between HB donor and acceptor atoms
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 2(-)CAHB
Negative Charge-Assisted HBAcid-Base PApKa Matching
by Proton Loss[R-DHA-R]-
Chemical Leitmotif 3(+)CAHB
Positive Charge-Assisted HBAcid-Base PApKa Matching
by Proton Gain[R-DHA-R]+
2II
2III
2IIa
2IIb
2IIIb
2IIIa
2VIa
pKa = pKAH(HO-H)-pKAH(HO-H) = 157 - 157 = 0
pKa = pKBH(H2O-H+)-pKBH(H2O-H
+) = -17 + 17 = 0
pKAH(HO-H) = 157
pKBH(H2O-H+) = -17
H
O H
H
O
H
(ndash)CAHB pKa = 00
VERYSTRONG~ 25-30 kcalmol
(+)CAHB pKa = 00
VERYSTRONG ~ 25-31 kcalmol
pKa = 175
OHB
WEAK ~ 4- 5kcalmol
ndash H+
+ H+
H
O H O
H
H
O H O
H
H
OHO
H
H
O
H
H
H
O
H
H
O
H
H
O
H
H H
O
H
H
H
O
H
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 4RAHB
Resonance-Assisted or -Bond Cooperative HBPApKa Matching by -Conjugated-Bond Polarization
R-D-HA=R R=DH-A-R
pKAH(RO-H) = 1518
pKBH(R2C=O-H+) = -(67)
O OH
O H O
R
R
R
Rn-RAHB pKa = ~ 21-25
WEAK ~ 4- 5kcalmol
EKO O
H
KEOO
H
pKa = 00
STRONG ~ 15-22 kcalmol
2IV
2IVa
2IVb
2VIb
OHB
The HB Empirical RulesThe HB Empirical Rules
The empirical analysis of experimental data joined with homeopathic doses of VB theory leads us to formulate two important HB Empirical Rules which have been called elsewhere ECHBM (Electrostatic-Covalent HB Model Gilli amp Gilli J Mol Struct 2000) and can be summarized as follows
Any given D-HA system may form HBs in a wide range of strengths lengths symmetries and proton locations the two extremes being represented
by the weak long dissymmetric and proton-out-centred HB of electrostatic nature
and by the very strong very short symmetric and proton-centred HB
classifiable as a true 3-center-4-electron covalent bond
The driving variable able to transform strong into weak HBs is dimensionally a free enthalpy corresponding to the difference between the Proton Affinities (PA) or related Acid-Base Dissociation Constants (pKa) of the Donor and Acceptor moieties
These rules have been verified beyond any reasonable doubt for the Conventional HBs of the following classification
Provisional Conclusions and New ControlsProvisional Conclusions and New Controls
We have so far established a sound set of empirical rules which include A full classification of all existing HBs A full classification of all strong HBs (The Chemical Leitmotifs) A plausible correlation between HB strengths and acid-base properties of the interacting molecules (The PApKa Equalization Principle)
To confirm this last point we have undertaken two years ago
a new research program aimed at assessing the Full Validity of the PApKa Equalization Principle
by comparing extended tables of pKa values arranged for chemical classes
withthe corresponding CSD-derived HB geometries
Hundreds of pKa were collected and more than 11000 crystal structures examined
The pThe pKKa Slide Rulea Slide Rule
It is a tool for the graphical evaluation of the difference
pKa = pKAH(DH) - pKBH+(AH+)
HB Acceptors on the left and HB Donors on the right
pKa values given for chemical class
Results expected
ΔpKagtgt0 DHmiddotmiddotmiddotmiddotA weak amp neutral
ΔpKa asymp 0 DmiddotmiddotmiddotHmiddotmiddotmiddotA strong amp
centeredΔpKa ltlt0DmiddotmiddotmiddotmiddotHA+ weak amp charged
pKa ranges of organic compounds
C-H acids -11 ltpKalt 53
Other Donors -1 ltpKalt 40
Acceptors -12 ltpKalt 16
All -15 ltpKalt 53
Water 0 ltpKalt 14
50
-10
0
10
20
30
40
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
ALDEHYDES
ETHERSALCOHOLS
AMIDES
NITRILES
ANILINES
CF3-SO3H
HClO4HI
HBrHCl
H2SO4
HSO4
HNO3
HBF4
H3PO4
H2PO4
HPO42
HF HNO2
HNNN
NH2OHH2CO3
HCO3
H2S
HS-
HCN H3BO3
H2BO3
H4SiO4
H2O2
HO
HSCN
H-H
SULFONICACIDS
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
OXIMES
ALCOHOLS
THIOLES
HB ACCEPTORS (A)pK BH+
HB DONORS (D-H)pK AH
C-H ACIDS pK AH
BE
TT
ER
HB
AC
CE
PT
OR
BE
TT
ER
BA
SE
BE
TT
ER
HB
DO
NO
R
BE
TT
ER
AC
ID
N-OXIDES
AMIDINES
UREA
THIOUREA
BARBITURICURIC ACID
MONO DIPHOSPHINES
TRIPHOSPHINES
TRINITROANILINES
AMINES
ANILINES
MONO DINITROANILINES
AMIDES
CARBOXYLIC ACIDS
HALOGENOANILINES
AZOCOMPS
TRINITROANILINES
PROTONSPONGES
ACIDSESTERS
H2O
H2O
MONODINITROANILINES
KETONES
SULFIDES
HALOGENCARB ACIDS
TRINITROPHENOLS
ENOLS
MONO DINITROPHENOLS
PHENOLSNAPHTHOLS
HALOGENOPHENOLS
HALOGENOALCOHOLS
SULFOXIDES
(NC)5-CYCLO
PENTADIENE
(NC)3CH
(O2N)2=CH2
HCCHNC-CH3
CH3-CO-CH3INDENE
O2N-CH3
(NC)2=CH2
(O2N)3CH
H2C=CH2
C6H6
CH4
CYCLOPENTADIENE
CYCLOPROPENE
Ar3CH
Ar2=CH2
Ar-CH3
NITROCOMPS
SELENOXIDES
AZOLES
AZINESDIAZINES
AMINES
Cl5-PHENOL
CH3-CH3
(CH3)3CH
NH3
NH3
51
53
51
53
Chemical Leitmotifs and PApChemical Leitmotifs and PApKKaa Equalization Rules Equalization Rules RAHB RAHB cannot be treated by pKa equalization methods because π-delocalization
modifies the pKarsquos of the donor and acceptor moieties (+)CAHB is a true proton transfer from an acid (HB donor) to a base (HB acceptor)
RndashDndashHAndashRrsquo Rndash12DH+A12ndashndashRrsquo RndashDHndashA+ndashRrsquoΔpKa = pKAH(RDH) pKBH+(RrsquoA)
()CAHB is a proton sharing between two acids (HB donors)
RndashDndashHDrsquondashRrsquo [RDHDrsquoRrsquo] RDHDrsquoRrsquoΔpKa = pKAH(RDH) pKAH(RDH)
(+)CAHB is a proton sharing between two bases (HB acceptors)
R+AHArsquoRrsquo [RAHArsquoRrsquo]+ RAHArsquo+RrsquoΔpKa = pKBH+(RA) pKBH+(RrsquoArsquo)
Whenever () and (+)CAHBs are both homonuclear (D = Drsquo or A = Arsquo) and
homomolecular (R = Rrsquo) the matching condition ΔpKa= 0 will hold irrespective of the
actual pKarsquos of the two interacting moieties All HBs formed will be strong
Some Famous HBsSome Famous HBs
The NThe NHmiddotmiddotmiddotOOHmiddotmiddotmiddotOOHmiddotmiddotmiddotN System over the Full HmiddotmiddotmiddotN System over the Full ppKKaa Range Range
When evaluated from the pKa slide rule the total pKa range is extremely wide
ndash30 pa 60 So far we have been able to shown that the pKa equalization rule certainly holds in
a restricted interval around zero The problem is now Does this rule hold in the full pKa range
We will try to prove that by a full analysis the N-HmiddotmiddotmiddotOO-HmiddotmiddotmiddotN system
Procedure In a first CSD search functional groups of known pKa value and more frequently
implied in NHmiddotmiddotmiddotOOHmiddotmiddotmiddotN bonds were identified Finally 10 classes of donors and 11 of acceptors were selected and the search restarted for each separate donor-acceptor group Altogether 9078 different bonds were analyzed (4364 NHmiddotmiddotmiddotO 2289 OHmiddotmiddotmiddotN and
2425 OmiddotmiddotmiddotHN+) For each bond the NmiddotmiddotmiddotO distances were evaluated as dNH + dHO to account for the
N-H-O angle and for each group the shortest and average distances [dNmiddotmiddotmiddotO (min)
and dNmiddotmiddotmiddotO (mean)] were registered
These values were compared (see next slide) with the acid-base features of the donors (pKAH range) acceptors (pKBH+ range) and with their combinations
(pKa range)
pKa large amp positive
pKa largeamp negative
Increasing Acidity of the Protonated A H+ Acceptor Increasing Basicity of the A Acceptor
ppKKaa versusversus HB Geometry Correlation - Conclusions HB Geometry Correlation - Conclusions The PApKa Equalization Principle is therefore fully confirmed in its two forms All strong HBs correspond to very small pKa values
pKa values modulate the HB strength over the full pKa range These conclusions are of great practical importance in at least two respects pKa is definitively established as the driving force which controls the HB
strength by modulating the HB covalent contribution It is definitively established that an accurate analysis of structural crystal data
leads to the same conclusions suggested but never proved on a general base by thermodynamic and spectroscopic methods
References Huyskens and Zeegers-Huyskens 1964 Zeegers-Huyskens 1986 1988 Ault and Pimentel 1975 Ratajczak and Sobczyk 1969 Sobczyk et al 1982 Barnes 1983 Kebarle et al 1974-1979 Meot-Ner (Mautner) et al
1984-1988
Towards a General HB TheoryTowards a General HB Theory
The results so far obtained are not a True HB Theory but rather a Set of Empirical Rules (or an Empirical Natural Law) that is a great collection of HB experimental data neatly organized in tables which all together represent a General Taxonomy of the HB Phenomenon exactly as the Carl Linnaeusrsquo classification of plants A scientific theory is something different It is the casting of the empirical natural law into the frame of a theory which is more fundamental down to the reductionistic chain of the scientific disciplines For instance the kinetic gas theory is the casting of the empirical gas laws (the empirical natural law) into Newtonrsquos classical mechanics
How to make a HB TheoryHow to make a HB Theory
HB Properties = FF (HB Driving Variable)where
HB Driving Variable = PApKa and FF = Transition-State Theory
The Transition-State HB TheoryThe Transition-State HB Theory(Gilli et al JACS 2002 2005 Gilli et al J Mol Struct 2006)
Though it has taken us more than 12 years to develop it
the basic idea is very simpleAny DndashHmiddotmiddotmiddotA bond can be considered as a chemical reaction which is
bimolecular in both directions and proceeds via transition-state (TS) formation
AndashB + C AmiddotmiddotmiddotBmiddotmiddotmiddotC A + BndashCDndashHmiddotmiddotmiddotA DmiddotmiddotmiddotHmiddotmiddotmiddotA DmiddotmiddotmiddotHndashA
Changes of nomenclatureReaction Pathway PTPathwayActivation Energy DaggerE PTBarrierReaction Energy Er PApKa Transition State (TS) PTTS
Reaction Coordinate RC=[d(DH)ndashd(AH)] Experimentals Variable-Temperature X-allographyCalculations DFTEmulated PTPathwaysInterpretation Marcus Rate-Equilibrium Theory LefflerHammond Postulate
AcknowledgmentsAcknowledgments I have to thank my direct coworkers without whose help this work could have not been accomplished
Valerio BERTOLASI Paola GILLI
Valeria FERRETTI Loretta PRETTO
and the scientific institutions which made available to us the databases without which this work could not even be started
CCDCCambridge Crystallographic
Data Centrefor the use of the
Cambridge Structural Database
NIST National Institute of Standards and
Technologyfor the use of the
NIST Chemistry WebBook
Electrostatic and Covalent HBs The Paulingrsquos ModelElectrostatic and Covalent HBs The Paulingrsquos Model
Linus Pauling (The Nature of the Chemical Bond 1939 1940 1960) describes two distinct classes of HBs
Weak and dissymmetric HBs of electrostatic nature It is recognized that the hydrogen atom with only one stable orbital (the 1s orbital) can form only one covalent bond that the hydrogen bond is largely ionic in character and that it is formed only between the most electronegative atoms (HB Chapter - Page 1)
Strong and symmetric HBs of covalent nature These ldquoare exceptionsrdquo described as ldquo the hydrogen bond in the [HF2]
ion lies midway the two fluorine atoms and
may be considered to form a half-bond with eachrdquo (HB Chapter - Page 49)
[FHF] [OHO][OHO]+ [OHO]+
Coulsonrsquos VB Treatment (The Standard HB Model)Coulsonrsquos VB Treatment (The Standard HB Model)
Paulingrsquos ideas acquired theoretical dignity with the VB treatment of Coulson and Danielsson in 1954 where the O-HO bond is described as a mixture of three main VB forms two covalent and one ionic
This line of thought was embraced by
Pimentel and McClellan in their famous book The Hydrogen Bond (1960)
They write ldquoAt the 1957 Ljubljana Conference one of the important points of fairly general accord was that the electro-static model does not account for all of the phenomena associated with H bond formationrdquo
E E
NCT
CT
CTNCT
COV2
IONIC
COV1
IONIC
COV1 COV2
NCT
NCT
(a) Electrostatic HB (b) Covalent HB
The Birth of the Simple Electrostatic ParadigmThe Birth of the Simple Electrostatic Paradigm For reasons difficult to understand the Standard HB Model was abandoned
in the mid-lsquo60ies and the HB became the weak electrostatic interaction of some 4-6 kcal mol-1 everyone has heard of while strong HBs just disappeared from the chemical horizon
From there on the HB was divided between a small group of specialists (who still believed in the Standard Model) and the great majority of other scientists (who trusted more the much simpler Electrostatic Paradigm)
The effect on HB studies was disastrous and it took more than twenty years to put it right
Why Paulingrsquos Thought was AbandonedWhy Paulingrsquos Thought was Abandoned Weak electrostatic HBs are quoted on page 1 and strong covalent ones at
page 49 Since most people read only the first few pages helliphellip On page 50 strong HBs are defined ldquoexceptionsrdquo Most readers may have
thought Why to bother about exceptions when there are already so many regular HBs to bother about These are things for specialists
In VB terms ldquothe hydrogen atom can form only one covalent bondhelliprdquo does not mean that there is only one bond but that there may be any combination of two bonds whose bond orders sum up to one from 1+0 to 0+1 through frac12+ frac12 Probably very few people understood that correctly
Another Unsolved Problem The HB PuzzleAnother Unsolved Problem The HB Puzzle
Bond lengths and energies of normal chemical bonds are found to depend on the nature of the interacting atoms
and are weakly perturbed by their external environment
Conversely binding energies (EHB) and DmiddotmiddotmiddotA distances (dDmiddotmiddotmiddotA) of DHmiddotmiddotmiddotA bonds
do not simply depend on the donor (D) and acceptor (A) nature but show very large variations even for the same donor-acceptor couple
This is what we have called for the sake of brevity
the HB Puzzlethe HB PuzzleAn extreme example of this behavior comes from the effects produced on
the OHmiddotmiddotmiddotO bond by the changing acid-base properties of its environment The weak HOHmiddotmiddotmiddotOH2 bond in water [EHB5 kcal mol-1 dOmiddotmiddotmiddotO270-275 Aring]
is switched in acidic or basic medium to the very strong [H2OmiddotmiddotmiddotHmiddotmiddotmiddotOH2]+ or
[HOmiddotmiddotmiddotHmiddotmiddotmiddotOH] bonds with EHB up to 30-31 kcal mol-1 and dOmiddotmiddotmiddotO down to 238-242 Aring
How to Solve the HB Puzzle How to Solve the HB Puzzle the Problem of the Driving Variablethe Problem of the Driving Variable
The Electrostatic Paradigm cannot explain the HB Puzzle
Neither the Standard Model provides a full interpretation of it because while it can explain what covalent and electrostatic HBs are
it cannot suggest which circumstances can produce them
To put the problem in more general terms there are dozens of physicochemical variables commonly measured in connection with the HB (energies geometries IR frequencies NMR chemical shifts NQR couplings and isotopic effects of the HB itself and in addiction a large number of other properties of the interacting molecules) and most if not all appear to be strongly inter-correlated But
whatrsquos the driving variablewhatrsquos the driving variable
whatrsquos the variable which among the many intercorrelated ones drives the transformation from weak and electrostatic
to strong and covalent HB
A Proposal The PApA Proposal The PApKKaa Equalization Principle Equalization Principle
Two very similar proposals come from early thermodynamic or spectroscopic investigations and are both centered on the
matching of the acid-base properties of the HB donor and acceptors moieties what we like too call for the sake of brevity the
PApPApKKaa Equalization Principle Equalization Principle
With reference to any generic DHmiddotmiddotmiddotA bond this principle states that the HB becomes the stronger the smaller is the difference of the donor-acceptor
proton affinities proton affinities PA = PA(DPA = PA(D) ) PA(A) PA(A)or
acidic constants acidic constants ppKKa a = p= pKKAHAH(D(DH) H) p pKKBH+BH+(A(AHH++))
------------------------------------------------------------------------------------------------------------------------- Ault BS and Pimentel GG (1975) J Phys Chem 79 615 Huyskens PL and Zeegers-Huyskens Th (1964) J Chim Phys Phys- Chim Biol
61 81
Our First Steps in the HB FieldOur First Steps in the HB Field As usual we entered the field by chance In 1985 we were studying the ligands
of the benzadiazepine membrane receptor One of these ligands was CGS8216 where we noticed something strange a rather short N-HhellipO bond of 2694 Aring associated with an interleaving β-enaminone hellipO=C-C=C-NHhellip fragment which was almost completely π-delocalized
It was the first indication of a possible correlation between -delocalization and H-bond strength what was called a few years later the
Resonance-Assisted H-Bond (RAHB)Resonance-Assisted H-Bond (RAHB) (Gilli Bellucci Ferretti amp Bertolasi JACS 1989 Bertolasi Gilli Ferretti amp Gilli JACS 1991) Since at the time few -enaminones were known the work started on the analogous class of -enolones (or -diketone enols) which were already known to give strong O-HO bonds through the equally resonant O=C-C=C-OH fragment
The Development of the OThe Development of the OHO RAHBHO RAHB
The OThe OHO RAHBsHO RAHBs
Very interesting Class of Strong HBs Different lengths of the resonant spacer Rn
(n = 1 3 5 7) The HBs formed were all much stronger than normal (non-resonant) OHO bonds withd(OO)INTRA =
239-255 Aringd(OO)INTER =
246-265 Aring
R1-RAHBR5-RAHB
24256 Aring
N
N
O M e
N
N
OM e
M eM e
H
lt 257 gt1 Aring
P
O H
OO
O H
H P
O H
OO
O H
H
R3-RAHB
O OH
237-255 Aring
262-267 Aring
O
O H O
OH
262-270 Aring
O
O
H
O
O H
R7-RAHB
24462 Aring
NOO
OO
M eM e
H
OOH
O
O
H
CARBOXYLIC ACIDS
DIBENZOYLMETHANE ENOLS
CYCLOHEXANEDIONE ENOLS
PHOPHORIC ACID
A Model for RAHB Electrostatic or CovalentA Model for RAHB Electrostatic or Covalent
At first (JACS 1989) we suggested a RAHB Electrostatic Model but it became rapidly evident that an efficient RAHB treatment would require a Covalent Model
All hell broke loose because as we discovered with surprise the concept itself of covalent HB had been banned some twenty years before and substituted by the acritical but more comfortable Simple Electrostatic Paradigm RAHB seriously risked to became a kind of bizarre covalent hypothesis
I must thank George A Jeffrey with his inimitable unbiased and skeptical style if RAHB was not immediately cast aside by the scientific establishment but started to be quoted in important books and reviews during the lsquo90ties
A RAHB Electrostatic ModelA RAHB Electrostatic Model A RAHB Covalent ModelA RAHB Covalent Model
Starting Again The Purely Empirical ApproachStarting Again The Purely Empirical Approach Fortunately we were realistic enough not to try to confute the Electrostatic
Paradigm On the other hand it was perfectly useless because too deeply rooted in the Weltanschaung of so many important and self-confident scientists
I have already given a short critical account of the very nature of these scientific paradigms at the ECM-2000 of Nancy based on the ideas of Thomas S Kuhn (The Structure of Scientific Revolutions The University of Chicago 1962 and 1970)
Anyway to get out of this impasse at the beginning of 1993 we decided to change approach and to restart to investigate the O-HO bond problem from the very beginning by adopting a purely empirical strategy
(i) suspend any previous ideas on the electrostatic or covalent nature of the HB (ii) define the OHmiddotmiddotmiddotO bond as a simple topological structure where a H atom is connected to two or more oxygen atoms(iii) collect all crystal structures having OHmiddotmiddotmiddotO bonds with d(OmiddotmiddotmiddotO) 270 Aring(iv) collect all available IR (O-H) and NMR (H) data of H-bonded protons(v) collect all available HB energy data from thermodynamic measurements in gas phase and non-polar solvents(vi) try to infer a conclusion on the very nature of the OHmiddotmiddotmiddotO bond from the ensemble of the data collected
A Full Classification of Strong HBsA Full Classification of Strong HBs
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs)CHARGE - ASSISTED HBs
PENTACHLOROPHENOL - p-TOLUIDINE
pKa = -070
12
12
N
CH3
O
ClCl
Cl
Cl
Cl
H25062 AringCL 1 (+ndash)CAHB SHB VSHB
Double Charge-Assisted HBDirect Acid-Base PApKa Matching
CL 2 (ndash)CAHB SHB VSHBNegative Charge-Assisted HB
Acid-Base PApKa Matching by Proton Loss R
OOH
R
O O24371 Aring
CARBOXYLIC ACID - CARBOXYLATE
CL 3 (+)CAHB SHB VSHBPositive Charge-Assisted HB
Acid-Base PApKa Matching by Proton Gain
O
HH H
O
HH
24303 Aring
WATER - HYDRONIUM
-BOND POLARIZATION - ASSISTED HBs
237-255 Aring
O OH
ArAr
DIBENZOYLMETHANE ENOLS
CL 4 RAHB SHB VSHB Resonance-Assisted or -Cooperative HB
PApKa Matching by -Conjugated-Bond Polarization
27501 Aring
OO
O
O O
WATER
CL 5 PAHB MHBPolarization-Assisted or -Cooperative HB(Partial) PApKa Matching by -Bond Polarization
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs) The most interesting aspect of a HB classification based on HB strength is that strong HBs belong only to a small number of chemical schemes that we have called Chemical Leitmotifs
The Alchemic Piper plays the Five Magic Tunes that make any Hydrogen Bond stronger The Chemical Leitmotifs
Symmetry and Covalency (1)Symmetry and Covalency (1)The covalent nature of the strong OHmiddotmiddotmiddotO bond was assessed by interpreting the
experimental results in terms of the Coulsonrsquos VB formalismWe cannot measure covalency but can evaluate molecular symmetry the
Coulsonrsquos model being the algorithm able to translate one concept into the other
In fact total symmetry across the HB implies energy equivalence between the two covalent VB forms ie E(ΨCOV1) = E(ΨCOV2) which is just the situation
associated with formation of the covalent HB
E E
NCT
CT
CTNCT
COV2
IONIC
COV1
IONIC
COV1 COV2
NCT
NCT
(a) Electrostatic HB (b) Covalent HB
Symmetry and Covalency (2)Symmetry and Covalency (2)
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 1
(+-)CAHBDouble Charge-Assisted HB
Direct Acid-Base PApKa Matching
R12DH+A12R
The role played by the PApKa equalization in HB strengthening
is self-evident for the (+-)CAHB chemical leitmotif
RDHARrsquo R12DH+A12Rrsquo RDHA+Rrsquo
which collects by definition all strong HBs formed by the acid-base pairs with a pKa matching within say ndash3 divide 3 pKa units
But what about the other leitmotifs Can we prove that
all chemical leitmotifs are simple artificesthat molecules can use to obliterate the normally
very large pKa between HB donor and acceptor atoms
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 2(-)CAHB
Negative Charge-Assisted HBAcid-Base PApKa Matching
by Proton Loss[R-DHA-R]-
Chemical Leitmotif 3(+)CAHB
Positive Charge-Assisted HBAcid-Base PApKa Matching
by Proton Gain[R-DHA-R]+
2II
2III
2IIa
2IIb
2IIIb
2IIIa
2VIa
pKa = pKAH(HO-H)-pKAH(HO-H) = 157 - 157 = 0
pKa = pKBH(H2O-H+)-pKBH(H2O-H
+) = -17 + 17 = 0
pKAH(HO-H) = 157
pKBH(H2O-H+) = -17
H
O H
H
O
H
(ndash)CAHB pKa = 00
VERYSTRONG~ 25-30 kcalmol
(+)CAHB pKa = 00
VERYSTRONG ~ 25-31 kcalmol
pKa = 175
OHB
WEAK ~ 4- 5kcalmol
ndash H+
+ H+
H
O H O
H
H
O H O
H
H
OHO
H
H
O
H
H
H
O
H
H
O
H
H
O
H
H H
O
H
H
H
O
H
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 4RAHB
Resonance-Assisted or -Bond Cooperative HBPApKa Matching by -Conjugated-Bond Polarization
R-D-HA=R R=DH-A-R
pKAH(RO-H) = 1518
pKBH(R2C=O-H+) = -(67)
O OH
O H O
R
R
R
Rn-RAHB pKa = ~ 21-25
WEAK ~ 4- 5kcalmol
EKO O
H
KEOO
H
pKa = 00
STRONG ~ 15-22 kcalmol
2IV
2IVa
2IVb
2VIb
OHB
The HB Empirical RulesThe HB Empirical Rules
The empirical analysis of experimental data joined with homeopathic doses of VB theory leads us to formulate two important HB Empirical Rules which have been called elsewhere ECHBM (Electrostatic-Covalent HB Model Gilli amp Gilli J Mol Struct 2000) and can be summarized as follows
Any given D-HA system may form HBs in a wide range of strengths lengths symmetries and proton locations the two extremes being represented
by the weak long dissymmetric and proton-out-centred HB of electrostatic nature
and by the very strong very short symmetric and proton-centred HB
classifiable as a true 3-center-4-electron covalent bond
The driving variable able to transform strong into weak HBs is dimensionally a free enthalpy corresponding to the difference between the Proton Affinities (PA) or related Acid-Base Dissociation Constants (pKa) of the Donor and Acceptor moieties
These rules have been verified beyond any reasonable doubt for the Conventional HBs of the following classification
Provisional Conclusions and New ControlsProvisional Conclusions and New Controls
We have so far established a sound set of empirical rules which include A full classification of all existing HBs A full classification of all strong HBs (The Chemical Leitmotifs) A plausible correlation between HB strengths and acid-base properties of the interacting molecules (The PApKa Equalization Principle)
To confirm this last point we have undertaken two years ago
a new research program aimed at assessing the Full Validity of the PApKa Equalization Principle
by comparing extended tables of pKa values arranged for chemical classes
withthe corresponding CSD-derived HB geometries
Hundreds of pKa were collected and more than 11000 crystal structures examined
The pThe pKKa Slide Rulea Slide Rule
It is a tool for the graphical evaluation of the difference
pKa = pKAH(DH) - pKBH+(AH+)
HB Acceptors on the left and HB Donors on the right
pKa values given for chemical class
Results expected
ΔpKagtgt0 DHmiddotmiddotmiddotmiddotA weak amp neutral
ΔpKa asymp 0 DmiddotmiddotmiddotHmiddotmiddotmiddotA strong amp
centeredΔpKa ltlt0DmiddotmiddotmiddotmiddotHA+ weak amp charged
pKa ranges of organic compounds
C-H acids -11 ltpKalt 53
Other Donors -1 ltpKalt 40
Acceptors -12 ltpKalt 16
All -15 ltpKalt 53
Water 0 ltpKalt 14
50
-10
0
10
20
30
40
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
ALDEHYDES
ETHERSALCOHOLS
AMIDES
NITRILES
ANILINES
CF3-SO3H
HClO4HI
HBrHCl
H2SO4
HSO4
HNO3
HBF4
H3PO4
H2PO4
HPO42
HF HNO2
HNNN
NH2OHH2CO3
HCO3
H2S
HS-
HCN H3BO3
H2BO3
H4SiO4
H2O2
HO
HSCN
H-H
SULFONICACIDS
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
OXIMES
ALCOHOLS
THIOLES
HB ACCEPTORS (A)pK BH+
HB DONORS (D-H)pK AH
C-H ACIDS pK AH
BE
TT
ER
HB
AC
CE
PT
OR
BE
TT
ER
BA
SE
BE
TT
ER
HB
DO
NO
R
BE
TT
ER
AC
ID
N-OXIDES
AMIDINES
UREA
THIOUREA
BARBITURICURIC ACID
MONO DIPHOSPHINES
TRIPHOSPHINES
TRINITROANILINES
AMINES
ANILINES
MONO DINITROANILINES
AMIDES
CARBOXYLIC ACIDS
HALOGENOANILINES
AZOCOMPS
TRINITROANILINES
PROTONSPONGES
ACIDSESTERS
H2O
H2O
MONODINITROANILINES
KETONES
SULFIDES
HALOGENCARB ACIDS
TRINITROPHENOLS
ENOLS
MONO DINITROPHENOLS
PHENOLSNAPHTHOLS
HALOGENOPHENOLS
HALOGENOALCOHOLS
SULFOXIDES
(NC)5-CYCLO
PENTADIENE
(NC)3CH
(O2N)2=CH2
HCCHNC-CH3
CH3-CO-CH3INDENE
O2N-CH3
(NC)2=CH2
(O2N)3CH
H2C=CH2
C6H6
CH4
CYCLOPENTADIENE
CYCLOPROPENE
Ar3CH
Ar2=CH2
Ar-CH3
NITROCOMPS
SELENOXIDES
AZOLES
AZINESDIAZINES
AMINES
Cl5-PHENOL
CH3-CH3
(CH3)3CH
NH3
NH3
51
53
51
53
Chemical Leitmotifs and PApChemical Leitmotifs and PApKKaa Equalization Rules Equalization Rules RAHB RAHB cannot be treated by pKa equalization methods because π-delocalization
modifies the pKarsquos of the donor and acceptor moieties (+)CAHB is a true proton transfer from an acid (HB donor) to a base (HB acceptor)
RndashDndashHAndashRrsquo Rndash12DH+A12ndashndashRrsquo RndashDHndashA+ndashRrsquoΔpKa = pKAH(RDH) pKBH+(RrsquoA)
()CAHB is a proton sharing between two acids (HB donors)
RndashDndashHDrsquondashRrsquo [RDHDrsquoRrsquo] RDHDrsquoRrsquoΔpKa = pKAH(RDH) pKAH(RDH)
(+)CAHB is a proton sharing between two bases (HB acceptors)
R+AHArsquoRrsquo [RAHArsquoRrsquo]+ RAHArsquo+RrsquoΔpKa = pKBH+(RA) pKBH+(RrsquoArsquo)
Whenever () and (+)CAHBs are both homonuclear (D = Drsquo or A = Arsquo) and
homomolecular (R = Rrsquo) the matching condition ΔpKa= 0 will hold irrespective of the
actual pKarsquos of the two interacting moieties All HBs formed will be strong
Some Famous HBsSome Famous HBs
The NThe NHmiddotmiddotmiddotOOHmiddotmiddotmiddotOOHmiddotmiddotmiddotN System over the Full HmiddotmiddotmiddotN System over the Full ppKKaa Range Range
When evaluated from the pKa slide rule the total pKa range is extremely wide
ndash30 pa 60 So far we have been able to shown that the pKa equalization rule certainly holds in
a restricted interval around zero The problem is now Does this rule hold in the full pKa range
We will try to prove that by a full analysis the N-HmiddotmiddotmiddotOO-HmiddotmiddotmiddotN system
Procedure In a first CSD search functional groups of known pKa value and more frequently
implied in NHmiddotmiddotmiddotOOHmiddotmiddotmiddotN bonds were identified Finally 10 classes of donors and 11 of acceptors were selected and the search restarted for each separate donor-acceptor group Altogether 9078 different bonds were analyzed (4364 NHmiddotmiddotmiddotO 2289 OHmiddotmiddotmiddotN and
2425 OmiddotmiddotmiddotHN+) For each bond the NmiddotmiddotmiddotO distances were evaluated as dNH + dHO to account for the
N-H-O angle and for each group the shortest and average distances [dNmiddotmiddotmiddotO (min)
and dNmiddotmiddotmiddotO (mean)] were registered
These values were compared (see next slide) with the acid-base features of the donors (pKAH range) acceptors (pKBH+ range) and with their combinations
(pKa range)
pKa large amp positive
pKa largeamp negative
Increasing Acidity of the Protonated A H+ Acceptor Increasing Basicity of the A Acceptor
ppKKaa versusversus HB Geometry Correlation - Conclusions HB Geometry Correlation - Conclusions The PApKa Equalization Principle is therefore fully confirmed in its two forms All strong HBs correspond to very small pKa values
pKa values modulate the HB strength over the full pKa range These conclusions are of great practical importance in at least two respects pKa is definitively established as the driving force which controls the HB
strength by modulating the HB covalent contribution It is definitively established that an accurate analysis of structural crystal data
leads to the same conclusions suggested but never proved on a general base by thermodynamic and spectroscopic methods
References Huyskens and Zeegers-Huyskens 1964 Zeegers-Huyskens 1986 1988 Ault and Pimentel 1975 Ratajczak and Sobczyk 1969 Sobczyk et al 1982 Barnes 1983 Kebarle et al 1974-1979 Meot-Ner (Mautner) et al
1984-1988
Towards a General HB TheoryTowards a General HB Theory
The results so far obtained are not a True HB Theory but rather a Set of Empirical Rules (or an Empirical Natural Law) that is a great collection of HB experimental data neatly organized in tables which all together represent a General Taxonomy of the HB Phenomenon exactly as the Carl Linnaeusrsquo classification of plants A scientific theory is something different It is the casting of the empirical natural law into the frame of a theory which is more fundamental down to the reductionistic chain of the scientific disciplines For instance the kinetic gas theory is the casting of the empirical gas laws (the empirical natural law) into Newtonrsquos classical mechanics
How to make a HB TheoryHow to make a HB Theory
HB Properties = FF (HB Driving Variable)where
HB Driving Variable = PApKa and FF = Transition-State Theory
The Transition-State HB TheoryThe Transition-State HB Theory(Gilli et al JACS 2002 2005 Gilli et al J Mol Struct 2006)
Though it has taken us more than 12 years to develop it
the basic idea is very simpleAny DndashHmiddotmiddotmiddotA bond can be considered as a chemical reaction which is
bimolecular in both directions and proceeds via transition-state (TS) formation
AndashB + C AmiddotmiddotmiddotBmiddotmiddotmiddotC A + BndashCDndashHmiddotmiddotmiddotA DmiddotmiddotmiddotHmiddotmiddotmiddotA DmiddotmiddotmiddotHndashA
Changes of nomenclatureReaction Pathway PTPathwayActivation Energy DaggerE PTBarrierReaction Energy Er PApKa Transition State (TS) PTTS
Reaction Coordinate RC=[d(DH)ndashd(AH)] Experimentals Variable-Temperature X-allographyCalculations DFTEmulated PTPathwaysInterpretation Marcus Rate-Equilibrium Theory LefflerHammond Postulate
AcknowledgmentsAcknowledgments I have to thank my direct coworkers without whose help this work could have not been accomplished
Valerio BERTOLASI Paola GILLI
Valeria FERRETTI Loretta PRETTO
and the scientific institutions which made available to us the databases without which this work could not even be started
CCDCCambridge Crystallographic
Data Centrefor the use of the
Cambridge Structural Database
NIST National Institute of Standards and
Technologyfor the use of the
NIST Chemistry WebBook
Coulsonrsquos VB Treatment (The Standard HB Model)Coulsonrsquos VB Treatment (The Standard HB Model)
Paulingrsquos ideas acquired theoretical dignity with the VB treatment of Coulson and Danielsson in 1954 where the O-HO bond is described as a mixture of three main VB forms two covalent and one ionic
This line of thought was embraced by
Pimentel and McClellan in their famous book The Hydrogen Bond (1960)
They write ldquoAt the 1957 Ljubljana Conference one of the important points of fairly general accord was that the electro-static model does not account for all of the phenomena associated with H bond formationrdquo
E E
NCT
CT
CTNCT
COV2
IONIC
COV1
IONIC
COV1 COV2
NCT
NCT
(a) Electrostatic HB (b) Covalent HB
The Birth of the Simple Electrostatic ParadigmThe Birth of the Simple Electrostatic Paradigm For reasons difficult to understand the Standard HB Model was abandoned
in the mid-lsquo60ies and the HB became the weak electrostatic interaction of some 4-6 kcal mol-1 everyone has heard of while strong HBs just disappeared from the chemical horizon
From there on the HB was divided between a small group of specialists (who still believed in the Standard Model) and the great majority of other scientists (who trusted more the much simpler Electrostatic Paradigm)
The effect on HB studies was disastrous and it took more than twenty years to put it right
Why Paulingrsquos Thought was AbandonedWhy Paulingrsquos Thought was Abandoned Weak electrostatic HBs are quoted on page 1 and strong covalent ones at
page 49 Since most people read only the first few pages helliphellip On page 50 strong HBs are defined ldquoexceptionsrdquo Most readers may have
thought Why to bother about exceptions when there are already so many regular HBs to bother about These are things for specialists
In VB terms ldquothe hydrogen atom can form only one covalent bondhelliprdquo does not mean that there is only one bond but that there may be any combination of two bonds whose bond orders sum up to one from 1+0 to 0+1 through frac12+ frac12 Probably very few people understood that correctly
Another Unsolved Problem The HB PuzzleAnother Unsolved Problem The HB Puzzle
Bond lengths and energies of normal chemical bonds are found to depend on the nature of the interacting atoms
and are weakly perturbed by their external environment
Conversely binding energies (EHB) and DmiddotmiddotmiddotA distances (dDmiddotmiddotmiddotA) of DHmiddotmiddotmiddotA bonds
do not simply depend on the donor (D) and acceptor (A) nature but show very large variations even for the same donor-acceptor couple
This is what we have called for the sake of brevity
the HB Puzzlethe HB PuzzleAn extreme example of this behavior comes from the effects produced on
the OHmiddotmiddotmiddotO bond by the changing acid-base properties of its environment The weak HOHmiddotmiddotmiddotOH2 bond in water [EHB5 kcal mol-1 dOmiddotmiddotmiddotO270-275 Aring]
is switched in acidic or basic medium to the very strong [H2OmiddotmiddotmiddotHmiddotmiddotmiddotOH2]+ or
[HOmiddotmiddotmiddotHmiddotmiddotmiddotOH] bonds with EHB up to 30-31 kcal mol-1 and dOmiddotmiddotmiddotO down to 238-242 Aring
How to Solve the HB Puzzle How to Solve the HB Puzzle the Problem of the Driving Variablethe Problem of the Driving Variable
The Electrostatic Paradigm cannot explain the HB Puzzle
Neither the Standard Model provides a full interpretation of it because while it can explain what covalent and electrostatic HBs are
it cannot suggest which circumstances can produce them
To put the problem in more general terms there are dozens of physicochemical variables commonly measured in connection with the HB (energies geometries IR frequencies NMR chemical shifts NQR couplings and isotopic effects of the HB itself and in addiction a large number of other properties of the interacting molecules) and most if not all appear to be strongly inter-correlated But
whatrsquos the driving variablewhatrsquos the driving variable
whatrsquos the variable which among the many intercorrelated ones drives the transformation from weak and electrostatic
to strong and covalent HB
A Proposal The PApA Proposal The PApKKaa Equalization Principle Equalization Principle
Two very similar proposals come from early thermodynamic or spectroscopic investigations and are both centered on the
matching of the acid-base properties of the HB donor and acceptors moieties what we like too call for the sake of brevity the
PApPApKKaa Equalization Principle Equalization Principle
With reference to any generic DHmiddotmiddotmiddotA bond this principle states that the HB becomes the stronger the smaller is the difference of the donor-acceptor
proton affinities proton affinities PA = PA(DPA = PA(D) ) PA(A) PA(A)or
acidic constants acidic constants ppKKa a = p= pKKAHAH(D(DH) H) p pKKBH+BH+(A(AHH++))
------------------------------------------------------------------------------------------------------------------------- Ault BS and Pimentel GG (1975) J Phys Chem 79 615 Huyskens PL and Zeegers-Huyskens Th (1964) J Chim Phys Phys- Chim Biol
61 81
Our First Steps in the HB FieldOur First Steps in the HB Field As usual we entered the field by chance In 1985 we were studying the ligands
of the benzadiazepine membrane receptor One of these ligands was CGS8216 where we noticed something strange a rather short N-HhellipO bond of 2694 Aring associated with an interleaving β-enaminone hellipO=C-C=C-NHhellip fragment which was almost completely π-delocalized
It was the first indication of a possible correlation between -delocalization and H-bond strength what was called a few years later the
Resonance-Assisted H-Bond (RAHB)Resonance-Assisted H-Bond (RAHB) (Gilli Bellucci Ferretti amp Bertolasi JACS 1989 Bertolasi Gilli Ferretti amp Gilli JACS 1991) Since at the time few -enaminones were known the work started on the analogous class of -enolones (or -diketone enols) which were already known to give strong O-HO bonds through the equally resonant O=C-C=C-OH fragment
The Development of the OThe Development of the OHO RAHBHO RAHB
The OThe OHO RAHBsHO RAHBs
Very interesting Class of Strong HBs Different lengths of the resonant spacer Rn
(n = 1 3 5 7) The HBs formed were all much stronger than normal (non-resonant) OHO bonds withd(OO)INTRA =
239-255 Aringd(OO)INTER =
246-265 Aring
R1-RAHBR5-RAHB
24256 Aring
N
N
O M e
N
N
OM e
M eM e
H
lt 257 gt1 Aring
P
O H
OO
O H
H P
O H
OO
O H
H
R3-RAHB
O OH
237-255 Aring
262-267 Aring
O
O H O
OH
262-270 Aring
O
O
H
O
O H
R7-RAHB
24462 Aring
NOO
OO
M eM e
H
OOH
O
O
H
CARBOXYLIC ACIDS
DIBENZOYLMETHANE ENOLS
CYCLOHEXANEDIONE ENOLS
PHOPHORIC ACID
A Model for RAHB Electrostatic or CovalentA Model for RAHB Electrostatic or Covalent
At first (JACS 1989) we suggested a RAHB Electrostatic Model but it became rapidly evident that an efficient RAHB treatment would require a Covalent Model
All hell broke loose because as we discovered with surprise the concept itself of covalent HB had been banned some twenty years before and substituted by the acritical but more comfortable Simple Electrostatic Paradigm RAHB seriously risked to became a kind of bizarre covalent hypothesis
I must thank George A Jeffrey with his inimitable unbiased and skeptical style if RAHB was not immediately cast aside by the scientific establishment but started to be quoted in important books and reviews during the lsquo90ties
A RAHB Electrostatic ModelA RAHB Electrostatic Model A RAHB Covalent ModelA RAHB Covalent Model
Starting Again The Purely Empirical ApproachStarting Again The Purely Empirical Approach Fortunately we were realistic enough not to try to confute the Electrostatic
Paradigm On the other hand it was perfectly useless because too deeply rooted in the Weltanschaung of so many important and self-confident scientists
I have already given a short critical account of the very nature of these scientific paradigms at the ECM-2000 of Nancy based on the ideas of Thomas S Kuhn (The Structure of Scientific Revolutions The University of Chicago 1962 and 1970)
Anyway to get out of this impasse at the beginning of 1993 we decided to change approach and to restart to investigate the O-HO bond problem from the very beginning by adopting a purely empirical strategy
(i) suspend any previous ideas on the electrostatic or covalent nature of the HB (ii) define the OHmiddotmiddotmiddotO bond as a simple topological structure where a H atom is connected to two or more oxygen atoms(iii) collect all crystal structures having OHmiddotmiddotmiddotO bonds with d(OmiddotmiddotmiddotO) 270 Aring(iv) collect all available IR (O-H) and NMR (H) data of H-bonded protons(v) collect all available HB energy data from thermodynamic measurements in gas phase and non-polar solvents(vi) try to infer a conclusion on the very nature of the OHmiddotmiddotmiddotO bond from the ensemble of the data collected
A Full Classification of Strong HBsA Full Classification of Strong HBs
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs)CHARGE - ASSISTED HBs
PENTACHLOROPHENOL - p-TOLUIDINE
pKa = -070
12
12
N
CH3
O
ClCl
Cl
Cl
Cl
H25062 AringCL 1 (+ndash)CAHB SHB VSHB
Double Charge-Assisted HBDirect Acid-Base PApKa Matching
CL 2 (ndash)CAHB SHB VSHBNegative Charge-Assisted HB
Acid-Base PApKa Matching by Proton Loss R
OOH
R
O O24371 Aring
CARBOXYLIC ACID - CARBOXYLATE
CL 3 (+)CAHB SHB VSHBPositive Charge-Assisted HB
Acid-Base PApKa Matching by Proton Gain
O
HH H
O
HH
24303 Aring
WATER - HYDRONIUM
-BOND POLARIZATION - ASSISTED HBs
237-255 Aring
O OH
ArAr
DIBENZOYLMETHANE ENOLS
CL 4 RAHB SHB VSHB Resonance-Assisted or -Cooperative HB
PApKa Matching by -Conjugated-Bond Polarization
27501 Aring
OO
O
O O
WATER
CL 5 PAHB MHBPolarization-Assisted or -Cooperative HB(Partial) PApKa Matching by -Bond Polarization
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs) The most interesting aspect of a HB classification based on HB strength is that strong HBs belong only to a small number of chemical schemes that we have called Chemical Leitmotifs
The Alchemic Piper plays the Five Magic Tunes that make any Hydrogen Bond stronger The Chemical Leitmotifs
Symmetry and Covalency (1)Symmetry and Covalency (1)The covalent nature of the strong OHmiddotmiddotmiddotO bond was assessed by interpreting the
experimental results in terms of the Coulsonrsquos VB formalismWe cannot measure covalency but can evaluate molecular symmetry the
Coulsonrsquos model being the algorithm able to translate one concept into the other
In fact total symmetry across the HB implies energy equivalence between the two covalent VB forms ie E(ΨCOV1) = E(ΨCOV2) which is just the situation
associated with formation of the covalent HB
E E
NCT
CT
CTNCT
COV2
IONIC
COV1
IONIC
COV1 COV2
NCT
NCT
(a) Electrostatic HB (b) Covalent HB
Symmetry and Covalency (2)Symmetry and Covalency (2)
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 1
(+-)CAHBDouble Charge-Assisted HB
Direct Acid-Base PApKa Matching
R12DH+A12R
The role played by the PApKa equalization in HB strengthening
is self-evident for the (+-)CAHB chemical leitmotif
RDHARrsquo R12DH+A12Rrsquo RDHA+Rrsquo
which collects by definition all strong HBs formed by the acid-base pairs with a pKa matching within say ndash3 divide 3 pKa units
But what about the other leitmotifs Can we prove that
all chemical leitmotifs are simple artificesthat molecules can use to obliterate the normally
very large pKa between HB donor and acceptor atoms
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 2(-)CAHB
Negative Charge-Assisted HBAcid-Base PApKa Matching
by Proton Loss[R-DHA-R]-
Chemical Leitmotif 3(+)CAHB
Positive Charge-Assisted HBAcid-Base PApKa Matching
by Proton Gain[R-DHA-R]+
2II
2III
2IIa
2IIb
2IIIb
2IIIa
2VIa
pKa = pKAH(HO-H)-pKAH(HO-H) = 157 - 157 = 0
pKa = pKBH(H2O-H+)-pKBH(H2O-H
+) = -17 + 17 = 0
pKAH(HO-H) = 157
pKBH(H2O-H+) = -17
H
O H
H
O
H
(ndash)CAHB pKa = 00
VERYSTRONG~ 25-30 kcalmol
(+)CAHB pKa = 00
VERYSTRONG ~ 25-31 kcalmol
pKa = 175
OHB
WEAK ~ 4- 5kcalmol
ndash H+
+ H+
H
O H O
H
H
O H O
H
H
OHO
H
H
O
H
H
H
O
H
H
O
H
H
O
H
H H
O
H
H
H
O
H
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 4RAHB
Resonance-Assisted or -Bond Cooperative HBPApKa Matching by -Conjugated-Bond Polarization
R-D-HA=R R=DH-A-R
pKAH(RO-H) = 1518
pKBH(R2C=O-H+) = -(67)
O OH
O H O
R
R
R
Rn-RAHB pKa = ~ 21-25
WEAK ~ 4- 5kcalmol
EKO O
H
KEOO
H
pKa = 00
STRONG ~ 15-22 kcalmol
2IV
2IVa
2IVb
2VIb
OHB
The HB Empirical RulesThe HB Empirical Rules
The empirical analysis of experimental data joined with homeopathic doses of VB theory leads us to formulate two important HB Empirical Rules which have been called elsewhere ECHBM (Electrostatic-Covalent HB Model Gilli amp Gilli J Mol Struct 2000) and can be summarized as follows
Any given D-HA system may form HBs in a wide range of strengths lengths symmetries and proton locations the two extremes being represented
by the weak long dissymmetric and proton-out-centred HB of electrostatic nature
and by the very strong very short symmetric and proton-centred HB
classifiable as a true 3-center-4-electron covalent bond
The driving variable able to transform strong into weak HBs is dimensionally a free enthalpy corresponding to the difference between the Proton Affinities (PA) or related Acid-Base Dissociation Constants (pKa) of the Donor and Acceptor moieties
These rules have been verified beyond any reasonable doubt for the Conventional HBs of the following classification
Provisional Conclusions and New ControlsProvisional Conclusions and New Controls
We have so far established a sound set of empirical rules which include A full classification of all existing HBs A full classification of all strong HBs (The Chemical Leitmotifs) A plausible correlation between HB strengths and acid-base properties of the interacting molecules (The PApKa Equalization Principle)
To confirm this last point we have undertaken two years ago
a new research program aimed at assessing the Full Validity of the PApKa Equalization Principle
by comparing extended tables of pKa values arranged for chemical classes
withthe corresponding CSD-derived HB geometries
Hundreds of pKa were collected and more than 11000 crystal structures examined
The pThe pKKa Slide Rulea Slide Rule
It is a tool for the graphical evaluation of the difference
pKa = pKAH(DH) - pKBH+(AH+)
HB Acceptors on the left and HB Donors on the right
pKa values given for chemical class
Results expected
ΔpKagtgt0 DHmiddotmiddotmiddotmiddotA weak amp neutral
ΔpKa asymp 0 DmiddotmiddotmiddotHmiddotmiddotmiddotA strong amp
centeredΔpKa ltlt0DmiddotmiddotmiddotmiddotHA+ weak amp charged
pKa ranges of organic compounds
C-H acids -11 ltpKalt 53
Other Donors -1 ltpKalt 40
Acceptors -12 ltpKalt 16
All -15 ltpKalt 53
Water 0 ltpKalt 14
50
-10
0
10
20
30
40
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
ALDEHYDES
ETHERSALCOHOLS
AMIDES
NITRILES
ANILINES
CF3-SO3H
HClO4HI
HBrHCl
H2SO4
HSO4
HNO3
HBF4
H3PO4
H2PO4
HPO42
HF HNO2
HNNN
NH2OHH2CO3
HCO3
H2S
HS-
HCN H3BO3
H2BO3
H4SiO4
H2O2
HO
HSCN
H-H
SULFONICACIDS
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
OXIMES
ALCOHOLS
THIOLES
HB ACCEPTORS (A)pK BH+
HB DONORS (D-H)pK AH
C-H ACIDS pK AH
BE
TT
ER
HB
AC
CE
PT
OR
BE
TT
ER
BA
SE
BE
TT
ER
HB
DO
NO
R
BE
TT
ER
AC
ID
N-OXIDES
AMIDINES
UREA
THIOUREA
BARBITURICURIC ACID
MONO DIPHOSPHINES
TRIPHOSPHINES
TRINITROANILINES
AMINES
ANILINES
MONO DINITROANILINES
AMIDES
CARBOXYLIC ACIDS
HALOGENOANILINES
AZOCOMPS
TRINITROANILINES
PROTONSPONGES
ACIDSESTERS
H2O
H2O
MONODINITROANILINES
KETONES
SULFIDES
HALOGENCARB ACIDS
TRINITROPHENOLS
ENOLS
MONO DINITROPHENOLS
PHENOLSNAPHTHOLS
HALOGENOPHENOLS
HALOGENOALCOHOLS
SULFOXIDES
(NC)5-CYCLO
PENTADIENE
(NC)3CH
(O2N)2=CH2
HCCHNC-CH3
CH3-CO-CH3INDENE
O2N-CH3
(NC)2=CH2
(O2N)3CH
H2C=CH2
C6H6
CH4
CYCLOPENTADIENE
CYCLOPROPENE
Ar3CH
Ar2=CH2
Ar-CH3
NITROCOMPS
SELENOXIDES
AZOLES
AZINESDIAZINES
AMINES
Cl5-PHENOL
CH3-CH3
(CH3)3CH
NH3
NH3
51
53
51
53
Chemical Leitmotifs and PApChemical Leitmotifs and PApKKaa Equalization Rules Equalization Rules RAHB RAHB cannot be treated by pKa equalization methods because π-delocalization
modifies the pKarsquos of the donor and acceptor moieties (+)CAHB is a true proton transfer from an acid (HB donor) to a base (HB acceptor)
RndashDndashHAndashRrsquo Rndash12DH+A12ndashndashRrsquo RndashDHndashA+ndashRrsquoΔpKa = pKAH(RDH) pKBH+(RrsquoA)
()CAHB is a proton sharing between two acids (HB donors)
RndashDndashHDrsquondashRrsquo [RDHDrsquoRrsquo] RDHDrsquoRrsquoΔpKa = pKAH(RDH) pKAH(RDH)
(+)CAHB is a proton sharing between two bases (HB acceptors)
R+AHArsquoRrsquo [RAHArsquoRrsquo]+ RAHArsquo+RrsquoΔpKa = pKBH+(RA) pKBH+(RrsquoArsquo)
Whenever () and (+)CAHBs are both homonuclear (D = Drsquo or A = Arsquo) and
homomolecular (R = Rrsquo) the matching condition ΔpKa= 0 will hold irrespective of the
actual pKarsquos of the two interacting moieties All HBs formed will be strong
Some Famous HBsSome Famous HBs
The NThe NHmiddotmiddotmiddotOOHmiddotmiddotmiddotOOHmiddotmiddotmiddotN System over the Full HmiddotmiddotmiddotN System over the Full ppKKaa Range Range
When evaluated from the pKa slide rule the total pKa range is extremely wide
ndash30 pa 60 So far we have been able to shown that the pKa equalization rule certainly holds in
a restricted interval around zero The problem is now Does this rule hold in the full pKa range
We will try to prove that by a full analysis the N-HmiddotmiddotmiddotOO-HmiddotmiddotmiddotN system
Procedure In a first CSD search functional groups of known pKa value and more frequently
implied in NHmiddotmiddotmiddotOOHmiddotmiddotmiddotN bonds were identified Finally 10 classes of donors and 11 of acceptors were selected and the search restarted for each separate donor-acceptor group Altogether 9078 different bonds were analyzed (4364 NHmiddotmiddotmiddotO 2289 OHmiddotmiddotmiddotN and
2425 OmiddotmiddotmiddotHN+) For each bond the NmiddotmiddotmiddotO distances were evaluated as dNH + dHO to account for the
N-H-O angle and for each group the shortest and average distances [dNmiddotmiddotmiddotO (min)
and dNmiddotmiddotmiddotO (mean)] were registered
These values were compared (see next slide) with the acid-base features of the donors (pKAH range) acceptors (pKBH+ range) and with their combinations
(pKa range)
pKa large amp positive
pKa largeamp negative
Increasing Acidity of the Protonated A H+ Acceptor Increasing Basicity of the A Acceptor
ppKKaa versusversus HB Geometry Correlation - Conclusions HB Geometry Correlation - Conclusions The PApKa Equalization Principle is therefore fully confirmed in its two forms All strong HBs correspond to very small pKa values
pKa values modulate the HB strength over the full pKa range These conclusions are of great practical importance in at least two respects pKa is definitively established as the driving force which controls the HB
strength by modulating the HB covalent contribution It is definitively established that an accurate analysis of structural crystal data
leads to the same conclusions suggested but never proved on a general base by thermodynamic and spectroscopic methods
References Huyskens and Zeegers-Huyskens 1964 Zeegers-Huyskens 1986 1988 Ault and Pimentel 1975 Ratajczak and Sobczyk 1969 Sobczyk et al 1982 Barnes 1983 Kebarle et al 1974-1979 Meot-Ner (Mautner) et al
1984-1988
Towards a General HB TheoryTowards a General HB Theory
The results so far obtained are not a True HB Theory but rather a Set of Empirical Rules (or an Empirical Natural Law) that is a great collection of HB experimental data neatly organized in tables which all together represent a General Taxonomy of the HB Phenomenon exactly as the Carl Linnaeusrsquo classification of plants A scientific theory is something different It is the casting of the empirical natural law into the frame of a theory which is more fundamental down to the reductionistic chain of the scientific disciplines For instance the kinetic gas theory is the casting of the empirical gas laws (the empirical natural law) into Newtonrsquos classical mechanics
How to make a HB TheoryHow to make a HB Theory
HB Properties = FF (HB Driving Variable)where
HB Driving Variable = PApKa and FF = Transition-State Theory
The Transition-State HB TheoryThe Transition-State HB Theory(Gilli et al JACS 2002 2005 Gilli et al J Mol Struct 2006)
Though it has taken us more than 12 years to develop it
the basic idea is very simpleAny DndashHmiddotmiddotmiddotA bond can be considered as a chemical reaction which is
bimolecular in both directions and proceeds via transition-state (TS) formation
AndashB + C AmiddotmiddotmiddotBmiddotmiddotmiddotC A + BndashCDndashHmiddotmiddotmiddotA DmiddotmiddotmiddotHmiddotmiddotmiddotA DmiddotmiddotmiddotHndashA
Changes of nomenclatureReaction Pathway PTPathwayActivation Energy DaggerE PTBarrierReaction Energy Er PApKa Transition State (TS) PTTS
Reaction Coordinate RC=[d(DH)ndashd(AH)] Experimentals Variable-Temperature X-allographyCalculations DFTEmulated PTPathwaysInterpretation Marcus Rate-Equilibrium Theory LefflerHammond Postulate
AcknowledgmentsAcknowledgments I have to thank my direct coworkers without whose help this work could have not been accomplished
Valerio BERTOLASI Paola GILLI
Valeria FERRETTI Loretta PRETTO
and the scientific institutions which made available to us the databases without which this work could not even be started
CCDCCambridge Crystallographic
Data Centrefor the use of the
Cambridge Structural Database
NIST National Institute of Standards and
Technologyfor the use of the
NIST Chemistry WebBook
The Birth of the Simple Electrostatic ParadigmThe Birth of the Simple Electrostatic Paradigm For reasons difficult to understand the Standard HB Model was abandoned
in the mid-lsquo60ies and the HB became the weak electrostatic interaction of some 4-6 kcal mol-1 everyone has heard of while strong HBs just disappeared from the chemical horizon
From there on the HB was divided between a small group of specialists (who still believed in the Standard Model) and the great majority of other scientists (who trusted more the much simpler Electrostatic Paradigm)
The effect on HB studies was disastrous and it took more than twenty years to put it right
Why Paulingrsquos Thought was AbandonedWhy Paulingrsquos Thought was Abandoned Weak electrostatic HBs are quoted on page 1 and strong covalent ones at
page 49 Since most people read only the first few pages helliphellip On page 50 strong HBs are defined ldquoexceptionsrdquo Most readers may have
thought Why to bother about exceptions when there are already so many regular HBs to bother about These are things for specialists
In VB terms ldquothe hydrogen atom can form only one covalent bondhelliprdquo does not mean that there is only one bond but that there may be any combination of two bonds whose bond orders sum up to one from 1+0 to 0+1 through frac12+ frac12 Probably very few people understood that correctly
Another Unsolved Problem The HB PuzzleAnother Unsolved Problem The HB Puzzle
Bond lengths and energies of normal chemical bonds are found to depend on the nature of the interacting atoms
and are weakly perturbed by their external environment
Conversely binding energies (EHB) and DmiddotmiddotmiddotA distances (dDmiddotmiddotmiddotA) of DHmiddotmiddotmiddotA bonds
do not simply depend on the donor (D) and acceptor (A) nature but show very large variations even for the same donor-acceptor couple
This is what we have called for the sake of brevity
the HB Puzzlethe HB PuzzleAn extreme example of this behavior comes from the effects produced on
the OHmiddotmiddotmiddotO bond by the changing acid-base properties of its environment The weak HOHmiddotmiddotmiddotOH2 bond in water [EHB5 kcal mol-1 dOmiddotmiddotmiddotO270-275 Aring]
is switched in acidic or basic medium to the very strong [H2OmiddotmiddotmiddotHmiddotmiddotmiddotOH2]+ or
[HOmiddotmiddotmiddotHmiddotmiddotmiddotOH] bonds with EHB up to 30-31 kcal mol-1 and dOmiddotmiddotmiddotO down to 238-242 Aring
How to Solve the HB Puzzle How to Solve the HB Puzzle the Problem of the Driving Variablethe Problem of the Driving Variable
The Electrostatic Paradigm cannot explain the HB Puzzle
Neither the Standard Model provides a full interpretation of it because while it can explain what covalent and electrostatic HBs are
it cannot suggest which circumstances can produce them
To put the problem in more general terms there are dozens of physicochemical variables commonly measured in connection with the HB (energies geometries IR frequencies NMR chemical shifts NQR couplings and isotopic effects of the HB itself and in addiction a large number of other properties of the interacting molecules) and most if not all appear to be strongly inter-correlated But
whatrsquos the driving variablewhatrsquos the driving variable
whatrsquos the variable which among the many intercorrelated ones drives the transformation from weak and electrostatic
to strong and covalent HB
A Proposal The PApA Proposal The PApKKaa Equalization Principle Equalization Principle
Two very similar proposals come from early thermodynamic or spectroscopic investigations and are both centered on the
matching of the acid-base properties of the HB donor and acceptors moieties what we like too call for the sake of brevity the
PApPApKKaa Equalization Principle Equalization Principle
With reference to any generic DHmiddotmiddotmiddotA bond this principle states that the HB becomes the stronger the smaller is the difference of the donor-acceptor
proton affinities proton affinities PA = PA(DPA = PA(D) ) PA(A) PA(A)or
acidic constants acidic constants ppKKa a = p= pKKAHAH(D(DH) H) p pKKBH+BH+(A(AHH++))
------------------------------------------------------------------------------------------------------------------------- Ault BS and Pimentel GG (1975) J Phys Chem 79 615 Huyskens PL and Zeegers-Huyskens Th (1964) J Chim Phys Phys- Chim Biol
61 81
Our First Steps in the HB FieldOur First Steps in the HB Field As usual we entered the field by chance In 1985 we were studying the ligands
of the benzadiazepine membrane receptor One of these ligands was CGS8216 where we noticed something strange a rather short N-HhellipO bond of 2694 Aring associated with an interleaving β-enaminone hellipO=C-C=C-NHhellip fragment which was almost completely π-delocalized
It was the first indication of a possible correlation between -delocalization and H-bond strength what was called a few years later the
Resonance-Assisted H-Bond (RAHB)Resonance-Assisted H-Bond (RAHB) (Gilli Bellucci Ferretti amp Bertolasi JACS 1989 Bertolasi Gilli Ferretti amp Gilli JACS 1991) Since at the time few -enaminones were known the work started on the analogous class of -enolones (or -diketone enols) which were already known to give strong O-HO bonds through the equally resonant O=C-C=C-OH fragment
The Development of the OThe Development of the OHO RAHBHO RAHB
The OThe OHO RAHBsHO RAHBs
Very interesting Class of Strong HBs Different lengths of the resonant spacer Rn
(n = 1 3 5 7) The HBs formed were all much stronger than normal (non-resonant) OHO bonds withd(OO)INTRA =
239-255 Aringd(OO)INTER =
246-265 Aring
R1-RAHBR5-RAHB
24256 Aring
N
N
O M e
N
N
OM e
M eM e
H
lt 257 gt1 Aring
P
O H
OO
O H
H P
O H
OO
O H
H
R3-RAHB
O OH
237-255 Aring
262-267 Aring
O
O H O
OH
262-270 Aring
O
O
H
O
O H
R7-RAHB
24462 Aring
NOO
OO
M eM e
H
OOH
O
O
H
CARBOXYLIC ACIDS
DIBENZOYLMETHANE ENOLS
CYCLOHEXANEDIONE ENOLS
PHOPHORIC ACID
A Model for RAHB Electrostatic or CovalentA Model for RAHB Electrostatic or Covalent
At first (JACS 1989) we suggested a RAHB Electrostatic Model but it became rapidly evident that an efficient RAHB treatment would require a Covalent Model
All hell broke loose because as we discovered with surprise the concept itself of covalent HB had been banned some twenty years before and substituted by the acritical but more comfortable Simple Electrostatic Paradigm RAHB seriously risked to became a kind of bizarre covalent hypothesis
I must thank George A Jeffrey with his inimitable unbiased and skeptical style if RAHB was not immediately cast aside by the scientific establishment but started to be quoted in important books and reviews during the lsquo90ties
A RAHB Electrostatic ModelA RAHB Electrostatic Model A RAHB Covalent ModelA RAHB Covalent Model
Starting Again The Purely Empirical ApproachStarting Again The Purely Empirical Approach Fortunately we were realistic enough not to try to confute the Electrostatic
Paradigm On the other hand it was perfectly useless because too deeply rooted in the Weltanschaung of so many important and self-confident scientists
I have already given a short critical account of the very nature of these scientific paradigms at the ECM-2000 of Nancy based on the ideas of Thomas S Kuhn (The Structure of Scientific Revolutions The University of Chicago 1962 and 1970)
Anyway to get out of this impasse at the beginning of 1993 we decided to change approach and to restart to investigate the O-HO bond problem from the very beginning by adopting a purely empirical strategy
(i) suspend any previous ideas on the electrostatic or covalent nature of the HB (ii) define the OHmiddotmiddotmiddotO bond as a simple topological structure where a H atom is connected to two or more oxygen atoms(iii) collect all crystal structures having OHmiddotmiddotmiddotO bonds with d(OmiddotmiddotmiddotO) 270 Aring(iv) collect all available IR (O-H) and NMR (H) data of H-bonded protons(v) collect all available HB energy data from thermodynamic measurements in gas phase and non-polar solvents(vi) try to infer a conclusion on the very nature of the OHmiddotmiddotmiddotO bond from the ensemble of the data collected
A Full Classification of Strong HBsA Full Classification of Strong HBs
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs)CHARGE - ASSISTED HBs
PENTACHLOROPHENOL - p-TOLUIDINE
pKa = -070
12
12
N
CH3
O
ClCl
Cl
Cl
Cl
H25062 AringCL 1 (+ndash)CAHB SHB VSHB
Double Charge-Assisted HBDirect Acid-Base PApKa Matching
CL 2 (ndash)CAHB SHB VSHBNegative Charge-Assisted HB
Acid-Base PApKa Matching by Proton Loss R
OOH
R
O O24371 Aring
CARBOXYLIC ACID - CARBOXYLATE
CL 3 (+)CAHB SHB VSHBPositive Charge-Assisted HB
Acid-Base PApKa Matching by Proton Gain
O
HH H
O
HH
24303 Aring
WATER - HYDRONIUM
-BOND POLARIZATION - ASSISTED HBs
237-255 Aring
O OH
ArAr
DIBENZOYLMETHANE ENOLS
CL 4 RAHB SHB VSHB Resonance-Assisted or -Cooperative HB
PApKa Matching by -Conjugated-Bond Polarization
27501 Aring
OO
O
O O
WATER
CL 5 PAHB MHBPolarization-Assisted or -Cooperative HB(Partial) PApKa Matching by -Bond Polarization
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs) The most interesting aspect of a HB classification based on HB strength is that strong HBs belong only to a small number of chemical schemes that we have called Chemical Leitmotifs
The Alchemic Piper plays the Five Magic Tunes that make any Hydrogen Bond stronger The Chemical Leitmotifs
Symmetry and Covalency (1)Symmetry and Covalency (1)The covalent nature of the strong OHmiddotmiddotmiddotO bond was assessed by interpreting the
experimental results in terms of the Coulsonrsquos VB formalismWe cannot measure covalency but can evaluate molecular symmetry the
Coulsonrsquos model being the algorithm able to translate one concept into the other
In fact total symmetry across the HB implies energy equivalence between the two covalent VB forms ie E(ΨCOV1) = E(ΨCOV2) which is just the situation
associated with formation of the covalent HB
E E
NCT
CT
CTNCT
COV2
IONIC
COV1
IONIC
COV1 COV2
NCT
NCT
(a) Electrostatic HB (b) Covalent HB
Symmetry and Covalency (2)Symmetry and Covalency (2)
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 1
(+-)CAHBDouble Charge-Assisted HB
Direct Acid-Base PApKa Matching
R12DH+A12R
The role played by the PApKa equalization in HB strengthening
is self-evident for the (+-)CAHB chemical leitmotif
RDHARrsquo R12DH+A12Rrsquo RDHA+Rrsquo
which collects by definition all strong HBs formed by the acid-base pairs with a pKa matching within say ndash3 divide 3 pKa units
But what about the other leitmotifs Can we prove that
all chemical leitmotifs are simple artificesthat molecules can use to obliterate the normally
very large pKa between HB donor and acceptor atoms
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 2(-)CAHB
Negative Charge-Assisted HBAcid-Base PApKa Matching
by Proton Loss[R-DHA-R]-
Chemical Leitmotif 3(+)CAHB
Positive Charge-Assisted HBAcid-Base PApKa Matching
by Proton Gain[R-DHA-R]+
2II
2III
2IIa
2IIb
2IIIb
2IIIa
2VIa
pKa = pKAH(HO-H)-pKAH(HO-H) = 157 - 157 = 0
pKa = pKBH(H2O-H+)-pKBH(H2O-H
+) = -17 + 17 = 0
pKAH(HO-H) = 157
pKBH(H2O-H+) = -17
H
O H
H
O
H
(ndash)CAHB pKa = 00
VERYSTRONG~ 25-30 kcalmol
(+)CAHB pKa = 00
VERYSTRONG ~ 25-31 kcalmol
pKa = 175
OHB
WEAK ~ 4- 5kcalmol
ndash H+
+ H+
H
O H O
H
H
O H O
H
H
OHO
H
H
O
H
H
H
O
H
H
O
H
H
O
H
H H
O
H
H
H
O
H
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 4RAHB
Resonance-Assisted or -Bond Cooperative HBPApKa Matching by -Conjugated-Bond Polarization
R-D-HA=R R=DH-A-R
pKAH(RO-H) = 1518
pKBH(R2C=O-H+) = -(67)
O OH
O H O
R
R
R
Rn-RAHB pKa = ~ 21-25
WEAK ~ 4- 5kcalmol
EKO O
H
KEOO
H
pKa = 00
STRONG ~ 15-22 kcalmol
2IV
2IVa
2IVb
2VIb
OHB
The HB Empirical RulesThe HB Empirical Rules
The empirical analysis of experimental data joined with homeopathic doses of VB theory leads us to formulate two important HB Empirical Rules which have been called elsewhere ECHBM (Electrostatic-Covalent HB Model Gilli amp Gilli J Mol Struct 2000) and can be summarized as follows
Any given D-HA system may form HBs in a wide range of strengths lengths symmetries and proton locations the two extremes being represented
by the weak long dissymmetric and proton-out-centred HB of electrostatic nature
and by the very strong very short symmetric and proton-centred HB
classifiable as a true 3-center-4-electron covalent bond
The driving variable able to transform strong into weak HBs is dimensionally a free enthalpy corresponding to the difference between the Proton Affinities (PA) or related Acid-Base Dissociation Constants (pKa) of the Donor and Acceptor moieties
These rules have been verified beyond any reasonable doubt for the Conventional HBs of the following classification
Provisional Conclusions and New ControlsProvisional Conclusions and New Controls
We have so far established a sound set of empirical rules which include A full classification of all existing HBs A full classification of all strong HBs (The Chemical Leitmotifs) A plausible correlation between HB strengths and acid-base properties of the interacting molecules (The PApKa Equalization Principle)
To confirm this last point we have undertaken two years ago
a new research program aimed at assessing the Full Validity of the PApKa Equalization Principle
by comparing extended tables of pKa values arranged for chemical classes
withthe corresponding CSD-derived HB geometries
Hundreds of pKa were collected and more than 11000 crystal structures examined
The pThe pKKa Slide Rulea Slide Rule
It is a tool for the graphical evaluation of the difference
pKa = pKAH(DH) - pKBH+(AH+)
HB Acceptors on the left and HB Donors on the right
pKa values given for chemical class
Results expected
ΔpKagtgt0 DHmiddotmiddotmiddotmiddotA weak amp neutral
ΔpKa asymp 0 DmiddotmiddotmiddotHmiddotmiddotmiddotA strong amp
centeredΔpKa ltlt0DmiddotmiddotmiddotmiddotHA+ weak amp charged
pKa ranges of organic compounds
C-H acids -11 ltpKalt 53
Other Donors -1 ltpKalt 40
Acceptors -12 ltpKalt 16
All -15 ltpKalt 53
Water 0 ltpKalt 14
50
-10
0
10
20
30
40
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
ALDEHYDES
ETHERSALCOHOLS
AMIDES
NITRILES
ANILINES
CF3-SO3H
HClO4HI
HBrHCl
H2SO4
HSO4
HNO3
HBF4
H3PO4
H2PO4
HPO42
HF HNO2
HNNN
NH2OHH2CO3
HCO3
H2S
HS-
HCN H3BO3
H2BO3
H4SiO4
H2O2
HO
HSCN
H-H
SULFONICACIDS
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
OXIMES
ALCOHOLS
THIOLES
HB ACCEPTORS (A)pK BH+
HB DONORS (D-H)pK AH
C-H ACIDS pK AH
BE
TT
ER
HB
AC
CE
PT
OR
BE
TT
ER
BA
SE
BE
TT
ER
HB
DO
NO
R
BE
TT
ER
AC
ID
N-OXIDES
AMIDINES
UREA
THIOUREA
BARBITURICURIC ACID
MONO DIPHOSPHINES
TRIPHOSPHINES
TRINITROANILINES
AMINES
ANILINES
MONO DINITROANILINES
AMIDES
CARBOXYLIC ACIDS
HALOGENOANILINES
AZOCOMPS
TRINITROANILINES
PROTONSPONGES
ACIDSESTERS
H2O
H2O
MONODINITROANILINES
KETONES
SULFIDES
HALOGENCARB ACIDS
TRINITROPHENOLS
ENOLS
MONO DINITROPHENOLS
PHENOLSNAPHTHOLS
HALOGENOPHENOLS
HALOGENOALCOHOLS
SULFOXIDES
(NC)5-CYCLO
PENTADIENE
(NC)3CH
(O2N)2=CH2
HCCHNC-CH3
CH3-CO-CH3INDENE
O2N-CH3
(NC)2=CH2
(O2N)3CH
H2C=CH2
C6H6
CH4
CYCLOPENTADIENE
CYCLOPROPENE
Ar3CH
Ar2=CH2
Ar-CH3
NITROCOMPS
SELENOXIDES
AZOLES
AZINESDIAZINES
AMINES
Cl5-PHENOL
CH3-CH3
(CH3)3CH
NH3
NH3
51
53
51
53
Chemical Leitmotifs and PApChemical Leitmotifs and PApKKaa Equalization Rules Equalization Rules RAHB RAHB cannot be treated by pKa equalization methods because π-delocalization
modifies the pKarsquos of the donor and acceptor moieties (+)CAHB is a true proton transfer from an acid (HB donor) to a base (HB acceptor)
RndashDndashHAndashRrsquo Rndash12DH+A12ndashndashRrsquo RndashDHndashA+ndashRrsquoΔpKa = pKAH(RDH) pKBH+(RrsquoA)
()CAHB is a proton sharing between two acids (HB donors)
RndashDndashHDrsquondashRrsquo [RDHDrsquoRrsquo] RDHDrsquoRrsquoΔpKa = pKAH(RDH) pKAH(RDH)
(+)CAHB is a proton sharing between two bases (HB acceptors)
R+AHArsquoRrsquo [RAHArsquoRrsquo]+ RAHArsquo+RrsquoΔpKa = pKBH+(RA) pKBH+(RrsquoArsquo)
Whenever () and (+)CAHBs are both homonuclear (D = Drsquo or A = Arsquo) and
homomolecular (R = Rrsquo) the matching condition ΔpKa= 0 will hold irrespective of the
actual pKarsquos of the two interacting moieties All HBs formed will be strong
Some Famous HBsSome Famous HBs
The NThe NHmiddotmiddotmiddotOOHmiddotmiddotmiddotOOHmiddotmiddotmiddotN System over the Full HmiddotmiddotmiddotN System over the Full ppKKaa Range Range
When evaluated from the pKa slide rule the total pKa range is extremely wide
ndash30 pa 60 So far we have been able to shown that the pKa equalization rule certainly holds in
a restricted interval around zero The problem is now Does this rule hold in the full pKa range
We will try to prove that by a full analysis the N-HmiddotmiddotmiddotOO-HmiddotmiddotmiddotN system
Procedure In a first CSD search functional groups of known pKa value and more frequently
implied in NHmiddotmiddotmiddotOOHmiddotmiddotmiddotN bonds were identified Finally 10 classes of donors and 11 of acceptors were selected and the search restarted for each separate donor-acceptor group Altogether 9078 different bonds were analyzed (4364 NHmiddotmiddotmiddotO 2289 OHmiddotmiddotmiddotN and
2425 OmiddotmiddotmiddotHN+) For each bond the NmiddotmiddotmiddotO distances were evaluated as dNH + dHO to account for the
N-H-O angle and for each group the shortest and average distances [dNmiddotmiddotmiddotO (min)
and dNmiddotmiddotmiddotO (mean)] were registered
These values were compared (see next slide) with the acid-base features of the donors (pKAH range) acceptors (pKBH+ range) and with their combinations
(pKa range)
pKa large amp positive
pKa largeamp negative
Increasing Acidity of the Protonated A H+ Acceptor Increasing Basicity of the A Acceptor
ppKKaa versusversus HB Geometry Correlation - Conclusions HB Geometry Correlation - Conclusions The PApKa Equalization Principle is therefore fully confirmed in its two forms All strong HBs correspond to very small pKa values
pKa values modulate the HB strength over the full pKa range These conclusions are of great practical importance in at least two respects pKa is definitively established as the driving force which controls the HB
strength by modulating the HB covalent contribution It is definitively established that an accurate analysis of structural crystal data
leads to the same conclusions suggested but never proved on a general base by thermodynamic and spectroscopic methods
References Huyskens and Zeegers-Huyskens 1964 Zeegers-Huyskens 1986 1988 Ault and Pimentel 1975 Ratajczak and Sobczyk 1969 Sobczyk et al 1982 Barnes 1983 Kebarle et al 1974-1979 Meot-Ner (Mautner) et al
1984-1988
Towards a General HB TheoryTowards a General HB Theory
The results so far obtained are not a True HB Theory but rather a Set of Empirical Rules (or an Empirical Natural Law) that is a great collection of HB experimental data neatly organized in tables which all together represent a General Taxonomy of the HB Phenomenon exactly as the Carl Linnaeusrsquo classification of plants A scientific theory is something different It is the casting of the empirical natural law into the frame of a theory which is more fundamental down to the reductionistic chain of the scientific disciplines For instance the kinetic gas theory is the casting of the empirical gas laws (the empirical natural law) into Newtonrsquos classical mechanics
How to make a HB TheoryHow to make a HB Theory
HB Properties = FF (HB Driving Variable)where
HB Driving Variable = PApKa and FF = Transition-State Theory
The Transition-State HB TheoryThe Transition-State HB Theory(Gilli et al JACS 2002 2005 Gilli et al J Mol Struct 2006)
Though it has taken us more than 12 years to develop it
the basic idea is very simpleAny DndashHmiddotmiddotmiddotA bond can be considered as a chemical reaction which is
bimolecular in both directions and proceeds via transition-state (TS) formation
AndashB + C AmiddotmiddotmiddotBmiddotmiddotmiddotC A + BndashCDndashHmiddotmiddotmiddotA DmiddotmiddotmiddotHmiddotmiddotmiddotA DmiddotmiddotmiddotHndashA
Changes of nomenclatureReaction Pathway PTPathwayActivation Energy DaggerE PTBarrierReaction Energy Er PApKa Transition State (TS) PTTS
Reaction Coordinate RC=[d(DH)ndashd(AH)] Experimentals Variable-Temperature X-allographyCalculations DFTEmulated PTPathwaysInterpretation Marcus Rate-Equilibrium Theory LefflerHammond Postulate
AcknowledgmentsAcknowledgments I have to thank my direct coworkers without whose help this work could have not been accomplished
Valerio BERTOLASI Paola GILLI
Valeria FERRETTI Loretta PRETTO
and the scientific institutions which made available to us the databases without which this work could not even be started
CCDCCambridge Crystallographic
Data Centrefor the use of the
Cambridge Structural Database
NIST National Institute of Standards and
Technologyfor the use of the
NIST Chemistry WebBook
Another Unsolved Problem The HB PuzzleAnother Unsolved Problem The HB Puzzle
Bond lengths and energies of normal chemical bonds are found to depend on the nature of the interacting atoms
and are weakly perturbed by their external environment
Conversely binding energies (EHB) and DmiddotmiddotmiddotA distances (dDmiddotmiddotmiddotA) of DHmiddotmiddotmiddotA bonds
do not simply depend on the donor (D) and acceptor (A) nature but show very large variations even for the same donor-acceptor couple
This is what we have called for the sake of brevity
the HB Puzzlethe HB PuzzleAn extreme example of this behavior comes from the effects produced on
the OHmiddotmiddotmiddotO bond by the changing acid-base properties of its environment The weak HOHmiddotmiddotmiddotOH2 bond in water [EHB5 kcal mol-1 dOmiddotmiddotmiddotO270-275 Aring]
is switched in acidic or basic medium to the very strong [H2OmiddotmiddotmiddotHmiddotmiddotmiddotOH2]+ or
[HOmiddotmiddotmiddotHmiddotmiddotmiddotOH] bonds with EHB up to 30-31 kcal mol-1 and dOmiddotmiddotmiddotO down to 238-242 Aring
How to Solve the HB Puzzle How to Solve the HB Puzzle the Problem of the Driving Variablethe Problem of the Driving Variable
The Electrostatic Paradigm cannot explain the HB Puzzle
Neither the Standard Model provides a full interpretation of it because while it can explain what covalent and electrostatic HBs are
it cannot suggest which circumstances can produce them
To put the problem in more general terms there are dozens of physicochemical variables commonly measured in connection with the HB (energies geometries IR frequencies NMR chemical shifts NQR couplings and isotopic effects of the HB itself and in addiction a large number of other properties of the interacting molecules) and most if not all appear to be strongly inter-correlated But
whatrsquos the driving variablewhatrsquos the driving variable
whatrsquos the variable which among the many intercorrelated ones drives the transformation from weak and electrostatic
to strong and covalent HB
A Proposal The PApA Proposal The PApKKaa Equalization Principle Equalization Principle
Two very similar proposals come from early thermodynamic or spectroscopic investigations and are both centered on the
matching of the acid-base properties of the HB donor and acceptors moieties what we like too call for the sake of brevity the
PApPApKKaa Equalization Principle Equalization Principle
With reference to any generic DHmiddotmiddotmiddotA bond this principle states that the HB becomes the stronger the smaller is the difference of the donor-acceptor
proton affinities proton affinities PA = PA(DPA = PA(D) ) PA(A) PA(A)or
acidic constants acidic constants ppKKa a = p= pKKAHAH(D(DH) H) p pKKBH+BH+(A(AHH++))
------------------------------------------------------------------------------------------------------------------------- Ault BS and Pimentel GG (1975) J Phys Chem 79 615 Huyskens PL and Zeegers-Huyskens Th (1964) J Chim Phys Phys- Chim Biol
61 81
Our First Steps in the HB FieldOur First Steps in the HB Field As usual we entered the field by chance In 1985 we were studying the ligands
of the benzadiazepine membrane receptor One of these ligands was CGS8216 where we noticed something strange a rather short N-HhellipO bond of 2694 Aring associated with an interleaving β-enaminone hellipO=C-C=C-NHhellip fragment which was almost completely π-delocalized
It was the first indication of a possible correlation between -delocalization and H-bond strength what was called a few years later the
Resonance-Assisted H-Bond (RAHB)Resonance-Assisted H-Bond (RAHB) (Gilli Bellucci Ferretti amp Bertolasi JACS 1989 Bertolasi Gilli Ferretti amp Gilli JACS 1991) Since at the time few -enaminones were known the work started on the analogous class of -enolones (or -diketone enols) which were already known to give strong O-HO bonds through the equally resonant O=C-C=C-OH fragment
The Development of the OThe Development of the OHO RAHBHO RAHB
The OThe OHO RAHBsHO RAHBs
Very interesting Class of Strong HBs Different lengths of the resonant spacer Rn
(n = 1 3 5 7) The HBs formed were all much stronger than normal (non-resonant) OHO bonds withd(OO)INTRA =
239-255 Aringd(OO)INTER =
246-265 Aring
R1-RAHBR5-RAHB
24256 Aring
N
N
O M e
N
N
OM e
M eM e
H
lt 257 gt1 Aring
P
O H
OO
O H
H P
O H
OO
O H
H
R3-RAHB
O OH
237-255 Aring
262-267 Aring
O
O H O
OH
262-270 Aring
O
O
H
O
O H
R7-RAHB
24462 Aring
NOO
OO
M eM e
H
OOH
O
O
H
CARBOXYLIC ACIDS
DIBENZOYLMETHANE ENOLS
CYCLOHEXANEDIONE ENOLS
PHOPHORIC ACID
A Model for RAHB Electrostatic or CovalentA Model for RAHB Electrostatic or Covalent
At first (JACS 1989) we suggested a RAHB Electrostatic Model but it became rapidly evident that an efficient RAHB treatment would require a Covalent Model
All hell broke loose because as we discovered with surprise the concept itself of covalent HB had been banned some twenty years before and substituted by the acritical but more comfortable Simple Electrostatic Paradigm RAHB seriously risked to became a kind of bizarre covalent hypothesis
I must thank George A Jeffrey with his inimitable unbiased and skeptical style if RAHB was not immediately cast aside by the scientific establishment but started to be quoted in important books and reviews during the lsquo90ties
A RAHB Electrostatic ModelA RAHB Electrostatic Model A RAHB Covalent ModelA RAHB Covalent Model
Starting Again The Purely Empirical ApproachStarting Again The Purely Empirical Approach Fortunately we were realistic enough not to try to confute the Electrostatic
Paradigm On the other hand it was perfectly useless because too deeply rooted in the Weltanschaung of so many important and self-confident scientists
I have already given a short critical account of the very nature of these scientific paradigms at the ECM-2000 of Nancy based on the ideas of Thomas S Kuhn (The Structure of Scientific Revolutions The University of Chicago 1962 and 1970)
Anyway to get out of this impasse at the beginning of 1993 we decided to change approach and to restart to investigate the O-HO bond problem from the very beginning by adopting a purely empirical strategy
(i) suspend any previous ideas on the electrostatic or covalent nature of the HB (ii) define the OHmiddotmiddotmiddotO bond as a simple topological structure where a H atom is connected to two or more oxygen atoms(iii) collect all crystal structures having OHmiddotmiddotmiddotO bonds with d(OmiddotmiddotmiddotO) 270 Aring(iv) collect all available IR (O-H) and NMR (H) data of H-bonded protons(v) collect all available HB energy data from thermodynamic measurements in gas phase and non-polar solvents(vi) try to infer a conclusion on the very nature of the OHmiddotmiddotmiddotO bond from the ensemble of the data collected
A Full Classification of Strong HBsA Full Classification of Strong HBs
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs)CHARGE - ASSISTED HBs
PENTACHLOROPHENOL - p-TOLUIDINE
pKa = -070
12
12
N
CH3
O
ClCl
Cl
Cl
Cl
H25062 AringCL 1 (+ndash)CAHB SHB VSHB
Double Charge-Assisted HBDirect Acid-Base PApKa Matching
CL 2 (ndash)CAHB SHB VSHBNegative Charge-Assisted HB
Acid-Base PApKa Matching by Proton Loss R
OOH
R
O O24371 Aring
CARBOXYLIC ACID - CARBOXYLATE
CL 3 (+)CAHB SHB VSHBPositive Charge-Assisted HB
Acid-Base PApKa Matching by Proton Gain
O
HH H
O
HH
24303 Aring
WATER - HYDRONIUM
-BOND POLARIZATION - ASSISTED HBs
237-255 Aring
O OH
ArAr
DIBENZOYLMETHANE ENOLS
CL 4 RAHB SHB VSHB Resonance-Assisted or -Cooperative HB
PApKa Matching by -Conjugated-Bond Polarization
27501 Aring
OO
O
O O
WATER
CL 5 PAHB MHBPolarization-Assisted or -Cooperative HB(Partial) PApKa Matching by -Bond Polarization
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs) The most interesting aspect of a HB classification based on HB strength is that strong HBs belong only to a small number of chemical schemes that we have called Chemical Leitmotifs
The Alchemic Piper plays the Five Magic Tunes that make any Hydrogen Bond stronger The Chemical Leitmotifs
Symmetry and Covalency (1)Symmetry and Covalency (1)The covalent nature of the strong OHmiddotmiddotmiddotO bond was assessed by interpreting the
experimental results in terms of the Coulsonrsquos VB formalismWe cannot measure covalency but can evaluate molecular symmetry the
Coulsonrsquos model being the algorithm able to translate one concept into the other
In fact total symmetry across the HB implies energy equivalence between the two covalent VB forms ie E(ΨCOV1) = E(ΨCOV2) which is just the situation
associated with formation of the covalent HB
E E
NCT
CT
CTNCT
COV2
IONIC
COV1
IONIC
COV1 COV2
NCT
NCT
(a) Electrostatic HB (b) Covalent HB
Symmetry and Covalency (2)Symmetry and Covalency (2)
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 1
(+-)CAHBDouble Charge-Assisted HB
Direct Acid-Base PApKa Matching
R12DH+A12R
The role played by the PApKa equalization in HB strengthening
is self-evident for the (+-)CAHB chemical leitmotif
RDHARrsquo R12DH+A12Rrsquo RDHA+Rrsquo
which collects by definition all strong HBs formed by the acid-base pairs with a pKa matching within say ndash3 divide 3 pKa units
But what about the other leitmotifs Can we prove that
all chemical leitmotifs are simple artificesthat molecules can use to obliterate the normally
very large pKa between HB donor and acceptor atoms
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 2(-)CAHB
Negative Charge-Assisted HBAcid-Base PApKa Matching
by Proton Loss[R-DHA-R]-
Chemical Leitmotif 3(+)CAHB
Positive Charge-Assisted HBAcid-Base PApKa Matching
by Proton Gain[R-DHA-R]+
2II
2III
2IIa
2IIb
2IIIb
2IIIa
2VIa
pKa = pKAH(HO-H)-pKAH(HO-H) = 157 - 157 = 0
pKa = pKBH(H2O-H+)-pKBH(H2O-H
+) = -17 + 17 = 0
pKAH(HO-H) = 157
pKBH(H2O-H+) = -17
H
O H
H
O
H
(ndash)CAHB pKa = 00
VERYSTRONG~ 25-30 kcalmol
(+)CAHB pKa = 00
VERYSTRONG ~ 25-31 kcalmol
pKa = 175
OHB
WEAK ~ 4- 5kcalmol
ndash H+
+ H+
H
O H O
H
H
O H O
H
H
OHO
H
H
O
H
H
H
O
H
H
O
H
H
O
H
H H
O
H
H
H
O
H
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 4RAHB
Resonance-Assisted or -Bond Cooperative HBPApKa Matching by -Conjugated-Bond Polarization
R-D-HA=R R=DH-A-R
pKAH(RO-H) = 1518
pKBH(R2C=O-H+) = -(67)
O OH
O H O
R
R
R
Rn-RAHB pKa = ~ 21-25
WEAK ~ 4- 5kcalmol
EKO O
H
KEOO
H
pKa = 00
STRONG ~ 15-22 kcalmol
2IV
2IVa
2IVb
2VIb
OHB
The HB Empirical RulesThe HB Empirical Rules
The empirical analysis of experimental data joined with homeopathic doses of VB theory leads us to formulate two important HB Empirical Rules which have been called elsewhere ECHBM (Electrostatic-Covalent HB Model Gilli amp Gilli J Mol Struct 2000) and can be summarized as follows
Any given D-HA system may form HBs in a wide range of strengths lengths symmetries and proton locations the two extremes being represented
by the weak long dissymmetric and proton-out-centred HB of electrostatic nature
and by the very strong very short symmetric and proton-centred HB
classifiable as a true 3-center-4-electron covalent bond
The driving variable able to transform strong into weak HBs is dimensionally a free enthalpy corresponding to the difference between the Proton Affinities (PA) or related Acid-Base Dissociation Constants (pKa) of the Donor and Acceptor moieties
These rules have been verified beyond any reasonable doubt for the Conventional HBs of the following classification
Provisional Conclusions and New ControlsProvisional Conclusions and New Controls
We have so far established a sound set of empirical rules which include A full classification of all existing HBs A full classification of all strong HBs (The Chemical Leitmotifs) A plausible correlation between HB strengths and acid-base properties of the interacting molecules (The PApKa Equalization Principle)
To confirm this last point we have undertaken two years ago
a new research program aimed at assessing the Full Validity of the PApKa Equalization Principle
by comparing extended tables of pKa values arranged for chemical classes
withthe corresponding CSD-derived HB geometries
Hundreds of pKa were collected and more than 11000 crystal structures examined
The pThe pKKa Slide Rulea Slide Rule
It is a tool for the graphical evaluation of the difference
pKa = pKAH(DH) - pKBH+(AH+)
HB Acceptors on the left and HB Donors on the right
pKa values given for chemical class
Results expected
ΔpKagtgt0 DHmiddotmiddotmiddotmiddotA weak amp neutral
ΔpKa asymp 0 DmiddotmiddotmiddotHmiddotmiddotmiddotA strong amp
centeredΔpKa ltlt0DmiddotmiddotmiddotmiddotHA+ weak amp charged
pKa ranges of organic compounds
C-H acids -11 ltpKalt 53
Other Donors -1 ltpKalt 40
Acceptors -12 ltpKalt 16
All -15 ltpKalt 53
Water 0 ltpKalt 14
50
-10
0
10
20
30
40
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
ALDEHYDES
ETHERSALCOHOLS
AMIDES
NITRILES
ANILINES
CF3-SO3H
HClO4HI
HBrHCl
H2SO4
HSO4
HNO3
HBF4
H3PO4
H2PO4
HPO42
HF HNO2
HNNN
NH2OHH2CO3
HCO3
H2S
HS-
HCN H3BO3
H2BO3
H4SiO4
H2O2
HO
HSCN
H-H
SULFONICACIDS
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
OXIMES
ALCOHOLS
THIOLES
HB ACCEPTORS (A)pK BH+
HB DONORS (D-H)pK AH
C-H ACIDS pK AH
BE
TT
ER
HB
AC
CE
PT
OR
BE
TT
ER
BA
SE
BE
TT
ER
HB
DO
NO
R
BE
TT
ER
AC
ID
N-OXIDES
AMIDINES
UREA
THIOUREA
BARBITURICURIC ACID
MONO DIPHOSPHINES
TRIPHOSPHINES
TRINITROANILINES
AMINES
ANILINES
MONO DINITROANILINES
AMIDES
CARBOXYLIC ACIDS
HALOGENOANILINES
AZOCOMPS
TRINITROANILINES
PROTONSPONGES
ACIDSESTERS
H2O
H2O
MONODINITROANILINES
KETONES
SULFIDES
HALOGENCARB ACIDS
TRINITROPHENOLS
ENOLS
MONO DINITROPHENOLS
PHENOLSNAPHTHOLS
HALOGENOPHENOLS
HALOGENOALCOHOLS
SULFOXIDES
(NC)5-CYCLO
PENTADIENE
(NC)3CH
(O2N)2=CH2
HCCHNC-CH3
CH3-CO-CH3INDENE
O2N-CH3
(NC)2=CH2
(O2N)3CH
H2C=CH2
C6H6
CH4
CYCLOPENTADIENE
CYCLOPROPENE
Ar3CH
Ar2=CH2
Ar-CH3
NITROCOMPS
SELENOXIDES
AZOLES
AZINESDIAZINES
AMINES
Cl5-PHENOL
CH3-CH3
(CH3)3CH
NH3
NH3
51
53
51
53
Chemical Leitmotifs and PApChemical Leitmotifs and PApKKaa Equalization Rules Equalization Rules RAHB RAHB cannot be treated by pKa equalization methods because π-delocalization
modifies the pKarsquos of the donor and acceptor moieties (+)CAHB is a true proton transfer from an acid (HB donor) to a base (HB acceptor)
RndashDndashHAndashRrsquo Rndash12DH+A12ndashndashRrsquo RndashDHndashA+ndashRrsquoΔpKa = pKAH(RDH) pKBH+(RrsquoA)
()CAHB is a proton sharing between two acids (HB donors)
RndashDndashHDrsquondashRrsquo [RDHDrsquoRrsquo] RDHDrsquoRrsquoΔpKa = pKAH(RDH) pKAH(RDH)
(+)CAHB is a proton sharing between two bases (HB acceptors)
R+AHArsquoRrsquo [RAHArsquoRrsquo]+ RAHArsquo+RrsquoΔpKa = pKBH+(RA) pKBH+(RrsquoArsquo)
Whenever () and (+)CAHBs are both homonuclear (D = Drsquo or A = Arsquo) and
homomolecular (R = Rrsquo) the matching condition ΔpKa= 0 will hold irrespective of the
actual pKarsquos of the two interacting moieties All HBs formed will be strong
Some Famous HBsSome Famous HBs
The NThe NHmiddotmiddotmiddotOOHmiddotmiddotmiddotOOHmiddotmiddotmiddotN System over the Full HmiddotmiddotmiddotN System over the Full ppKKaa Range Range
When evaluated from the pKa slide rule the total pKa range is extremely wide
ndash30 pa 60 So far we have been able to shown that the pKa equalization rule certainly holds in
a restricted interval around zero The problem is now Does this rule hold in the full pKa range
We will try to prove that by a full analysis the N-HmiddotmiddotmiddotOO-HmiddotmiddotmiddotN system
Procedure In a first CSD search functional groups of known pKa value and more frequently
implied in NHmiddotmiddotmiddotOOHmiddotmiddotmiddotN bonds were identified Finally 10 classes of donors and 11 of acceptors were selected and the search restarted for each separate donor-acceptor group Altogether 9078 different bonds were analyzed (4364 NHmiddotmiddotmiddotO 2289 OHmiddotmiddotmiddotN and
2425 OmiddotmiddotmiddotHN+) For each bond the NmiddotmiddotmiddotO distances were evaluated as dNH + dHO to account for the
N-H-O angle and for each group the shortest and average distances [dNmiddotmiddotmiddotO (min)
and dNmiddotmiddotmiddotO (mean)] were registered
These values were compared (see next slide) with the acid-base features of the donors (pKAH range) acceptors (pKBH+ range) and with their combinations
(pKa range)
pKa large amp positive
pKa largeamp negative
Increasing Acidity of the Protonated A H+ Acceptor Increasing Basicity of the A Acceptor
ppKKaa versusversus HB Geometry Correlation - Conclusions HB Geometry Correlation - Conclusions The PApKa Equalization Principle is therefore fully confirmed in its two forms All strong HBs correspond to very small pKa values
pKa values modulate the HB strength over the full pKa range These conclusions are of great practical importance in at least two respects pKa is definitively established as the driving force which controls the HB
strength by modulating the HB covalent contribution It is definitively established that an accurate analysis of structural crystal data
leads to the same conclusions suggested but never proved on a general base by thermodynamic and spectroscopic methods
References Huyskens and Zeegers-Huyskens 1964 Zeegers-Huyskens 1986 1988 Ault and Pimentel 1975 Ratajczak and Sobczyk 1969 Sobczyk et al 1982 Barnes 1983 Kebarle et al 1974-1979 Meot-Ner (Mautner) et al
1984-1988
Towards a General HB TheoryTowards a General HB Theory
The results so far obtained are not a True HB Theory but rather a Set of Empirical Rules (or an Empirical Natural Law) that is a great collection of HB experimental data neatly organized in tables which all together represent a General Taxonomy of the HB Phenomenon exactly as the Carl Linnaeusrsquo classification of plants A scientific theory is something different It is the casting of the empirical natural law into the frame of a theory which is more fundamental down to the reductionistic chain of the scientific disciplines For instance the kinetic gas theory is the casting of the empirical gas laws (the empirical natural law) into Newtonrsquos classical mechanics
How to make a HB TheoryHow to make a HB Theory
HB Properties = FF (HB Driving Variable)where
HB Driving Variable = PApKa and FF = Transition-State Theory
The Transition-State HB TheoryThe Transition-State HB Theory(Gilli et al JACS 2002 2005 Gilli et al J Mol Struct 2006)
Though it has taken us more than 12 years to develop it
the basic idea is very simpleAny DndashHmiddotmiddotmiddotA bond can be considered as a chemical reaction which is
bimolecular in both directions and proceeds via transition-state (TS) formation
AndashB + C AmiddotmiddotmiddotBmiddotmiddotmiddotC A + BndashCDndashHmiddotmiddotmiddotA DmiddotmiddotmiddotHmiddotmiddotmiddotA DmiddotmiddotmiddotHndashA
Changes of nomenclatureReaction Pathway PTPathwayActivation Energy DaggerE PTBarrierReaction Energy Er PApKa Transition State (TS) PTTS
Reaction Coordinate RC=[d(DH)ndashd(AH)] Experimentals Variable-Temperature X-allographyCalculations DFTEmulated PTPathwaysInterpretation Marcus Rate-Equilibrium Theory LefflerHammond Postulate
AcknowledgmentsAcknowledgments I have to thank my direct coworkers without whose help this work could have not been accomplished
Valerio BERTOLASI Paola GILLI
Valeria FERRETTI Loretta PRETTO
and the scientific institutions which made available to us the databases without which this work could not even be started
CCDCCambridge Crystallographic
Data Centrefor the use of the
Cambridge Structural Database
NIST National Institute of Standards and
Technologyfor the use of the
NIST Chemistry WebBook
How to Solve the HB Puzzle How to Solve the HB Puzzle the Problem of the Driving Variablethe Problem of the Driving Variable
The Electrostatic Paradigm cannot explain the HB Puzzle
Neither the Standard Model provides a full interpretation of it because while it can explain what covalent and electrostatic HBs are
it cannot suggest which circumstances can produce them
To put the problem in more general terms there are dozens of physicochemical variables commonly measured in connection with the HB (energies geometries IR frequencies NMR chemical shifts NQR couplings and isotopic effects of the HB itself and in addiction a large number of other properties of the interacting molecules) and most if not all appear to be strongly inter-correlated But
whatrsquos the driving variablewhatrsquos the driving variable
whatrsquos the variable which among the many intercorrelated ones drives the transformation from weak and electrostatic
to strong and covalent HB
A Proposal The PApA Proposal The PApKKaa Equalization Principle Equalization Principle
Two very similar proposals come from early thermodynamic or spectroscopic investigations and are both centered on the
matching of the acid-base properties of the HB donor and acceptors moieties what we like too call for the sake of brevity the
PApPApKKaa Equalization Principle Equalization Principle
With reference to any generic DHmiddotmiddotmiddotA bond this principle states that the HB becomes the stronger the smaller is the difference of the donor-acceptor
proton affinities proton affinities PA = PA(DPA = PA(D) ) PA(A) PA(A)or
acidic constants acidic constants ppKKa a = p= pKKAHAH(D(DH) H) p pKKBH+BH+(A(AHH++))
------------------------------------------------------------------------------------------------------------------------- Ault BS and Pimentel GG (1975) J Phys Chem 79 615 Huyskens PL and Zeegers-Huyskens Th (1964) J Chim Phys Phys- Chim Biol
61 81
Our First Steps in the HB FieldOur First Steps in the HB Field As usual we entered the field by chance In 1985 we were studying the ligands
of the benzadiazepine membrane receptor One of these ligands was CGS8216 where we noticed something strange a rather short N-HhellipO bond of 2694 Aring associated with an interleaving β-enaminone hellipO=C-C=C-NHhellip fragment which was almost completely π-delocalized
It was the first indication of a possible correlation between -delocalization and H-bond strength what was called a few years later the
Resonance-Assisted H-Bond (RAHB)Resonance-Assisted H-Bond (RAHB) (Gilli Bellucci Ferretti amp Bertolasi JACS 1989 Bertolasi Gilli Ferretti amp Gilli JACS 1991) Since at the time few -enaminones were known the work started on the analogous class of -enolones (or -diketone enols) which were already known to give strong O-HO bonds through the equally resonant O=C-C=C-OH fragment
The Development of the OThe Development of the OHO RAHBHO RAHB
The OThe OHO RAHBsHO RAHBs
Very interesting Class of Strong HBs Different lengths of the resonant spacer Rn
(n = 1 3 5 7) The HBs formed were all much stronger than normal (non-resonant) OHO bonds withd(OO)INTRA =
239-255 Aringd(OO)INTER =
246-265 Aring
R1-RAHBR5-RAHB
24256 Aring
N
N
O M e
N
N
OM e
M eM e
H
lt 257 gt1 Aring
P
O H
OO
O H
H P
O H
OO
O H
H
R3-RAHB
O OH
237-255 Aring
262-267 Aring
O
O H O
OH
262-270 Aring
O
O
H
O
O H
R7-RAHB
24462 Aring
NOO
OO
M eM e
H
OOH
O
O
H
CARBOXYLIC ACIDS
DIBENZOYLMETHANE ENOLS
CYCLOHEXANEDIONE ENOLS
PHOPHORIC ACID
A Model for RAHB Electrostatic or CovalentA Model for RAHB Electrostatic or Covalent
At first (JACS 1989) we suggested a RAHB Electrostatic Model but it became rapidly evident that an efficient RAHB treatment would require a Covalent Model
All hell broke loose because as we discovered with surprise the concept itself of covalent HB had been banned some twenty years before and substituted by the acritical but more comfortable Simple Electrostatic Paradigm RAHB seriously risked to became a kind of bizarre covalent hypothesis
I must thank George A Jeffrey with his inimitable unbiased and skeptical style if RAHB was not immediately cast aside by the scientific establishment but started to be quoted in important books and reviews during the lsquo90ties
A RAHB Electrostatic ModelA RAHB Electrostatic Model A RAHB Covalent ModelA RAHB Covalent Model
Starting Again The Purely Empirical ApproachStarting Again The Purely Empirical Approach Fortunately we were realistic enough not to try to confute the Electrostatic
Paradigm On the other hand it was perfectly useless because too deeply rooted in the Weltanschaung of so many important and self-confident scientists
I have already given a short critical account of the very nature of these scientific paradigms at the ECM-2000 of Nancy based on the ideas of Thomas S Kuhn (The Structure of Scientific Revolutions The University of Chicago 1962 and 1970)
Anyway to get out of this impasse at the beginning of 1993 we decided to change approach and to restart to investigate the O-HO bond problem from the very beginning by adopting a purely empirical strategy
(i) suspend any previous ideas on the electrostatic or covalent nature of the HB (ii) define the OHmiddotmiddotmiddotO bond as a simple topological structure where a H atom is connected to two or more oxygen atoms(iii) collect all crystal structures having OHmiddotmiddotmiddotO bonds with d(OmiddotmiddotmiddotO) 270 Aring(iv) collect all available IR (O-H) and NMR (H) data of H-bonded protons(v) collect all available HB energy data from thermodynamic measurements in gas phase and non-polar solvents(vi) try to infer a conclusion on the very nature of the OHmiddotmiddotmiddotO bond from the ensemble of the data collected
A Full Classification of Strong HBsA Full Classification of Strong HBs
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs)CHARGE - ASSISTED HBs
PENTACHLOROPHENOL - p-TOLUIDINE
pKa = -070
12
12
N
CH3
O
ClCl
Cl
Cl
Cl
H25062 AringCL 1 (+ndash)CAHB SHB VSHB
Double Charge-Assisted HBDirect Acid-Base PApKa Matching
CL 2 (ndash)CAHB SHB VSHBNegative Charge-Assisted HB
Acid-Base PApKa Matching by Proton Loss R
OOH
R
O O24371 Aring
CARBOXYLIC ACID - CARBOXYLATE
CL 3 (+)CAHB SHB VSHBPositive Charge-Assisted HB
Acid-Base PApKa Matching by Proton Gain
O
HH H
O
HH
24303 Aring
WATER - HYDRONIUM
-BOND POLARIZATION - ASSISTED HBs
237-255 Aring
O OH
ArAr
DIBENZOYLMETHANE ENOLS
CL 4 RAHB SHB VSHB Resonance-Assisted or -Cooperative HB
PApKa Matching by -Conjugated-Bond Polarization
27501 Aring
OO
O
O O
WATER
CL 5 PAHB MHBPolarization-Assisted or -Cooperative HB(Partial) PApKa Matching by -Bond Polarization
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs) The most interesting aspect of a HB classification based on HB strength is that strong HBs belong only to a small number of chemical schemes that we have called Chemical Leitmotifs
The Alchemic Piper plays the Five Magic Tunes that make any Hydrogen Bond stronger The Chemical Leitmotifs
Symmetry and Covalency (1)Symmetry and Covalency (1)The covalent nature of the strong OHmiddotmiddotmiddotO bond was assessed by interpreting the
experimental results in terms of the Coulsonrsquos VB formalismWe cannot measure covalency but can evaluate molecular symmetry the
Coulsonrsquos model being the algorithm able to translate one concept into the other
In fact total symmetry across the HB implies energy equivalence between the two covalent VB forms ie E(ΨCOV1) = E(ΨCOV2) which is just the situation
associated with formation of the covalent HB
E E
NCT
CT
CTNCT
COV2
IONIC
COV1
IONIC
COV1 COV2
NCT
NCT
(a) Electrostatic HB (b) Covalent HB
Symmetry and Covalency (2)Symmetry and Covalency (2)
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 1
(+-)CAHBDouble Charge-Assisted HB
Direct Acid-Base PApKa Matching
R12DH+A12R
The role played by the PApKa equalization in HB strengthening
is self-evident for the (+-)CAHB chemical leitmotif
RDHARrsquo R12DH+A12Rrsquo RDHA+Rrsquo
which collects by definition all strong HBs formed by the acid-base pairs with a pKa matching within say ndash3 divide 3 pKa units
But what about the other leitmotifs Can we prove that
all chemical leitmotifs are simple artificesthat molecules can use to obliterate the normally
very large pKa between HB donor and acceptor atoms
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 2(-)CAHB
Negative Charge-Assisted HBAcid-Base PApKa Matching
by Proton Loss[R-DHA-R]-
Chemical Leitmotif 3(+)CAHB
Positive Charge-Assisted HBAcid-Base PApKa Matching
by Proton Gain[R-DHA-R]+
2II
2III
2IIa
2IIb
2IIIb
2IIIa
2VIa
pKa = pKAH(HO-H)-pKAH(HO-H) = 157 - 157 = 0
pKa = pKBH(H2O-H+)-pKBH(H2O-H
+) = -17 + 17 = 0
pKAH(HO-H) = 157
pKBH(H2O-H+) = -17
H
O H
H
O
H
(ndash)CAHB pKa = 00
VERYSTRONG~ 25-30 kcalmol
(+)CAHB pKa = 00
VERYSTRONG ~ 25-31 kcalmol
pKa = 175
OHB
WEAK ~ 4- 5kcalmol
ndash H+
+ H+
H
O H O
H
H
O H O
H
H
OHO
H
H
O
H
H
H
O
H
H
O
H
H
O
H
H H
O
H
H
H
O
H
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 4RAHB
Resonance-Assisted or -Bond Cooperative HBPApKa Matching by -Conjugated-Bond Polarization
R-D-HA=R R=DH-A-R
pKAH(RO-H) = 1518
pKBH(R2C=O-H+) = -(67)
O OH
O H O
R
R
R
Rn-RAHB pKa = ~ 21-25
WEAK ~ 4- 5kcalmol
EKO O
H
KEOO
H
pKa = 00
STRONG ~ 15-22 kcalmol
2IV
2IVa
2IVb
2VIb
OHB
The HB Empirical RulesThe HB Empirical Rules
The empirical analysis of experimental data joined with homeopathic doses of VB theory leads us to formulate two important HB Empirical Rules which have been called elsewhere ECHBM (Electrostatic-Covalent HB Model Gilli amp Gilli J Mol Struct 2000) and can be summarized as follows
Any given D-HA system may form HBs in a wide range of strengths lengths symmetries and proton locations the two extremes being represented
by the weak long dissymmetric and proton-out-centred HB of electrostatic nature
and by the very strong very short symmetric and proton-centred HB
classifiable as a true 3-center-4-electron covalent bond
The driving variable able to transform strong into weak HBs is dimensionally a free enthalpy corresponding to the difference between the Proton Affinities (PA) or related Acid-Base Dissociation Constants (pKa) of the Donor and Acceptor moieties
These rules have been verified beyond any reasonable doubt for the Conventional HBs of the following classification
Provisional Conclusions and New ControlsProvisional Conclusions and New Controls
We have so far established a sound set of empirical rules which include A full classification of all existing HBs A full classification of all strong HBs (The Chemical Leitmotifs) A plausible correlation between HB strengths and acid-base properties of the interacting molecules (The PApKa Equalization Principle)
To confirm this last point we have undertaken two years ago
a new research program aimed at assessing the Full Validity of the PApKa Equalization Principle
by comparing extended tables of pKa values arranged for chemical classes
withthe corresponding CSD-derived HB geometries
Hundreds of pKa were collected and more than 11000 crystal structures examined
The pThe pKKa Slide Rulea Slide Rule
It is a tool for the graphical evaluation of the difference
pKa = pKAH(DH) - pKBH+(AH+)
HB Acceptors on the left and HB Donors on the right
pKa values given for chemical class
Results expected
ΔpKagtgt0 DHmiddotmiddotmiddotmiddotA weak amp neutral
ΔpKa asymp 0 DmiddotmiddotmiddotHmiddotmiddotmiddotA strong amp
centeredΔpKa ltlt0DmiddotmiddotmiddotmiddotHA+ weak amp charged
pKa ranges of organic compounds
C-H acids -11 ltpKalt 53
Other Donors -1 ltpKalt 40
Acceptors -12 ltpKalt 16
All -15 ltpKalt 53
Water 0 ltpKalt 14
50
-10
0
10
20
30
40
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
ALDEHYDES
ETHERSALCOHOLS
AMIDES
NITRILES
ANILINES
CF3-SO3H
HClO4HI
HBrHCl
H2SO4
HSO4
HNO3
HBF4
H3PO4
H2PO4
HPO42
HF HNO2
HNNN
NH2OHH2CO3
HCO3
H2S
HS-
HCN H3BO3
H2BO3
H4SiO4
H2O2
HO
HSCN
H-H
SULFONICACIDS
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
OXIMES
ALCOHOLS
THIOLES
HB ACCEPTORS (A)pK BH+
HB DONORS (D-H)pK AH
C-H ACIDS pK AH
BE
TT
ER
HB
AC
CE
PT
OR
BE
TT
ER
BA
SE
BE
TT
ER
HB
DO
NO
R
BE
TT
ER
AC
ID
N-OXIDES
AMIDINES
UREA
THIOUREA
BARBITURICURIC ACID
MONO DIPHOSPHINES
TRIPHOSPHINES
TRINITROANILINES
AMINES
ANILINES
MONO DINITROANILINES
AMIDES
CARBOXYLIC ACIDS
HALOGENOANILINES
AZOCOMPS
TRINITROANILINES
PROTONSPONGES
ACIDSESTERS
H2O
H2O
MONODINITROANILINES
KETONES
SULFIDES
HALOGENCARB ACIDS
TRINITROPHENOLS
ENOLS
MONO DINITROPHENOLS
PHENOLSNAPHTHOLS
HALOGENOPHENOLS
HALOGENOALCOHOLS
SULFOXIDES
(NC)5-CYCLO
PENTADIENE
(NC)3CH
(O2N)2=CH2
HCCHNC-CH3
CH3-CO-CH3INDENE
O2N-CH3
(NC)2=CH2
(O2N)3CH
H2C=CH2
C6H6
CH4
CYCLOPENTADIENE
CYCLOPROPENE
Ar3CH
Ar2=CH2
Ar-CH3
NITROCOMPS
SELENOXIDES
AZOLES
AZINESDIAZINES
AMINES
Cl5-PHENOL
CH3-CH3
(CH3)3CH
NH3
NH3
51
53
51
53
Chemical Leitmotifs and PApChemical Leitmotifs and PApKKaa Equalization Rules Equalization Rules RAHB RAHB cannot be treated by pKa equalization methods because π-delocalization
modifies the pKarsquos of the donor and acceptor moieties (+)CAHB is a true proton transfer from an acid (HB donor) to a base (HB acceptor)
RndashDndashHAndashRrsquo Rndash12DH+A12ndashndashRrsquo RndashDHndashA+ndashRrsquoΔpKa = pKAH(RDH) pKBH+(RrsquoA)
()CAHB is a proton sharing between two acids (HB donors)
RndashDndashHDrsquondashRrsquo [RDHDrsquoRrsquo] RDHDrsquoRrsquoΔpKa = pKAH(RDH) pKAH(RDH)
(+)CAHB is a proton sharing between two bases (HB acceptors)
R+AHArsquoRrsquo [RAHArsquoRrsquo]+ RAHArsquo+RrsquoΔpKa = pKBH+(RA) pKBH+(RrsquoArsquo)
Whenever () and (+)CAHBs are both homonuclear (D = Drsquo or A = Arsquo) and
homomolecular (R = Rrsquo) the matching condition ΔpKa= 0 will hold irrespective of the
actual pKarsquos of the two interacting moieties All HBs formed will be strong
Some Famous HBsSome Famous HBs
The NThe NHmiddotmiddotmiddotOOHmiddotmiddotmiddotOOHmiddotmiddotmiddotN System over the Full HmiddotmiddotmiddotN System over the Full ppKKaa Range Range
When evaluated from the pKa slide rule the total pKa range is extremely wide
ndash30 pa 60 So far we have been able to shown that the pKa equalization rule certainly holds in
a restricted interval around zero The problem is now Does this rule hold in the full pKa range
We will try to prove that by a full analysis the N-HmiddotmiddotmiddotOO-HmiddotmiddotmiddotN system
Procedure In a first CSD search functional groups of known pKa value and more frequently
implied in NHmiddotmiddotmiddotOOHmiddotmiddotmiddotN bonds were identified Finally 10 classes of donors and 11 of acceptors were selected and the search restarted for each separate donor-acceptor group Altogether 9078 different bonds were analyzed (4364 NHmiddotmiddotmiddotO 2289 OHmiddotmiddotmiddotN and
2425 OmiddotmiddotmiddotHN+) For each bond the NmiddotmiddotmiddotO distances were evaluated as dNH + dHO to account for the
N-H-O angle and for each group the shortest and average distances [dNmiddotmiddotmiddotO (min)
and dNmiddotmiddotmiddotO (mean)] were registered
These values were compared (see next slide) with the acid-base features of the donors (pKAH range) acceptors (pKBH+ range) and with their combinations
(pKa range)
pKa large amp positive
pKa largeamp negative
Increasing Acidity of the Protonated A H+ Acceptor Increasing Basicity of the A Acceptor
ppKKaa versusversus HB Geometry Correlation - Conclusions HB Geometry Correlation - Conclusions The PApKa Equalization Principle is therefore fully confirmed in its two forms All strong HBs correspond to very small pKa values
pKa values modulate the HB strength over the full pKa range These conclusions are of great practical importance in at least two respects pKa is definitively established as the driving force which controls the HB
strength by modulating the HB covalent contribution It is definitively established that an accurate analysis of structural crystal data
leads to the same conclusions suggested but never proved on a general base by thermodynamic and spectroscopic methods
References Huyskens and Zeegers-Huyskens 1964 Zeegers-Huyskens 1986 1988 Ault and Pimentel 1975 Ratajczak and Sobczyk 1969 Sobczyk et al 1982 Barnes 1983 Kebarle et al 1974-1979 Meot-Ner (Mautner) et al
1984-1988
Towards a General HB TheoryTowards a General HB Theory
The results so far obtained are not a True HB Theory but rather a Set of Empirical Rules (or an Empirical Natural Law) that is a great collection of HB experimental data neatly organized in tables which all together represent a General Taxonomy of the HB Phenomenon exactly as the Carl Linnaeusrsquo classification of plants A scientific theory is something different It is the casting of the empirical natural law into the frame of a theory which is more fundamental down to the reductionistic chain of the scientific disciplines For instance the kinetic gas theory is the casting of the empirical gas laws (the empirical natural law) into Newtonrsquos classical mechanics
How to make a HB TheoryHow to make a HB Theory
HB Properties = FF (HB Driving Variable)where
HB Driving Variable = PApKa and FF = Transition-State Theory
The Transition-State HB TheoryThe Transition-State HB Theory(Gilli et al JACS 2002 2005 Gilli et al J Mol Struct 2006)
Though it has taken us more than 12 years to develop it
the basic idea is very simpleAny DndashHmiddotmiddotmiddotA bond can be considered as a chemical reaction which is
bimolecular in both directions and proceeds via transition-state (TS) formation
AndashB + C AmiddotmiddotmiddotBmiddotmiddotmiddotC A + BndashCDndashHmiddotmiddotmiddotA DmiddotmiddotmiddotHmiddotmiddotmiddotA DmiddotmiddotmiddotHndashA
Changes of nomenclatureReaction Pathway PTPathwayActivation Energy DaggerE PTBarrierReaction Energy Er PApKa Transition State (TS) PTTS
Reaction Coordinate RC=[d(DH)ndashd(AH)] Experimentals Variable-Temperature X-allographyCalculations DFTEmulated PTPathwaysInterpretation Marcus Rate-Equilibrium Theory LefflerHammond Postulate
AcknowledgmentsAcknowledgments I have to thank my direct coworkers without whose help this work could have not been accomplished
Valerio BERTOLASI Paola GILLI
Valeria FERRETTI Loretta PRETTO
and the scientific institutions which made available to us the databases without which this work could not even be started
CCDCCambridge Crystallographic
Data Centrefor the use of the
Cambridge Structural Database
NIST National Institute of Standards and
Technologyfor the use of the
NIST Chemistry WebBook
A Proposal The PApA Proposal The PApKKaa Equalization Principle Equalization Principle
Two very similar proposals come from early thermodynamic or spectroscopic investigations and are both centered on the
matching of the acid-base properties of the HB donor and acceptors moieties what we like too call for the sake of brevity the
PApPApKKaa Equalization Principle Equalization Principle
With reference to any generic DHmiddotmiddotmiddotA bond this principle states that the HB becomes the stronger the smaller is the difference of the donor-acceptor
proton affinities proton affinities PA = PA(DPA = PA(D) ) PA(A) PA(A)or
acidic constants acidic constants ppKKa a = p= pKKAHAH(D(DH) H) p pKKBH+BH+(A(AHH++))
------------------------------------------------------------------------------------------------------------------------- Ault BS and Pimentel GG (1975) J Phys Chem 79 615 Huyskens PL and Zeegers-Huyskens Th (1964) J Chim Phys Phys- Chim Biol
61 81
Our First Steps in the HB FieldOur First Steps in the HB Field As usual we entered the field by chance In 1985 we were studying the ligands
of the benzadiazepine membrane receptor One of these ligands was CGS8216 where we noticed something strange a rather short N-HhellipO bond of 2694 Aring associated with an interleaving β-enaminone hellipO=C-C=C-NHhellip fragment which was almost completely π-delocalized
It was the first indication of a possible correlation between -delocalization and H-bond strength what was called a few years later the
Resonance-Assisted H-Bond (RAHB)Resonance-Assisted H-Bond (RAHB) (Gilli Bellucci Ferretti amp Bertolasi JACS 1989 Bertolasi Gilli Ferretti amp Gilli JACS 1991) Since at the time few -enaminones were known the work started on the analogous class of -enolones (or -diketone enols) which were already known to give strong O-HO bonds through the equally resonant O=C-C=C-OH fragment
The Development of the OThe Development of the OHO RAHBHO RAHB
The OThe OHO RAHBsHO RAHBs
Very interesting Class of Strong HBs Different lengths of the resonant spacer Rn
(n = 1 3 5 7) The HBs formed were all much stronger than normal (non-resonant) OHO bonds withd(OO)INTRA =
239-255 Aringd(OO)INTER =
246-265 Aring
R1-RAHBR5-RAHB
24256 Aring
N
N
O M e
N
N
OM e
M eM e
H
lt 257 gt1 Aring
P
O H
OO
O H
H P
O H
OO
O H
H
R3-RAHB
O OH
237-255 Aring
262-267 Aring
O
O H O
OH
262-270 Aring
O
O
H
O
O H
R7-RAHB
24462 Aring
NOO
OO
M eM e
H
OOH
O
O
H
CARBOXYLIC ACIDS
DIBENZOYLMETHANE ENOLS
CYCLOHEXANEDIONE ENOLS
PHOPHORIC ACID
A Model for RAHB Electrostatic or CovalentA Model for RAHB Electrostatic or Covalent
At first (JACS 1989) we suggested a RAHB Electrostatic Model but it became rapidly evident that an efficient RAHB treatment would require a Covalent Model
All hell broke loose because as we discovered with surprise the concept itself of covalent HB had been banned some twenty years before and substituted by the acritical but more comfortable Simple Electrostatic Paradigm RAHB seriously risked to became a kind of bizarre covalent hypothesis
I must thank George A Jeffrey with his inimitable unbiased and skeptical style if RAHB was not immediately cast aside by the scientific establishment but started to be quoted in important books and reviews during the lsquo90ties
A RAHB Electrostatic ModelA RAHB Electrostatic Model A RAHB Covalent ModelA RAHB Covalent Model
Starting Again The Purely Empirical ApproachStarting Again The Purely Empirical Approach Fortunately we were realistic enough not to try to confute the Electrostatic
Paradigm On the other hand it was perfectly useless because too deeply rooted in the Weltanschaung of so many important and self-confident scientists
I have already given a short critical account of the very nature of these scientific paradigms at the ECM-2000 of Nancy based on the ideas of Thomas S Kuhn (The Structure of Scientific Revolutions The University of Chicago 1962 and 1970)
Anyway to get out of this impasse at the beginning of 1993 we decided to change approach and to restart to investigate the O-HO bond problem from the very beginning by adopting a purely empirical strategy
(i) suspend any previous ideas on the electrostatic or covalent nature of the HB (ii) define the OHmiddotmiddotmiddotO bond as a simple topological structure where a H atom is connected to two or more oxygen atoms(iii) collect all crystal structures having OHmiddotmiddotmiddotO bonds with d(OmiddotmiddotmiddotO) 270 Aring(iv) collect all available IR (O-H) and NMR (H) data of H-bonded protons(v) collect all available HB energy data from thermodynamic measurements in gas phase and non-polar solvents(vi) try to infer a conclusion on the very nature of the OHmiddotmiddotmiddotO bond from the ensemble of the data collected
A Full Classification of Strong HBsA Full Classification of Strong HBs
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs)CHARGE - ASSISTED HBs
PENTACHLOROPHENOL - p-TOLUIDINE
pKa = -070
12
12
N
CH3
O
ClCl
Cl
Cl
Cl
H25062 AringCL 1 (+ndash)CAHB SHB VSHB
Double Charge-Assisted HBDirect Acid-Base PApKa Matching
CL 2 (ndash)CAHB SHB VSHBNegative Charge-Assisted HB
Acid-Base PApKa Matching by Proton Loss R
OOH
R
O O24371 Aring
CARBOXYLIC ACID - CARBOXYLATE
CL 3 (+)CAHB SHB VSHBPositive Charge-Assisted HB
Acid-Base PApKa Matching by Proton Gain
O
HH H
O
HH
24303 Aring
WATER - HYDRONIUM
-BOND POLARIZATION - ASSISTED HBs
237-255 Aring
O OH
ArAr
DIBENZOYLMETHANE ENOLS
CL 4 RAHB SHB VSHB Resonance-Assisted or -Cooperative HB
PApKa Matching by -Conjugated-Bond Polarization
27501 Aring
OO
O
O O
WATER
CL 5 PAHB MHBPolarization-Assisted or -Cooperative HB(Partial) PApKa Matching by -Bond Polarization
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs) The most interesting aspect of a HB classification based on HB strength is that strong HBs belong only to a small number of chemical schemes that we have called Chemical Leitmotifs
The Alchemic Piper plays the Five Magic Tunes that make any Hydrogen Bond stronger The Chemical Leitmotifs
Symmetry and Covalency (1)Symmetry and Covalency (1)The covalent nature of the strong OHmiddotmiddotmiddotO bond was assessed by interpreting the
experimental results in terms of the Coulsonrsquos VB formalismWe cannot measure covalency but can evaluate molecular symmetry the
Coulsonrsquos model being the algorithm able to translate one concept into the other
In fact total symmetry across the HB implies energy equivalence between the two covalent VB forms ie E(ΨCOV1) = E(ΨCOV2) which is just the situation
associated with formation of the covalent HB
E E
NCT
CT
CTNCT
COV2
IONIC
COV1
IONIC
COV1 COV2
NCT
NCT
(a) Electrostatic HB (b) Covalent HB
Symmetry and Covalency (2)Symmetry and Covalency (2)
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 1
(+-)CAHBDouble Charge-Assisted HB
Direct Acid-Base PApKa Matching
R12DH+A12R
The role played by the PApKa equalization in HB strengthening
is self-evident for the (+-)CAHB chemical leitmotif
RDHARrsquo R12DH+A12Rrsquo RDHA+Rrsquo
which collects by definition all strong HBs formed by the acid-base pairs with a pKa matching within say ndash3 divide 3 pKa units
But what about the other leitmotifs Can we prove that
all chemical leitmotifs are simple artificesthat molecules can use to obliterate the normally
very large pKa between HB donor and acceptor atoms
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 2(-)CAHB
Negative Charge-Assisted HBAcid-Base PApKa Matching
by Proton Loss[R-DHA-R]-
Chemical Leitmotif 3(+)CAHB
Positive Charge-Assisted HBAcid-Base PApKa Matching
by Proton Gain[R-DHA-R]+
2II
2III
2IIa
2IIb
2IIIb
2IIIa
2VIa
pKa = pKAH(HO-H)-pKAH(HO-H) = 157 - 157 = 0
pKa = pKBH(H2O-H+)-pKBH(H2O-H
+) = -17 + 17 = 0
pKAH(HO-H) = 157
pKBH(H2O-H+) = -17
H
O H
H
O
H
(ndash)CAHB pKa = 00
VERYSTRONG~ 25-30 kcalmol
(+)CAHB pKa = 00
VERYSTRONG ~ 25-31 kcalmol
pKa = 175
OHB
WEAK ~ 4- 5kcalmol
ndash H+
+ H+
H
O H O
H
H
O H O
H
H
OHO
H
H
O
H
H
H
O
H
H
O
H
H
O
H
H H
O
H
H
H
O
H
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 4RAHB
Resonance-Assisted or -Bond Cooperative HBPApKa Matching by -Conjugated-Bond Polarization
R-D-HA=R R=DH-A-R
pKAH(RO-H) = 1518
pKBH(R2C=O-H+) = -(67)
O OH
O H O
R
R
R
Rn-RAHB pKa = ~ 21-25
WEAK ~ 4- 5kcalmol
EKO O
H
KEOO
H
pKa = 00
STRONG ~ 15-22 kcalmol
2IV
2IVa
2IVb
2VIb
OHB
The HB Empirical RulesThe HB Empirical Rules
The empirical analysis of experimental data joined with homeopathic doses of VB theory leads us to formulate two important HB Empirical Rules which have been called elsewhere ECHBM (Electrostatic-Covalent HB Model Gilli amp Gilli J Mol Struct 2000) and can be summarized as follows
Any given D-HA system may form HBs in a wide range of strengths lengths symmetries and proton locations the two extremes being represented
by the weak long dissymmetric and proton-out-centred HB of electrostatic nature
and by the very strong very short symmetric and proton-centred HB
classifiable as a true 3-center-4-electron covalent bond
The driving variable able to transform strong into weak HBs is dimensionally a free enthalpy corresponding to the difference between the Proton Affinities (PA) or related Acid-Base Dissociation Constants (pKa) of the Donor and Acceptor moieties
These rules have been verified beyond any reasonable doubt for the Conventional HBs of the following classification
Provisional Conclusions and New ControlsProvisional Conclusions and New Controls
We have so far established a sound set of empirical rules which include A full classification of all existing HBs A full classification of all strong HBs (The Chemical Leitmotifs) A plausible correlation between HB strengths and acid-base properties of the interacting molecules (The PApKa Equalization Principle)
To confirm this last point we have undertaken two years ago
a new research program aimed at assessing the Full Validity of the PApKa Equalization Principle
by comparing extended tables of pKa values arranged for chemical classes
withthe corresponding CSD-derived HB geometries
Hundreds of pKa were collected and more than 11000 crystal structures examined
The pThe pKKa Slide Rulea Slide Rule
It is a tool for the graphical evaluation of the difference
pKa = pKAH(DH) - pKBH+(AH+)
HB Acceptors on the left and HB Donors on the right
pKa values given for chemical class
Results expected
ΔpKagtgt0 DHmiddotmiddotmiddotmiddotA weak amp neutral
ΔpKa asymp 0 DmiddotmiddotmiddotHmiddotmiddotmiddotA strong amp
centeredΔpKa ltlt0DmiddotmiddotmiddotmiddotHA+ weak amp charged
pKa ranges of organic compounds
C-H acids -11 ltpKalt 53
Other Donors -1 ltpKalt 40
Acceptors -12 ltpKalt 16
All -15 ltpKalt 53
Water 0 ltpKalt 14
50
-10
0
10
20
30
40
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
ALDEHYDES
ETHERSALCOHOLS
AMIDES
NITRILES
ANILINES
CF3-SO3H
HClO4HI
HBrHCl
H2SO4
HSO4
HNO3
HBF4
H3PO4
H2PO4
HPO42
HF HNO2
HNNN
NH2OHH2CO3
HCO3
H2S
HS-
HCN H3BO3
H2BO3
H4SiO4
H2O2
HO
HSCN
H-H
SULFONICACIDS
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
OXIMES
ALCOHOLS
THIOLES
HB ACCEPTORS (A)pK BH+
HB DONORS (D-H)pK AH
C-H ACIDS pK AH
BE
TT
ER
HB
AC
CE
PT
OR
BE
TT
ER
BA
SE
BE
TT
ER
HB
DO
NO
R
BE
TT
ER
AC
ID
N-OXIDES
AMIDINES
UREA
THIOUREA
BARBITURICURIC ACID
MONO DIPHOSPHINES
TRIPHOSPHINES
TRINITROANILINES
AMINES
ANILINES
MONO DINITROANILINES
AMIDES
CARBOXYLIC ACIDS
HALOGENOANILINES
AZOCOMPS
TRINITROANILINES
PROTONSPONGES
ACIDSESTERS
H2O
H2O
MONODINITROANILINES
KETONES
SULFIDES
HALOGENCARB ACIDS
TRINITROPHENOLS
ENOLS
MONO DINITROPHENOLS
PHENOLSNAPHTHOLS
HALOGENOPHENOLS
HALOGENOALCOHOLS
SULFOXIDES
(NC)5-CYCLO
PENTADIENE
(NC)3CH
(O2N)2=CH2
HCCHNC-CH3
CH3-CO-CH3INDENE
O2N-CH3
(NC)2=CH2
(O2N)3CH
H2C=CH2
C6H6
CH4
CYCLOPENTADIENE
CYCLOPROPENE
Ar3CH
Ar2=CH2
Ar-CH3
NITROCOMPS
SELENOXIDES
AZOLES
AZINESDIAZINES
AMINES
Cl5-PHENOL
CH3-CH3
(CH3)3CH
NH3
NH3
51
53
51
53
Chemical Leitmotifs and PApChemical Leitmotifs and PApKKaa Equalization Rules Equalization Rules RAHB RAHB cannot be treated by pKa equalization methods because π-delocalization
modifies the pKarsquos of the donor and acceptor moieties (+)CAHB is a true proton transfer from an acid (HB donor) to a base (HB acceptor)
RndashDndashHAndashRrsquo Rndash12DH+A12ndashndashRrsquo RndashDHndashA+ndashRrsquoΔpKa = pKAH(RDH) pKBH+(RrsquoA)
()CAHB is a proton sharing between two acids (HB donors)
RndashDndashHDrsquondashRrsquo [RDHDrsquoRrsquo] RDHDrsquoRrsquoΔpKa = pKAH(RDH) pKAH(RDH)
(+)CAHB is a proton sharing between two bases (HB acceptors)
R+AHArsquoRrsquo [RAHArsquoRrsquo]+ RAHArsquo+RrsquoΔpKa = pKBH+(RA) pKBH+(RrsquoArsquo)
Whenever () and (+)CAHBs are both homonuclear (D = Drsquo or A = Arsquo) and
homomolecular (R = Rrsquo) the matching condition ΔpKa= 0 will hold irrespective of the
actual pKarsquos of the two interacting moieties All HBs formed will be strong
Some Famous HBsSome Famous HBs
The NThe NHmiddotmiddotmiddotOOHmiddotmiddotmiddotOOHmiddotmiddotmiddotN System over the Full HmiddotmiddotmiddotN System over the Full ppKKaa Range Range
When evaluated from the pKa slide rule the total pKa range is extremely wide
ndash30 pa 60 So far we have been able to shown that the pKa equalization rule certainly holds in
a restricted interval around zero The problem is now Does this rule hold in the full pKa range
We will try to prove that by a full analysis the N-HmiddotmiddotmiddotOO-HmiddotmiddotmiddotN system
Procedure In a first CSD search functional groups of known pKa value and more frequently
implied in NHmiddotmiddotmiddotOOHmiddotmiddotmiddotN bonds were identified Finally 10 classes of donors and 11 of acceptors were selected and the search restarted for each separate donor-acceptor group Altogether 9078 different bonds were analyzed (4364 NHmiddotmiddotmiddotO 2289 OHmiddotmiddotmiddotN and
2425 OmiddotmiddotmiddotHN+) For each bond the NmiddotmiddotmiddotO distances were evaluated as dNH + dHO to account for the
N-H-O angle and for each group the shortest and average distances [dNmiddotmiddotmiddotO (min)
and dNmiddotmiddotmiddotO (mean)] were registered
These values were compared (see next slide) with the acid-base features of the donors (pKAH range) acceptors (pKBH+ range) and with their combinations
(pKa range)
pKa large amp positive
pKa largeamp negative
Increasing Acidity of the Protonated A H+ Acceptor Increasing Basicity of the A Acceptor
ppKKaa versusversus HB Geometry Correlation - Conclusions HB Geometry Correlation - Conclusions The PApKa Equalization Principle is therefore fully confirmed in its two forms All strong HBs correspond to very small pKa values
pKa values modulate the HB strength over the full pKa range These conclusions are of great practical importance in at least two respects pKa is definitively established as the driving force which controls the HB
strength by modulating the HB covalent contribution It is definitively established that an accurate analysis of structural crystal data
leads to the same conclusions suggested but never proved on a general base by thermodynamic and spectroscopic methods
References Huyskens and Zeegers-Huyskens 1964 Zeegers-Huyskens 1986 1988 Ault and Pimentel 1975 Ratajczak and Sobczyk 1969 Sobczyk et al 1982 Barnes 1983 Kebarle et al 1974-1979 Meot-Ner (Mautner) et al
1984-1988
Towards a General HB TheoryTowards a General HB Theory
The results so far obtained are not a True HB Theory but rather a Set of Empirical Rules (or an Empirical Natural Law) that is a great collection of HB experimental data neatly organized in tables which all together represent a General Taxonomy of the HB Phenomenon exactly as the Carl Linnaeusrsquo classification of plants A scientific theory is something different It is the casting of the empirical natural law into the frame of a theory which is more fundamental down to the reductionistic chain of the scientific disciplines For instance the kinetic gas theory is the casting of the empirical gas laws (the empirical natural law) into Newtonrsquos classical mechanics
How to make a HB TheoryHow to make a HB Theory
HB Properties = FF (HB Driving Variable)where
HB Driving Variable = PApKa and FF = Transition-State Theory
The Transition-State HB TheoryThe Transition-State HB Theory(Gilli et al JACS 2002 2005 Gilli et al J Mol Struct 2006)
Though it has taken us more than 12 years to develop it
the basic idea is very simpleAny DndashHmiddotmiddotmiddotA bond can be considered as a chemical reaction which is
bimolecular in both directions and proceeds via transition-state (TS) formation
AndashB + C AmiddotmiddotmiddotBmiddotmiddotmiddotC A + BndashCDndashHmiddotmiddotmiddotA DmiddotmiddotmiddotHmiddotmiddotmiddotA DmiddotmiddotmiddotHndashA
Changes of nomenclatureReaction Pathway PTPathwayActivation Energy DaggerE PTBarrierReaction Energy Er PApKa Transition State (TS) PTTS
Reaction Coordinate RC=[d(DH)ndashd(AH)] Experimentals Variable-Temperature X-allographyCalculations DFTEmulated PTPathwaysInterpretation Marcus Rate-Equilibrium Theory LefflerHammond Postulate
AcknowledgmentsAcknowledgments I have to thank my direct coworkers without whose help this work could have not been accomplished
Valerio BERTOLASI Paola GILLI
Valeria FERRETTI Loretta PRETTO
and the scientific institutions which made available to us the databases without which this work could not even be started
CCDCCambridge Crystallographic
Data Centrefor the use of the
Cambridge Structural Database
NIST National Institute of Standards and
Technologyfor the use of the
NIST Chemistry WebBook
Our First Steps in the HB FieldOur First Steps in the HB Field As usual we entered the field by chance In 1985 we were studying the ligands
of the benzadiazepine membrane receptor One of these ligands was CGS8216 where we noticed something strange a rather short N-HhellipO bond of 2694 Aring associated with an interleaving β-enaminone hellipO=C-C=C-NHhellip fragment which was almost completely π-delocalized
It was the first indication of a possible correlation between -delocalization and H-bond strength what was called a few years later the
Resonance-Assisted H-Bond (RAHB)Resonance-Assisted H-Bond (RAHB) (Gilli Bellucci Ferretti amp Bertolasi JACS 1989 Bertolasi Gilli Ferretti amp Gilli JACS 1991) Since at the time few -enaminones were known the work started on the analogous class of -enolones (or -diketone enols) which were already known to give strong O-HO bonds through the equally resonant O=C-C=C-OH fragment
The Development of the OThe Development of the OHO RAHBHO RAHB
The OThe OHO RAHBsHO RAHBs
Very interesting Class of Strong HBs Different lengths of the resonant spacer Rn
(n = 1 3 5 7) The HBs formed were all much stronger than normal (non-resonant) OHO bonds withd(OO)INTRA =
239-255 Aringd(OO)INTER =
246-265 Aring
R1-RAHBR5-RAHB
24256 Aring
N
N
O M e
N
N
OM e
M eM e
H
lt 257 gt1 Aring
P
O H
OO
O H
H P
O H
OO
O H
H
R3-RAHB
O OH
237-255 Aring
262-267 Aring
O
O H O
OH
262-270 Aring
O
O
H
O
O H
R7-RAHB
24462 Aring
NOO
OO
M eM e
H
OOH
O
O
H
CARBOXYLIC ACIDS
DIBENZOYLMETHANE ENOLS
CYCLOHEXANEDIONE ENOLS
PHOPHORIC ACID
A Model for RAHB Electrostatic or CovalentA Model for RAHB Electrostatic or Covalent
At first (JACS 1989) we suggested a RAHB Electrostatic Model but it became rapidly evident that an efficient RAHB treatment would require a Covalent Model
All hell broke loose because as we discovered with surprise the concept itself of covalent HB had been banned some twenty years before and substituted by the acritical but more comfortable Simple Electrostatic Paradigm RAHB seriously risked to became a kind of bizarre covalent hypothesis
I must thank George A Jeffrey with his inimitable unbiased and skeptical style if RAHB was not immediately cast aside by the scientific establishment but started to be quoted in important books and reviews during the lsquo90ties
A RAHB Electrostatic ModelA RAHB Electrostatic Model A RAHB Covalent ModelA RAHB Covalent Model
Starting Again The Purely Empirical ApproachStarting Again The Purely Empirical Approach Fortunately we were realistic enough not to try to confute the Electrostatic
Paradigm On the other hand it was perfectly useless because too deeply rooted in the Weltanschaung of so many important and self-confident scientists
I have already given a short critical account of the very nature of these scientific paradigms at the ECM-2000 of Nancy based on the ideas of Thomas S Kuhn (The Structure of Scientific Revolutions The University of Chicago 1962 and 1970)
Anyway to get out of this impasse at the beginning of 1993 we decided to change approach and to restart to investigate the O-HO bond problem from the very beginning by adopting a purely empirical strategy
(i) suspend any previous ideas on the electrostatic or covalent nature of the HB (ii) define the OHmiddotmiddotmiddotO bond as a simple topological structure where a H atom is connected to two or more oxygen atoms(iii) collect all crystal structures having OHmiddotmiddotmiddotO bonds with d(OmiddotmiddotmiddotO) 270 Aring(iv) collect all available IR (O-H) and NMR (H) data of H-bonded protons(v) collect all available HB energy data from thermodynamic measurements in gas phase and non-polar solvents(vi) try to infer a conclusion on the very nature of the OHmiddotmiddotmiddotO bond from the ensemble of the data collected
A Full Classification of Strong HBsA Full Classification of Strong HBs
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs)CHARGE - ASSISTED HBs
PENTACHLOROPHENOL - p-TOLUIDINE
pKa = -070
12
12
N
CH3
O
ClCl
Cl
Cl
Cl
H25062 AringCL 1 (+ndash)CAHB SHB VSHB
Double Charge-Assisted HBDirect Acid-Base PApKa Matching
CL 2 (ndash)CAHB SHB VSHBNegative Charge-Assisted HB
Acid-Base PApKa Matching by Proton Loss R
OOH
R
O O24371 Aring
CARBOXYLIC ACID - CARBOXYLATE
CL 3 (+)CAHB SHB VSHBPositive Charge-Assisted HB
Acid-Base PApKa Matching by Proton Gain
O
HH H
O
HH
24303 Aring
WATER - HYDRONIUM
-BOND POLARIZATION - ASSISTED HBs
237-255 Aring
O OH
ArAr
DIBENZOYLMETHANE ENOLS
CL 4 RAHB SHB VSHB Resonance-Assisted or -Cooperative HB
PApKa Matching by -Conjugated-Bond Polarization
27501 Aring
OO
O
O O
WATER
CL 5 PAHB MHBPolarization-Assisted or -Cooperative HB(Partial) PApKa Matching by -Bond Polarization
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs) The most interesting aspect of a HB classification based on HB strength is that strong HBs belong only to a small number of chemical schemes that we have called Chemical Leitmotifs
The Alchemic Piper plays the Five Magic Tunes that make any Hydrogen Bond stronger The Chemical Leitmotifs
Symmetry and Covalency (1)Symmetry and Covalency (1)The covalent nature of the strong OHmiddotmiddotmiddotO bond was assessed by interpreting the
experimental results in terms of the Coulsonrsquos VB formalismWe cannot measure covalency but can evaluate molecular symmetry the
Coulsonrsquos model being the algorithm able to translate one concept into the other
In fact total symmetry across the HB implies energy equivalence between the two covalent VB forms ie E(ΨCOV1) = E(ΨCOV2) which is just the situation
associated with formation of the covalent HB
E E
NCT
CT
CTNCT
COV2
IONIC
COV1
IONIC
COV1 COV2
NCT
NCT
(a) Electrostatic HB (b) Covalent HB
Symmetry and Covalency (2)Symmetry and Covalency (2)
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 1
(+-)CAHBDouble Charge-Assisted HB
Direct Acid-Base PApKa Matching
R12DH+A12R
The role played by the PApKa equalization in HB strengthening
is self-evident for the (+-)CAHB chemical leitmotif
RDHARrsquo R12DH+A12Rrsquo RDHA+Rrsquo
which collects by definition all strong HBs formed by the acid-base pairs with a pKa matching within say ndash3 divide 3 pKa units
But what about the other leitmotifs Can we prove that
all chemical leitmotifs are simple artificesthat molecules can use to obliterate the normally
very large pKa between HB donor and acceptor atoms
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 2(-)CAHB
Negative Charge-Assisted HBAcid-Base PApKa Matching
by Proton Loss[R-DHA-R]-
Chemical Leitmotif 3(+)CAHB
Positive Charge-Assisted HBAcid-Base PApKa Matching
by Proton Gain[R-DHA-R]+
2II
2III
2IIa
2IIb
2IIIb
2IIIa
2VIa
pKa = pKAH(HO-H)-pKAH(HO-H) = 157 - 157 = 0
pKa = pKBH(H2O-H+)-pKBH(H2O-H
+) = -17 + 17 = 0
pKAH(HO-H) = 157
pKBH(H2O-H+) = -17
H
O H
H
O
H
(ndash)CAHB pKa = 00
VERYSTRONG~ 25-30 kcalmol
(+)CAHB pKa = 00
VERYSTRONG ~ 25-31 kcalmol
pKa = 175
OHB
WEAK ~ 4- 5kcalmol
ndash H+
+ H+
H
O H O
H
H
O H O
H
H
OHO
H
H
O
H
H
H
O
H
H
O
H
H
O
H
H H
O
H
H
H
O
H
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 4RAHB
Resonance-Assisted or -Bond Cooperative HBPApKa Matching by -Conjugated-Bond Polarization
R-D-HA=R R=DH-A-R
pKAH(RO-H) = 1518
pKBH(R2C=O-H+) = -(67)
O OH
O H O
R
R
R
Rn-RAHB pKa = ~ 21-25
WEAK ~ 4- 5kcalmol
EKO O
H
KEOO
H
pKa = 00
STRONG ~ 15-22 kcalmol
2IV
2IVa
2IVb
2VIb
OHB
The HB Empirical RulesThe HB Empirical Rules
The empirical analysis of experimental data joined with homeopathic doses of VB theory leads us to formulate two important HB Empirical Rules which have been called elsewhere ECHBM (Electrostatic-Covalent HB Model Gilli amp Gilli J Mol Struct 2000) and can be summarized as follows
Any given D-HA system may form HBs in a wide range of strengths lengths symmetries and proton locations the two extremes being represented
by the weak long dissymmetric and proton-out-centred HB of electrostatic nature
and by the very strong very short symmetric and proton-centred HB
classifiable as a true 3-center-4-electron covalent bond
The driving variable able to transform strong into weak HBs is dimensionally a free enthalpy corresponding to the difference between the Proton Affinities (PA) or related Acid-Base Dissociation Constants (pKa) of the Donor and Acceptor moieties
These rules have been verified beyond any reasonable doubt for the Conventional HBs of the following classification
Provisional Conclusions and New ControlsProvisional Conclusions and New Controls
We have so far established a sound set of empirical rules which include A full classification of all existing HBs A full classification of all strong HBs (The Chemical Leitmotifs) A plausible correlation between HB strengths and acid-base properties of the interacting molecules (The PApKa Equalization Principle)
To confirm this last point we have undertaken two years ago
a new research program aimed at assessing the Full Validity of the PApKa Equalization Principle
by comparing extended tables of pKa values arranged for chemical classes
withthe corresponding CSD-derived HB geometries
Hundreds of pKa were collected and more than 11000 crystal structures examined
The pThe pKKa Slide Rulea Slide Rule
It is a tool for the graphical evaluation of the difference
pKa = pKAH(DH) - pKBH+(AH+)
HB Acceptors on the left and HB Donors on the right
pKa values given for chemical class
Results expected
ΔpKagtgt0 DHmiddotmiddotmiddotmiddotA weak amp neutral
ΔpKa asymp 0 DmiddotmiddotmiddotHmiddotmiddotmiddotA strong amp
centeredΔpKa ltlt0DmiddotmiddotmiddotmiddotHA+ weak amp charged
pKa ranges of organic compounds
C-H acids -11 ltpKalt 53
Other Donors -1 ltpKalt 40
Acceptors -12 ltpKalt 16
All -15 ltpKalt 53
Water 0 ltpKalt 14
50
-10
0
10
20
30
40
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
ALDEHYDES
ETHERSALCOHOLS
AMIDES
NITRILES
ANILINES
CF3-SO3H
HClO4HI
HBrHCl
H2SO4
HSO4
HNO3
HBF4
H3PO4
H2PO4
HPO42
HF HNO2
HNNN
NH2OHH2CO3
HCO3
H2S
HS-
HCN H3BO3
H2BO3
H4SiO4
H2O2
HO
HSCN
H-H
SULFONICACIDS
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
OXIMES
ALCOHOLS
THIOLES
HB ACCEPTORS (A)pK BH+
HB DONORS (D-H)pK AH
C-H ACIDS pK AH
BE
TT
ER
HB
AC
CE
PT
OR
BE
TT
ER
BA
SE
BE
TT
ER
HB
DO
NO
R
BE
TT
ER
AC
ID
N-OXIDES
AMIDINES
UREA
THIOUREA
BARBITURICURIC ACID
MONO DIPHOSPHINES
TRIPHOSPHINES
TRINITROANILINES
AMINES
ANILINES
MONO DINITROANILINES
AMIDES
CARBOXYLIC ACIDS
HALOGENOANILINES
AZOCOMPS
TRINITROANILINES
PROTONSPONGES
ACIDSESTERS
H2O
H2O
MONODINITROANILINES
KETONES
SULFIDES
HALOGENCARB ACIDS
TRINITROPHENOLS
ENOLS
MONO DINITROPHENOLS
PHENOLSNAPHTHOLS
HALOGENOPHENOLS
HALOGENOALCOHOLS
SULFOXIDES
(NC)5-CYCLO
PENTADIENE
(NC)3CH
(O2N)2=CH2
HCCHNC-CH3
CH3-CO-CH3INDENE
O2N-CH3
(NC)2=CH2
(O2N)3CH
H2C=CH2
C6H6
CH4
CYCLOPENTADIENE
CYCLOPROPENE
Ar3CH
Ar2=CH2
Ar-CH3
NITROCOMPS
SELENOXIDES
AZOLES
AZINESDIAZINES
AMINES
Cl5-PHENOL
CH3-CH3
(CH3)3CH
NH3
NH3
51
53
51
53
Chemical Leitmotifs and PApChemical Leitmotifs and PApKKaa Equalization Rules Equalization Rules RAHB RAHB cannot be treated by pKa equalization methods because π-delocalization
modifies the pKarsquos of the donor and acceptor moieties (+)CAHB is a true proton transfer from an acid (HB donor) to a base (HB acceptor)
RndashDndashHAndashRrsquo Rndash12DH+A12ndashndashRrsquo RndashDHndashA+ndashRrsquoΔpKa = pKAH(RDH) pKBH+(RrsquoA)
()CAHB is a proton sharing between two acids (HB donors)
RndashDndashHDrsquondashRrsquo [RDHDrsquoRrsquo] RDHDrsquoRrsquoΔpKa = pKAH(RDH) pKAH(RDH)
(+)CAHB is a proton sharing between two bases (HB acceptors)
R+AHArsquoRrsquo [RAHArsquoRrsquo]+ RAHArsquo+RrsquoΔpKa = pKBH+(RA) pKBH+(RrsquoArsquo)
Whenever () and (+)CAHBs are both homonuclear (D = Drsquo or A = Arsquo) and
homomolecular (R = Rrsquo) the matching condition ΔpKa= 0 will hold irrespective of the
actual pKarsquos of the two interacting moieties All HBs formed will be strong
Some Famous HBsSome Famous HBs
The NThe NHmiddotmiddotmiddotOOHmiddotmiddotmiddotOOHmiddotmiddotmiddotN System over the Full HmiddotmiddotmiddotN System over the Full ppKKaa Range Range
When evaluated from the pKa slide rule the total pKa range is extremely wide
ndash30 pa 60 So far we have been able to shown that the pKa equalization rule certainly holds in
a restricted interval around zero The problem is now Does this rule hold in the full pKa range
We will try to prove that by a full analysis the N-HmiddotmiddotmiddotOO-HmiddotmiddotmiddotN system
Procedure In a first CSD search functional groups of known pKa value and more frequently
implied in NHmiddotmiddotmiddotOOHmiddotmiddotmiddotN bonds were identified Finally 10 classes of donors and 11 of acceptors were selected and the search restarted for each separate donor-acceptor group Altogether 9078 different bonds were analyzed (4364 NHmiddotmiddotmiddotO 2289 OHmiddotmiddotmiddotN and
2425 OmiddotmiddotmiddotHN+) For each bond the NmiddotmiddotmiddotO distances were evaluated as dNH + dHO to account for the
N-H-O angle and for each group the shortest and average distances [dNmiddotmiddotmiddotO (min)
and dNmiddotmiddotmiddotO (mean)] were registered
These values were compared (see next slide) with the acid-base features of the donors (pKAH range) acceptors (pKBH+ range) and with their combinations
(pKa range)
pKa large amp positive
pKa largeamp negative
Increasing Acidity of the Protonated A H+ Acceptor Increasing Basicity of the A Acceptor
ppKKaa versusversus HB Geometry Correlation - Conclusions HB Geometry Correlation - Conclusions The PApKa Equalization Principle is therefore fully confirmed in its two forms All strong HBs correspond to very small pKa values
pKa values modulate the HB strength over the full pKa range These conclusions are of great practical importance in at least two respects pKa is definitively established as the driving force which controls the HB
strength by modulating the HB covalent contribution It is definitively established that an accurate analysis of structural crystal data
leads to the same conclusions suggested but never proved on a general base by thermodynamic and spectroscopic methods
References Huyskens and Zeegers-Huyskens 1964 Zeegers-Huyskens 1986 1988 Ault and Pimentel 1975 Ratajczak and Sobczyk 1969 Sobczyk et al 1982 Barnes 1983 Kebarle et al 1974-1979 Meot-Ner (Mautner) et al
1984-1988
Towards a General HB TheoryTowards a General HB Theory
The results so far obtained are not a True HB Theory but rather a Set of Empirical Rules (or an Empirical Natural Law) that is a great collection of HB experimental data neatly organized in tables which all together represent a General Taxonomy of the HB Phenomenon exactly as the Carl Linnaeusrsquo classification of plants A scientific theory is something different It is the casting of the empirical natural law into the frame of a theory which is more fundamental down to the reductionistic chain of the scientific disciplines For instance the kinetic gas theory is the casting of the empirical gas laws (the empirical natural law) into Newtonrsquos classical mechanics
How to make a HB TheoryHow to make a HB Theory
HB Properties = FF (HB Driving Variable)where
HB Driving Variable = PApKa and FF = Transition-State Theory
The Transition-State HB TheoryThe Transition-State HB Theory(Gilli et al JACS 2002 2005 Gilli et al J Mol Struct 2006)
Though it has taken us more than 12 years to develop it
the basic idea is very simpleAny DndashHmiddotmiddotmiddotA bond can be considered as a chemical reaction which is
bimolecular in both directions and proceeds via transition-state (TS) formation
AndashB + C AmiddotmiddotmiddotBmiddotmiddotmiddotC A + BndashCDndashHmiddotmiddotmiddotA DmiddotmiddotmiddotHmiddotmiddotmiddotA DmiddotmiddotmiddotHndashA
Changes of nomenclatureReaction Pathway PTPathwayActivation Energy DaggerE PTBarrierReaction Energy Er PApKa Transition State (TS) PTTS
Reaction Coordinate RC=[d(DH)ndashd(AH)] Experimentals Variable-Temperature X-allographyCalculations DFTEmulated PTPathwaysInterpretation Marcus Rate-Equilibrium Theory LefflerHammond Postulate
AcknowledgmentsAcknowledgments I have to thank my direct coworkers without whose help this work could have not been accomplished
Valerio BERTOLASI Paola GILLI
Valeria FERRETTI Loretta PRETTO
and the scientific institutions which made available to us the databases without which this work could not even be started
CCDCCambridge Crystallographic
Data Centrefor the use of the
Cambridge Structural Database
NIST National Institute of Standards and
Technologyfor the use of the
NIST Chemistry WebBook
The Development of the OThe Development of the OHO RAHBHO RAHB
The OThe OHO RAHBsHO RAHBs
Very interesting Class of Strong HBs Different lengths of the resonant spacer Rn
(n = 1 3 5 7) The HBs formed were all much stronger than normal (non-resonant) OHO bonds withd(OO)INTRA =
239-255 Aringd(OO)INTER =
246-265 Aring
R1-RAHBR5-RAHB
24256 Aring
N
N
O M e
N
N
OM e
M eM e
H
lt 257 gt1 Aring
P
O H
OO
O H
H P
O H
OO
O H
H
R3-RAHB
O OH
237-255 Aring
262-267 Aring
O
O H O
OH
262-270 Aring
O
O
H
O
O H
R7-RAHB
24462 Aring
NOO
OO
M eM e
H
OOH
O
O
H
CARBOXYLIC ACIDS
DIBENZOYLMETHANE ENOLS
CYCLOHEXANEDIONE ENOLS
PHOPHORIC ACID
A Model for RAHB Electrostatic or CovalentA Model for RAHB Electrostatic or Covalent
At first (JACS 1989) we suggested a RAHB Electrostatic Model but it became rapidly evident that an efficient RAHB treatment would require a Covalent Model
All hell broke loose because as we discovered with surprise the concept itself of covalent HB had been banned some twenty years before and substituted by the acritical but more comfortable Simple Electrostatic Paradigm RAHB seriously risked to became a kind of bizarre covalent hypothesis
I must thank George A Jeffrey with his inimitable unbiased and skeptical style if RAHB was not immediately cast aside by the scientific establishment but started to be quoted in important books and reviews during the lsquo90ties
A RAHB Electrostatic ModelA RAHB Electrostatic Model A RAHB Covalent ModelA RAHB Covalent Model
Starting Again The Purely Empirical ApproachStarting Again The Purely Empirical Approach Fortunately we were realistic enough not to try to confute the Electrostatic
Paradigm On the other hand it was perfectly useless because too deeply rooted in the Weltanschaung of so many important and self-confident scientists
I have already given a short critical account of the very nature of these scientific paradigms at the ECM-2000 of Nancy based on the ideas of Thomas S Kuhn (The Structure of Scientific Revolutions The University of Chicago 1962 and 1970)
Anyway to get out of this impasse at the beginning of 1993 we decided to change approach and to restart to investigate the O-HO bond problem from the very beginning by adopting a purely empirical strategy
(i) suspend any previous ideas on the electrostatic or covalent nature of the HB (ii) define the OHmiddotmiddotmiddotO bond as a simple topological structure where a H atom is connected to two or more oxygen atoms(iii) collect all crystal structures having OHmiddotmiddotmiddotO bonds with d(OmiddotmiddotmiddotO) 270 Aring(iv) collect all available IR (O-H) and NMR (H) data of H-bonded protons(v) collect all available HB energy data from thermodynamic measurements in gas phase and non-polar solvents(vi) try to infer a conclusion on the very nature of the OHmiddotmiddotmiddotO bond from the ensemble of the data collected
A Full Classification of Strong HBsA Full Classification of Strong HBs
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs)CHARGE - ASSISTED HBs
PENTACHLOROPHENOL - p-TOLUIDINE
pKa = -070
12
12
N
CH3
O
ClCl
Cl
Cl
Cl
H25062 AringCL 1 (+ndash)CAHB SHB VSHB
Double Charge-Assisted HBDirect Acid-Base PApKa Matching
CL 2 (ndash)CAHB SHB VSHBNegative Charge-Assisted HB
Acid-Base PApKa Matching by Proton Loss R
OOH
R
O O24371 Aring
CARBOXYLIC ACID - CARBOXYLATE
CL 3 (+)CAHB SHB VSHBPositive Charge-Assisted HB
Acid-Base PApKa Matching by Proton Gain
O
HH H
O
HH
24303 Aring
WATER - HYDRONIUM
-BOND POLARIZATION - ASSISTED HBs
237-255 Aring
O OH
ArAr
DIBENZOYLMETHANE ENOLS
CL 4 RAHB SHB VSHB Resonance-Assisted or -Cooperative HB
PApKa Matching by -Conjugated-Bond Polarization
27501 Aring
OO
O
O O
WATER
CL 5 PAHB MHBPolarization-Assisted or -Cooperative HB(Partial) PApKa Matching by -Bond Polarization
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs) The most interesting aspect of a HB classification based on HB strength is that strong HBs belong only to a small number of chemical schemes that we have called Chemical Leitmotifs
The Alchemic Piper plays the Five Magic Tunes that make any Hydrogen Bond stronger The Chemical Leitmotifs
Symmetry and Covalency (1)Symmetry and Covalency (1)The covalent nature of the strong OHmiddotmiddotmiddotO bond was assessed by interpreting the
experimental results in terms of the Coulsonrsquos VB formalismWe cannot measure covalency but can evaluate molecular symmetry the
Coulsonrsquos model being the algorithm able to translate one concept into the other
In fact total symmetry across the HB implies energy equivalence between the two covalent VB forms ie E(ΨCOV1) = E(ΨCOV2) which is just the situation
associated with formation of the covalent HB
E E
NCT
CT
CTNCT
COV2
IONIC
COV1
IONIC
COV1 COV2
NCT
NCT
(a) Electrostatic HB (b) Covalent HB
Symmetry and Covalency (2)Symmetry and Covalency (2)
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 1
(+-)CAHBDouble Charge-Assisted HB
Direct Acid-Base PApKa Matching
R12DH+A12R
The role played by the PApKa equalization in HB strengthening
is self-evident for the (+-)CAHB chemical leitmotif
RDHARrsquo R12DH+A12Rrsquo RDHA+Rrsquo
which collects by definition all strong HBs formed by the acid-base pairs with a pKa matching within say ndash3 divide 3 pKa units
But what about the other leitmotifs Can we prove that
all chemical leitmotifs are simple artificesthat molecules can use to obliterate the normally
very large pKa between HB donor and acceptor atoms
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 2(-)CAHB
Negative Charge-Assisted HBAcid-Base PApKa Matching
by Proton Loss[R-DHA-R]-
Chemical Leitmotif 3(+)CAHB
Positive Charge-Assisted HBAcid-Base PApKa Matching
by Proton Gain[R-DHA-R]+
2II
2III
2IIa
2IIb
2IIIb
2IIIa
2VIa
pKa = pKAH(HO-H)-pKAH(HO-H) = 157 - 157 = 0
pKa = pKBH(H2O-H+)-pKBH(H2O-H
+) = -17 + 17 = 0
pKAH(HO-H) = 157
pKBH(H2O-H+) = -17
H
O H
H
O
H
(ndash)CAHB pKa = 00
VERYSTRONG~ 25-30 kcalmol
(+)CAHB pKa = 00
VERYSTRONG ~ 25-31 kcalmol
pKa = 175
OHB
WEAK ~ 4- 5kcalmol
ndash H+
+ H+
H
O H O
H
H
O H O
H
H
OHO
H
H
O
H
H
H
O
H
H
O
H
H
O
H
H H
O
H
H
H
O
H
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 4RAHB
Resonance-Assisted or -Bond Cooperative HBPApKa Matching by -Conjugated-Bond Polarization
R-D-HA=R R=DH-A-R
pKAH(RO-H) = 1518
pKBH(R2C=O-H+) = -(67)
O OH
O H O
R
R
R
Rn-RAHB pKa = ~ 21-25
WEAK ~ 4- 5kcalmol
EKO O
H
KEOO
H
pKa = 00
STRONG ~ 15-22 kcalmol
2IV
2IVa
2IVb
2VIb
OHB
The HB Empirical RulesThe HB Empirical Rules
The empirical analysis of experimental data joined with homeopathic doses of VB theory leads us to formulate two important HB Empirical Rules which have been called elsewhere ECHBM (Electrostatic-Covalent HB Model Gilli amp Gilli J Mol Struct 2000) and can be summarized as follows
Any given D-HA system may form HBs in a wide range of strengths lengths symmetries and proton locations the two extremes being represented
by the weak long dissymmetric and proton-out-centred HB of electrostatic nature
and by the very strong very short symmetric and proton-centred HB
classifiable as a true 3-center-4-electron covalent bond
The driving variable able to transform strong into weak HBs is dimensionally a free enthalpy corresponding to the difference between the Proton Affinities (PA) or related Acid-Base Dissociation Constants (pKa) of the Donor and Acceptor moieties
These rules have been verified beyond any reasonable doubt for the Conventional HBs of the following classification
Provisional Conclusions and New ControlsProvisional Conclusions and New Controls
We have so far established a sound set of empirical rules which include A full classification of all existing HBs A full classification of all strong HBs (The Chemical Leitmotifs) A plausible correlation between HB strengths and acid-base properties of the interacting molecules (The PApKa Equalization Principle)
To confirm this last point we have undertaken two years ago
a new research program aimed at assessing the Full Validity of the PApKa Equalization Principle
by comparing extended tables of pKa values arranged for chemical classes
withthe corresponding CSD-derived HB geometries
Hundreds of pKa were collected and more than 11000 crystal structures examined
The pThe pKKa Slide Rulea Slide Rule
It is a tool for the graphical evaluation of the difference
pKa = pKAH(DH) - pKBH+(AH+)
HB Acceptors on the left and HB Donors on the right
pKa values given for chemical class
Results expected
ΔpKagtgt0 DHmiddotmiddotmiddotmiddotA weak amp neutral
ΔpKa asymp 0 DmiddotmiddotmiddotHmiddotmiddotmiddotA strong amp
centeredΔpKa ltlt0DmiddotmiddotmiddotmiddotHA+ weak amp charged
pKa ranges of organic compounds
C-H acids -11 ltpKalt 53
Other Donors -1 ltpKalt 40
Acceptors -12 ltpKalt 16
All -15 ltpKalt 53
Water 0 ltpKalt 14
50
-10
0
10
20
30
40
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
ALDEHYDES
ETHERSALCOHOLS
AMIDES
NITRILES
ANILINES
CF3-SO3H
HClO4HI
HBrHCl
H2SO4
HSO4
HNO3
HBF4
H3PO4
H2PO4
HPO42
HF HNO2
HNNN
NH2OHH2CO3
HCO3
H2S
HS-
HCN H3BO3
H2BO3
H4SiO4
H2O2
HO
HSCN
H-H
SULFONICACIDS
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
OXIMES
ALCOHOLS
THIOLES
HB ACCEPTORS (A)pK BH+
HB DONORS (D-H)pK AH
C-H ACIDS pK AH
BE
TT
ER
HB
AC
CE
PT
OR
BE
TT
ER
BA
SE
BE
TT
ER
HB
DO
NO
R
BE
TT
ER
AC
ID
N-OXIDES
AMIDINES
UREA
THIOUREA
BARBITURICURIC ACID
MONO DIPHOSPHINES
TRIPHOSPHINES
TRINITROANILINES
AMINES
ANILINES
MONO DINITROANILINES
AMIDES
CARBOXYLIC ACIDS
HALOGENOANILINES
AZOCOMPS
TRINITROANILINES
PROTONSPONGES
ACIDSESTERS
H2O
H2O
MONODINITROANILINES
KETONES
SULFIDES
HALOGENCARB ACIDS
TRINITROPHENOLS
ENOLS
MONO DINITROPHENOLS
PHENOLSNAPHTHOLS
HALOGENOPHENOLS
HALOGENOALCOHOLS
SULFOXIDES
(NC)5-CYCLO
PENTADIENE
(NC)3CH
(O2N)2=CH2
HCCHNC-CH3
CH3-CO-CH3INDENE
O2N-CH3
(NC)2=CH2
(O2N)3CH
H2C=CH2
C6H6
CH4
CYCLOPENTADIENE
CYCLOPROPENE
Ar3CH
Ar2=CH2
Ar-CH3
NITROCOMPS
SELENOXIDES
AZOLES
AZINESDIAZINES
AMINES
Cl5-PHENOL
CH3-CH3
(CH3)3CH
NH3
NH3
51
53
51
53
Chemical Leitmotifs and PApChemical Leitmotifs and PApKKaa Equalization Rules Equalization Rules RAHB RAHB cannot be treated by pKa equalization methods because π-delocalization
modifies the pKarsquos of the donor and acceptor moieties (+)CAHB is a true proton transfer from an acid (HB donor) to a base (HB acceptor)
RndashDndashHAndashRrsquo Rndash12DH+A12ndashndashRrsquo RndashDHndashA+ndashRrsquoΔpKa = pKAH(RDH) pKBH+(RrsquoA)
()CAHB is a proton sharing between two acids (HB donors)
RndashDndashHDrsquondashRrsquo [RDHDrsquoRrsquo] RDHDrsquoRrsquoΔpKa = pKAH(RDH) pKAH(RDH)
(+)CAHB is a proton sharing between two bases (HB acceptors)
R+AHArsquoRrsquo [RAHArsquoRrsquo]+ RAHArsquo+RrsquoΔpKa = pKBH+(RA) pKBH+(RrsquoArsquo)
Whenever () and (+)CAHBs are both homonuclear (D = Drsquo or A = Arsquo) and
homomolecular (R = Rrsquo) the matching condition ΔpKa= 0 will hold irrespective of the
actual pKarsquos of the two interacting moieties All HBs formed will be strong
Some Famous HBsSome Famous HBs
The NThe NHmiddotmiddotmiddotOOHmiddotmiddotmiddotOOHmiddotmiddotmiddotN System over the Full HmiddotmiddotmiddotN System over the Full ppKKaa Range Range
When evaluated from the pKa slide rule the total pKa range is extremely wide
ndash30 pa 60 So far we have been able to shown that the pKa equalization rule certainly holds in
a restricted interval around zero The problem is now Does this rule hold in the full pKa range
We will try to prove that by a full analysis the N-HmiddotmiddotmiddotOO-HmiddotmiddotmiddotN system
Procedure In a first CSD search functional groups of known pKa value and more frequently
implied in NHmiddotmiddotmiddotOOHmiddotmiddotmiddotN bonds were identified Finally 10 classes of donors and 11 of acceptors were selected and the search restarted for each separate donor-acceptor group Altogether 9078 different bonds were analyzed (4364 NHmiddotmiddotmiddotO 2289 OHmiddotmiddotmiddotN and
2425 OmiddotmiddotmiddotHN+) For each bond the NmiddotmiddotmiddotO distances were evaluated as dNH + dHO to account for the
N-H-O angle and for each group the shortest and average distances [dNmiddotmiddotmiddotO (min)
and dNmiddotmiddotmiddotO (mean)] were registered
These values were compared (see next slide) with the acid-base features of the donors (pKAH range) acceptors (pKBH+ range) and with their combinations
(pKa range)
pKa large amp positive
pKa largeamp negative
Increasing Acidity of the Protonated A H+ Acceptor Increasing Basicity of the A Acceptor
ppKKaa versusversus HB Geometry Correlation - Conclusions HB Geometry Correlation - Conclusions The PApKa Equalization Principle is therefore fully confirmed in its two forms All strong HBs correspond to very small pKa values
pKa values modulate the HB strength over the full pKa range These conclusions are of great practical importance in at least two respects pKa is definitively established as the driving force which controls the HB
strength by modulating the HB covalent contribution It is definitively established that an accurate analysis of structural crystal data
leads to the same conclusions suggested but never proved on a general base by thermodynamic and spectroscopic methods
References Huyskens and Zeegers-Huyskens 1964 Zeegers-Huyskens 1986 1988 Ault and Pimentel 1975 Ratajczak and Sobczyk 1969 Sobczyk et al 1982 Barnes 1983 Kebarle et al 1974-1979 Meot-Ner (Mautner) et al
1984-1988
Towards a General HB TheoryTowards a General HB Theory
The results so far obtained are not a True HB Theory but rather a Set of Empirical Rules (or an Empirical Natural Law) that is a great collection of HB experimental data neatly organized in tables which all together represent a General Taxonomy of the HB Phenomenon exactly as the Carl Linnaeusrsquo classification of plants A scientific theory is something different It is the casting of the empirical natural law into the frame of a theory which is more fundamental down to the reductionistic chain of the scientific disciplines For instance the kinetic gas theory is the casting of the empirical gas laws (the empirical natural law) into Newtonrsquos classical mechanics
How to make a HB TheoryHow to make a HB Theory
HB Properties = FF (HB Driving Variable)where
HB Driving Variable = PApKa and FF = Transition-State Theory
The Transition-State HB TheoryThe Transition-State HB Theory(Gilli et al JACS 2002 2005 Gilli et al J Mol Struct 2006)
Though it has taken us more than 12 years to develop it
the basic idea is very simpleAny DndashHmiddotmiddotmiddotA bond can be considered as a chemical reaction which is
bimolecular in both directions and proceeds via transition-state (TS) formation
AndashB + C AmiddotmiddotmiddotBmiddotmiddotmiddotC A + BndashCDndashHmiddotmiddotmiddotA DmiddotmiddotmiddotHmiddotmiddotmiddotA DmiddotmiddotmiddotHndashA
Changes of nomenclatureReaction Pathway PTPathwayActivation Energy DaggerE PTBarrierReaction Energy Er PApKa Transition State (TS) PTTS
Reaction Coordinate RC=[d(DH)ndashd(AH)] Experimentals Variable-Temperature X-allographyCalculations DFTEmulated PTPathwaysInterpretation Marcus Rate-Equilibrium Theory LefflerHammond Postulate
AcknowledgmentsAcknowledgments I have to thank my direct coworkers without whose help this work could have not been accomplished
Valerio BERTOLASI Paola GILLI
Valeria FERRETTI Loretta PRETTO
and the scientific institutions which made available to us the databases without which this work could not even be started
CCDCCambridge Crystallographic
Data Centrefor the use of the
Cambridge Structural Database
NIST National Institute of Standards and
Technologyfor the use of the
NIST Chemistry WebBook
The OThe OHO RAHBsHO RAHBs
Very interesting Class of Strong HBs Different lengths of the resonant spacer Rn
(n = 1 3 5 7) The HBs formed were all much stronger than normal (non-resonant) OHO bonds withd(OO)INTRA =
239-255 Aringd(OO)INTER =
246-265 Aring
R1-RAHBR5-RAHB
24256 Aring
N
N
O M e
N
N
OM e
M eM e
H
lt 257 gt1 Aring
P
O H
OO
O H
H P
O H
OO
O H
H
R3-RAHB
O OH
237-255 Aring
262-267 Aring
O
O H O
OH
262-270 Aring
O
O
H
O
O H
R7-RAHB
24462 Aring
NOO
OO
M eM e
H
OOH
O
O
H
CARBOXYLIC ACIDS
DIBENZOYLMETHANE ENOLS
CYCLOHEXANEDIONE ENOLS
PHOPHORIC ACID
A Model for RAHB Electrostatic or CovalentA Model for RAHB Electrostatic or Covalent
At first (JACS 1989) we suggested a RAHB Electrostatic Model but it became rapidly evident that an efficient RAHB treatment would require a Covalent Model
All hell broke loose because as we discovered with surprise the concept itself of covalent HB had been banned some twenty years before and substituted by the acritical but more comfortable Simple Electrostatic Paradigm RAHB seriously risked to became a kind of bizarre covalent hypothesis
I must thank George A Jeffrey with his inimitable unbiased and skeptical style if RAHB was not immediately cast aside by the scientific establishment but started to be quoted in important books and reviews during the lsquo90ties
A RAHB Electrostatic ModelA RAHB Electrostatic Model A RAHB Covalent ModelA RAHB Covalent Model
Starting Again The Purely Empirical ApproachStarting Again The Purely Empirical Approach Fortunately we were realistic enough not to try to confute the Electrostatic
Paradigm On the other hand it was perfectly useless because too deeply rooted in the Weltanschaung of so many important and self-confident scientists
I have already given a short critical account of the very nature of these scientific paradigms at the ECM-2000 of Nancy based on the ideas of Thomas S Kuhn (The Structure of Scientific Revolutions The University of Chicago 1962 and 1970)
Anyway to get out of this impasse at the beginning of 1993 we decided to change approach and to restart to investigate the O-HO bond problem from the very beginning by adopting a purely empirical strategy
(i) suspend any previous ideas on the electrostatic or covalent nature of the HB (ii) define the OHmiddotmiddotmiddotO bond as a simple topological structure where a H atom is connected to two or more oxygen atoms(iii) collect all crystal structures having OHmiddotmiddotmiddotO bonds with d(OmiddotmiddotmiddotO) 270 Aring(iv) collect all available IR (O-H) and NMR (H) data of H-bonded protons(v) collect all available HB energy data from thermodynamic measurements in gas phase and non-polar solvents(vi) try to infer a conclusion on the very nature of the OHmiddotmiddotmiddotO bond from the ensemble of the data collected
A Full Classification of Strong HBsA Full Classification of Strong HBs
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs)CHARGE - ASSISTED HBs
PENTACHLOROPHENOL - p-TOLUIDINE
pKa = -070
12
12
N
CH3
O
ClCl
Cl
Cl
Cl
H25062 AringCL 1 (+ndash)CAHB SHB VSHB
Double Charge-Assisted HBDirect Acid-Base PApKa Matching
CL 2 (ndash)CAHB SHB VSHBNegative Charge-Assisted HB
Acid-Base PApKa Matching by Proton Loss R
OOH
R
O O24371 Aring
CARBOXYLIC ACID - CARBOXYLATE
CL 3 (+)CAHB SHB VSHBPositive Charge-Assisted HB
Acid-Base PApKa Matching by Proton Gain
O
HH H
O
HH
24303 Aring
WATER - HYDRONIUM
-BOND POLARIZATION - ASSISTED HBs
237-255 Aring
O OH
ArAr
DIBENZOYLMETHANE ENOLS
CL 4 RAHB SHB VSHB Resonance-Assisted or -Cooperative HB
PApKa Matching by -Conjugated-Bond Polarization
27501 Aring
OO
O
O O
WATER
CL 5 PAHB MHBPolarization-Assisted or -Cooperative HB(Partial) PApKa Matching by -Bond Polarization
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs) The most interesting aspect of a HB classification based on HB strength is that strong HBs belong only to a small number of chemical schemes that we have called Chemical Leitmotifs
The Alchemic Piper plays the Five Magic Tunes that make any Hydrogen Bond stronger The Chemical Leitmotifs
Symmetry and Covalency (1)Symmetry and Covalency (1)The covalent nature of the strong OHmiddotmiddotmiddotO bond was assessed by interpreting the
experimental results in terms of the Coulsonrsquos VB formalismWe cannot measure covalency but can evaluate molecular symmetry the
Coulsonrsquos model being the algorithm able to translate one concept into the other
In fact total symmetry across the HB implies energy equivalence between the two covalent VB forms ie E(ΨCOV1) = E(ΨCOV2) which is just the situation
associated with formation of the covalent HB
E E
NCT
CT
CTNCT
COV2
IONIC
COV1
IONIC
COV1 COV2
NCT
NCT
(a) Electrostatic HB (b) Covalent HB
Symmetry and Covalency (2)Symmetry and Covalency (2)
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 1
(+-)CAHBDouble Charge-Assisted HB
Direct Acid-Base PApKa Matching
R12DH+A12R
The role played by the PApKa equalization in HB strengthening
is self-evident for the (+-)CAHB chemical leitmotif
RDHARrsquo R12DH+A12Rrsquo RDHA+Rrsquo
which collects by definition all strong HBs formed by the acid-base pairs with a pKa matching within say ndash3 divide 3 pKa units
But what about the other leitmotifs Can we prove that
all chemical leitmotifs are simple artificesthat molecules can use to obliterate the normally
very large pKa between HB donor and acceptor atoms
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 2(-)CAHB
Negative Charge-Assisted HBAcid-Base PApKa Matching
by Proton Loss[R-DHA-R]-
Chemical Leitmotif 3(+)CAHB
Positive Charge-Assisted HBAcid-Base PApKa Matching
by Proton Gain[R-DHA-R]+
2II
2III
2IIa
2IIb
2IIIb
2IIIa
2VIa
pKa = pKAH(HO-H)-pKAH(HO-H) = 157 - 157 = 0
pKa = pKBH(H2O-H+)-pKBH(H2O-H
+) = -17 + 17 = 0
pKAH(HO-H) = 157
pKBH(H2O-H+) = -17
H
O H
H
O
H
(ndash)CAHB pKa = 00
VERYSTRONG~ 25-30 kcalmol
(+)CAHB pKa = 00
VERYSTRONG ~ 25-31 kcalmol
pKa = 175
OHB
WEAK ~ 4- 5kcalmol
ndash H+
+ H+
H
O H O
H
H
O H O
H
H
OHO
H
H
O
H
H
H
O
H
H
O
H
H
O
H
H H
O
H
H
H
O
H
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 4RAHB
Resonance-Assisted or -Bond Cooperative HBPApKa Matching by -Conjugated-Bond Polarization
R-D-HA=R R=DH-A-R
pKAH(RO-H) = 1518
pKBH(R2C=O-H+) = -(67)
O OH
O H O
R
R
R
Rn-RAHB pKa = ~ 21-25
WEAK ~ 4- 5kcalmol
EKO O
H
KEOO
H
pKa = 00
STRONG ~ 15-22 kcalmol
2IV
2IVa
2IVb
2VIb
OHB
The HB Empirical RulesThe HB Empirical Rules
The empirical analysis of experimental data joined with homeopathic doses of VB theory leads us to formulate two important HB Empirical Rules which have been called elsewhere ECHBM (Electrostatic-Covalent HB Model Gilli amp Gilli J Mol Struct 2000) and can be summarized as follows
Any given D-HA system may form HBs in a wide range of strengths lengths symmetries and proton locations the two extremes being represented
by the weak long dissymmetric and proton-out-centred HB of electrostatic nature
and by the very strong very short symmetric and proton-centred HB
classifiable as a true 3-center-4-electron covalent bond
The driving variable able to transform strong into weak HBs is dimensionally a free enthalpy corresponding to the difference between the Proton Affinities (PA) or related Acid-Base Dissociation Constants (pKa) of the Donor and Acceptor moieties
These rules have been verified beyond any reasonable doubt for the Conventional HBs of the following classification
Provisional Conclusions and New ControlsProvisional Conclusions and New Controls
We have so far established a sound set of empirical rules which include A full classification of all existing HBs A full classification of all strong HBs (The Chemical Leitmotifs) A plausible correlation between HB strengths and acid-base properties of the interacting molecules (The PApKa Equalization Principle)
To confirm this last point we have undertaken two years ago
a new research program aimed at assessing the Full Validity of the PApKa Equalization Principle
by comparing extended tables of pKa values arranged for chemical classes
withthe corresponding CSD-derived HB geometries
Hundreds of pKa were collected and more than 11000 crystal structures examined
The pThe pKKa Slide Rulea Slide Rule
It is a tool for the graphical evaluation of the difference
pKa = pKAH(DH) - pKBH+(AH+)
HB Acceptors on the left and HB Donors on the right
pKa values given for chemical class
Results expected
ΔpKagtgt0 DHmiddotmiddotmiddotmiddotA weak amp neutral
ΔpKa asymp 0 DmiddotmiddotmiddotHmiddotmiddotmiddotA strong amp
centeredΔpKa ltlt0DmiddotmiddotmiddotmiddotHA+ weak amp charged
pKa ranges of organic compounds
C-H acids -11 ltpKalt 53
Other Donors -1 ltpKalt 40
Acceptors -12 ltpKalt 16
All -15 ltpKalt 53
Water 0 ltpKalt 14
50
-10
0
10
20
30
40
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
ALDEHYDES
ETHERSALCOHOLS
AMIDES
NITRILES
ANILINES
CF3-SO3H
HClO4HI
HBrHCl
H2SO4
HSO4
HNO3
HBF4
H3PO4
H2PO4
HPO42
HF HNO2
HNNN
NH2OHH2CO3
HCO3
H2S
HS-
HCN H3BO3
H2BO3
H4SiO4
H2O2
HO
HSCN
H-H
SULFONICACIDS
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
OXIMES
ALCOHOLS
THIOLES
HB ACCEPTORS (A)pK BH+
HB DONORS (D-H)pK AH
C-H ACIDS pK AH
BE
TT
ER
HB
AC
CE
PT
OR
BE
TT
ER
BA
SE
BE
TT
ER
HB
DO
NO
R
BE
TT
ER
AC
ID
N-OXIDES
AMIDINES
UREA
THIOUREA
BARBITURICURIC ACID
MONO DIPHOSPHINES
TRIPHOSPHINES
TRINITROANILINES
AMINES
ANILINES
MONO DINITROANILINES
AMIDES
CARBOXYLIC ACIDS
HALOGENOANILINES
AZOCOMPS
TRINITROANILINES
PROTONSPONGES
ACIDSESTERS
H2O
H2O
MONODINITROANILINES
KETONES
SULFIDES
HALOGENCARB ACIDS
TRINITROPHENOLS
ENOLS
MONO DINITROPHENOLS
PHENOLSNAPHTHOLS
HALOGENOPHENOLS
HALOGENOALCOHOLS
SULFOXIDES
(NC)5-CYCLO
PENTADIENE
(NC)3CH
(O2N)2=CH2
HCCHNC-CH3
CH3-CO-CH3INDENE
O2N-CH3
(NC)2=CH2
(O2N)3CH
H2C=CH2
C6H6
CH4
CYCLOPENTADIENE
CYCLOPROPENE
Ar3CH
Ar2=CH2
Ar-CH3
NITROCOMPS
SELENOXIDES
AZOLES
AZINESDIAZINES
AMINES
Cl5-PHENOL
CH3-CH3
(CH3)3CH
NH3
NH3
51
53
51
53
Chemical Leitmotifs and PApChemical Leitmotifs and PApKKaa Equalization Rules Equalization Rules RAHB RAHB cannot be treated by pKa equalization methods because π-delocalization
modifies the pKarsquos of the donor and acceptor moieties (+)CAHB is a true proton transfer from an acid (HB donor) to a base (HB acceptor)
RndashDndashHAndashRrsquo Rndash12DH+A12ndashndashRrsquo RndashDHndashA+ndashRrsquoΔpKa = pKAH(RDH) pKBH+(RrsquoA)
()CAHB is a proton sharing between two acids (HB donors)
RndashDndashHDrsquondashRrsquo [RDHDrsquoRrsquo] RDHDrsquoRrsquoΔpKa = pKAH(RDH) pKAH(RDH)
(+)CAHB is a proton sharing between two bases (HB acceptors)
R+AHArsquoRrsquo [RAHArsquoRrsquo]+ RAHArsquo+RrsquoΔpKa = pKBH+(RA) pKBH+(RrsquoArsquo)
Whenever () and (+)CAHBs are both homonuclear (D = Drsquo or A = Arsquo) and
homomolecular (R = Rrsquo) the matching condition ΔpKa= 0 will hold irrespective of the
actual pKarsquos of the two interacting moieties All HBs formed will be strong
Some Famous HBsSome Famous HBs
The NThe NHmiddotmiddotmiddotOOHmiddotmiddotmiddotOOHmiddotmiddotmiddotN System over the Full HmiddotmiddotmiddotN System over the Full ppKKaa Range Range
When evaluated from the pKa slide rule the total pKa range is extremely wide
ndash30 pa 60 So far we have been able to shown that the pKa equalization rule certainly holds in
a restricted interval around zero The problem is now Does this rule hold in the full pKa range
We will try to prove that by a full analysis the N-HmiddotmiddotmiddotOO-HmiddotmiddotmiddotN system
Procedure In a first CSD search functional groups of known pKa value and more frequently
implied in NHmiddotmiddotmiddotOOHmiddotmiddotmiddotN bonds were identified Finally 10 classes of donors and 11 of acceptors were selected and the search restarted for each separate donor-acceptor group Altogether 9078 different bonds were analyzed (4364 NHmiddotmiddotmiddotO 2289 OHmiddotmiddotmiddotN and
2425 OmiddotmiddotmiddotHN+) For each bond the NmiddotmiddotmiddotO distances were evaluated as dNH + dHO to account for the
N-H-O angle and for each group the shortest and average distances [dNmiddotmiddotmiddotO (min)
and dNmiddotmiddotmiddotO (mean)] were registered
These values were compared (see next slide) with the acid-base features of the donors (pKAH range) acceptors (pKBH+ range) and with their combinations
(pKa range)
pKa large amp positive
pKa largeamp negative
Increasing Acidity of the Protonated A H+ Acceptor Increasing Basicity of the A Acceptor
ppKKaa versusversus HB Geometry Correlation - Conclusions HB Geometry Correlation - Conclusions The PApKa Equalization Principle is therefore fully confirmed in its two forms All strong HBs correspond to very small pKa values
pKa values modulate the HB strength over the full pKa range These conclusions are of great practical importance in at least two respects pKa is definitively established as the driving force which controls the HB
strength by modulating the HB covalent contribution It is definitively established that an accurate analysis of structural crystal data
leads to the same conclusions suggested but never proved on a general base by thermodynamic and spectroscopic methods
References Huyskens and Zeegers-Huyskens 1964 Zeegers-Huyskens 1986 1988 Ault and Pimentel 1975 Ratajczak and Sobczyk 1969 Sobczyk et al 1982 Barnes 1983 Kebarle et al 1974-1979 Meot-Ner (Mautner) et al
1984-1988
Towards a General HB TheoryTowards a General HB Theory
The results so far obtained are not a True HB Theory but rather a Set of Empirical Rules (or an Empirical Natural Law) that is a great collection of HB experimental data neatly organized in tables which all together represent a General Taxonomy of the HB Phenomenon exactly as the Carl Linnaeusrsquo classification of plants A scientific theory is something different It is the casting of the empirical natural law into the frame of a theory which is more fundamental down to the reductionistic chain of the scientific disciplines For instance the kinetic gas theory is the casting of the empirical gas laws (the empirical natural law) into Newtonrsquos classical mechanics
How to make a HB TheoryHow to make a HB Theory
HB Properties = FF (HB Driving Variable)where
HB Driving Variable = PApKa and FF = Transition-State Theory
The Transition-State HB TheoryThe Transition-State HB Theory(Gilli et al JACS 2002 2005 Gilli et al J Mol Struct 2006)
Though it has taken us more than 12 years to develop it
the basic idea is very simpleAny DndashHmiddotmiddotmiddotA bond can be considered as a chemical reaction which is
bimolecular in both directions and proceeds via transition-state (TS) formation
AndashB + C AmiddotmiddotmiddotBmiddotmiddotmiddotC A + BndashCDndashHmiddotmiddotmiddotA DmiddotmiddotmiddotHmiddotmiddotmiddotA DmiddotmiddotmiddotHndashA
Changes of nomenclatureReaction Pathway PTPathwayActivation Energy DaggerE PTBarrierReaction Energy Er PApKa Transition State (TS) PTTS
Reaction Coordinate RC=[d(DH)ndashd(AH)] Experimentals Variable-Temperature X-allographyCalculations DFTEmulated PTPathwaysInterpretation Marcus Rate-Equilibrium Theory LefflerHammond Postulate
AcknowledgmentsAcknowledgments I have to thank my direct coworkers without whose help this work could have not been accomplished
Valerio BERTOLASI Paola GILLI
Valeria FERRETTI Loretta PRETTO
and the scientific institutions which made available to us the databases without which this work could not even be started
CCDCCambridge Crystallographic
Data Centrefor the use of the
Cambridge Structural Database
NIST National Institute of Standards and
Technologyfor the use of the
NIST Chemistry WebBook
A Model for RAHB Electrostatic or CovalentA Model for RAHB Electrostatic or Covalent
At first (JACS 1989) we suggested a RAHB Electrostatic Model but it became rapidly evident that an efficient RAHB treatment would require a Covalent Model
All hell broke loose because as we discovered with surprise the concept itself of covalent HB had been banned some twenty years before and substituted by the acritical but more comfortable Simple Electrostatic Paradigm RAHB seriously risked to became a kind of bizarre covalent hypothesis
I must thank George A Jeffrey with his inimitable unbiased and skeptical style if RAHB was not immediately cast aside by the scientific establishment but started to be quoted in important books and reviews during the lsquo90ties
A RAHB Electrostatic ModelA RAHB Electrostatic Model A RAHB Covalent ModelA RAHB Covalent Model
Starting Again The Purely Empirical ApproachStarting Again The Purely Empirical Approach Fortunately we were realistic enough not to try to confute the Electrostatic
Paradigm On the other hand it was perfectly useless because too deeply rooted in the Weltanschaung of so many important and self-confident scientists
I have already given a short critical account of the very nature of these scientific paradigms at the ECM-2000 of Nancy based on the ideas of Thomas S Kuhn (The Structure of Scientific Revolutions The University of Chicago 1962 and 1970)
Anyway to get out of this impasse at the beginning of 1993 we decided to change approach and to restart to investigate the O-HO bond problem from the very beginning by adopting a purely empirical strategy
(i) suspend any previous ideas on the electrostatic or covalent nature of the HB (ii) define the OHmiddotmiddotmiddotO bond as a simple topological structure where a H atom is connected to two or more oxygen atoms(iii) collect all crystal structures having OHmiddotmiddotmiddotO bonds with d(OmiddotmiddotmiddotO) 270 Aring(iv) collect all available IR (O-H) and NMR (H) data of H-bonded protons(v) collect all available HB energy data from thermodynamic measurements in gas phase and non-polar solvents(vi) try to infer a conclusion on the very nature of the OHmiddotmiddotmiddotO bond from the ensemble of the data collected
A Full Classification of Strong HBsA Full Classification of Strong HBs
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs)CHARGE - ASSISTED HBs
PENTACHLOROPHENOL - p-TOLUIDINE
pKa = -070
12
12
N
CH3
O
ClCl
Cl
Cl
Cl
H25062 AringCL 1 (+ndash)CAHB SHB VSHB
Double Charge-Assisted HBDirect Acid-Base PApKa Matching
CL 2 (ndash)CAHB SHB VSHBNegative Charge-Assisted HB
Acid-Base PApKa Matching by Proton Loss R
OOH
R
O O24371 Aring
CARBOXYLIC ACID - CARBOXYLATE
CL 3 (+)CAHB SHB VSHBPositive Charge-Assisted HB
Acid-Base PApKa Matching by Proton Gain
O
HH H
O
HH
24303 Aring
WATER - HYDRONIUM
-BOND POLARIZATION - ASSISTED HBs
237-255 Aring
O OH
ArAr
DIBENZOYLMETHANE ENOLS
CL 4 RAHB SHB VSHB Resonance-Assisted or -Cooperative HB
PApKa Matching by -Conjugated-Bond Polarization
27501 Aring
OO
O
O O
WATER
CL 5 PAHB MHBPolarization-Assisted or -Cooperative HB(Partial) PApKa Matching by -Bond Polarization
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs) The most interesting aspect of a HB classification based on HB strength is that strong HBs belong only to a small number of chemical schemes that we have called Chemical Leitmotifs
The Alchemic Piper plays the Five Magic Tunes that make any Hydrogen Bond stronger The Chemical Leitmotifs
Symmetry and Covalency (1)Symmetry and Covalency (1)The covalent nature of the strong OHmiddotmiddotmiddotO bond was assessed by interpreting the
experimental results in terms of the Coulsonrsquos VB formalismWe cannot measure covalency but can evaluate molecular symmetry the
Coulsonrsquos model being the algorithm able to translate one concept into the other
In fact total symmetry across the HB implies energy equivalence between the two covalent VB forms ie E(ΨCOV1) = E(ΨCOV2) which is just the situation
associated with formation of the covalent HB
E E
NCT
CT
CTNCT
COV2
IONIC
COV1
IONIC
COV1 COV2
NCT
NCT
(a) Electrostatic HB (b) Covalent HB
Symmetry and Covalency (2)Symmetry and Covalency (2)
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 1
(+-)CAHBDouble Charge-Assisted HB
Direct Acid-Base PApKa Matching
R12DH+A12R
The role played by the PApKa equalization in HB strengthening
is self-evident for the (+-)CAHB chemical leitmotif
RDHARrsquo R12DH+A12Rrsquo RDHA+Rrsquo
which collects by definition all strong HBs formed by the acid-base pairs with a pKa matching within say ndash3 divide 3 pKa units
But what about the other leitmotifs Can we prove that
all chemical leitmotifs are simple artificesthat molecules can use to obliterate the normally
very large pKa between HB donor and acceptor atoms
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 2(-)CAHB
Negative Charge-Assisted HBAcid-Base PApKa Matching
by Proton Loss[R-DHA-R]-
Chemical Leitmotif 3(+)CAHB
Positive Charge-Assisted HBAcid-Base PApKa Matching
by Proton Gain[R-DHA-R]+
2II
2III
2IIa
2IIb
2IIIb
2IIIa
2VIa
pKa = pKAH(HO-H)-pKAH(HO-H) = 157 - 157 = 0
pKa = pKBH(H2O-H+)-pKBH(H2O-H
+) = -17 + 17 = 0
pKAH(HO-H) = 157
pKBH(H2O-H+) = -17
H
O H
H
O
H
(ndash)CAHB pKa = 00
VERYSTRONG~ 25-30 kcalmol
(+)CAHB pKa = 00
VERYSTRONG ~ 25-31 kcalmol
pKa = 175
OHB
WEAK ~ 4- 5kcalmol
ndash H+
+ H+
H
O H O
H
H
O H O
H
H
OHO
H
H
O
H
H
H
O
H
H
O
H
H
O
H
H H
O
H
H
H
O
H
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 4RAHB
Resonance-Assisted or -Bond Cooperative HBPApKa Matching by -Conjugated-Bond Polarization
R-D-HA=R R=DH-A-R
pKAH(RO-H) = 1518
pKBH(R2C=O-H+) = -(67)
O OH
O H O
R
R
R
Rn-RAHB pKa = ~ 21-25
WEAK ~ 4- 5kcalmol
EKO O
H
KEOO
H
pKa = 00
STRONG ~ 15-22 kcalmol
2IV
2IVa
2IVb
2VIb
OHB
The HB Empirical RulesThe HB Empirical Rules
The empirical analysis of experimental data joined with homeopathic doses of VB theory leads us to formulate two important HB Empirical Rules which have been called elsewhere ECHBM (Electrostatic-Covalent HB Model Gilli amp Gilli J Mol Struct 2000) and can be summarized as follows
Any given D-HA system may form HBs in a wide range of strengths lengths symmetries and proton locations the two extremes being represented
by the weak long dissymmetric and proton-out-centred HB of electrostatic nature
and by the very strong very short symmetric and proton-centred HB
classifiable as a true 3-center-4-electron covalent bond
The driving variable able to transform strong into weak HBs is dimensionally a free enthalpy corresponding to the difference between the Proton Affinities (PA) or related Acid-Base Dissociation Constants (pKa) of the Donor and Acceptor moieties
These rules have been verified beyond any reasonable doubt for the Conventional HBs of the following classification
Provisional Conclusions and New ControlsProvisional Conclusions and New Controls
We have so far established a sound set of empirical rules which include A full classification of all existing HBs A full classification of all strong HBs (The Chemical Leitmotifs) A plausible correlation between HB strengths and acid-base properties of the interacting molecules (The PApKa Equalization Principle)
To confirm this last point we have undertaken two years ago
a new research program aimed at assessing the Full Validity of the PApKa Equalization Principle
by comparing extended tables of pKa values arranged for chemical classes
withthe corresponding CSD-derived HB geometries
Hundreds of pKa were collected and more than 11000 crystal structures examined
The pThe pKKa Slide Rulea Slide Rule
It is a tool for the graphical evaluation of the difference
pKa = pKAH(DH) - pKBH+(AH+)
HB Acceptors on the left and HB Donors on the right
pKa values given for chemical class
Results expected
ΔpKagtgt0 DHmiddotmiddotmiddotmiddotA weak amp neutral
ΔpKa asymp 0 DmiddotmiddotmiddotHmiddotmiddotmiddotA strong amp
centeredΔpKa ltlt0DmiddotmiddotmiddotmiddotHA+ weak amp charged
pKa ranges of organic compounds
C-H acids -11 ltpKalt 53
Other Donors -1 ltpKalt 40
Acceptors -12 ltpKalt 16
All -15 ltpKalt 53
Water 0 ltpKalt 14
50
-10
0
10
20
30
40
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
ALDEHYDES
ETHERSALCOHOLS
AMIDES
NITRILES
ANILINES
CF3-SO3H
HClO4HI
HBrHCl
H2SO4
HSO4
HNO3
HBF4
H3PO4
H2PO4
HPO42
HF HNO2
HNNN
NH2OHH2CO3
HCO3
H2S
HS-
HCN H3BO3
H2BO3
H4SiO4
H2O2
HO
HSCN
H-H
SULFONICACIDS
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
OXIMES
ALCOHOLS
THIOLES
HB ACCEPTORS (A)pK BH+
HB DONORS (D-H)pK AH
C-H ACIDS pK AH
BE
TT
ER
HB
AC
CE
PT
OR
BE
TT
ER
BA
SE
BE
TT
ER
HB
DO
NO
R
BE
TT
ER
AC
ID
N-OXIDES
AMIDINES
UREA
THIOUREA
BARBITURICURIC ACID
MONO DIPHOSPHINES
TRIPHOSPHINES
TRINITROANILINES
AMINES
ANILINES
MONO DINITROANILINES
AMIDES
CARBOXYLIC ACIDS
HALOGENOANILINES
AZOCOMPS
TRINITROANILINES
PROTONSPONGES
ACIDSESTERS
H2O
H2O
MONODINITROANILINES
KETONES
SULFIDES
HALOGENCARB ACIDS
TRINITROPHENOLS
ENOLS
MONO DINITROPHENOLS
PHENOLSNAPHTHOLS
HALOGENOPHENOLS
HALOGENOALCOHOLS
SULFOXIDES
(NC)5-CYCLO
PENTADIENE
(NC)3CH
(O2N)2=CH2
HCCHNC-CH3
CH3-CO-CH3INDENE
O2N-CH3
(NC)2=CH2
(O2N)3CH
H2C=CH2
C6H6
CH4
CYCLOPENTADIENE
CYCLOPROPENE
Ar3CH
Ar2=CH2
Ar-CH3
NITROCOMPS
SELENOXIDES
AZOLES
AZINESDIAZINES
AMINES
Cl5-PHENOL
CH3-CH3
(CH3)3CH
NH3
NH3
51
53
51
53
Chemical Leitmotifs and PApChemical Leitmotifs and PApKKaa Equalization Rules Equalization Rules RAHB RAHB cannot be treated by pKa equalization methods because π-delocalization
modifies the pKarsquos of the donor and acceptor moieties (+)CAHB is a true proton transfer from an acid (HB donor) to a base (HB acceptor)
RndashDndashHAndashRrsquo Rndash12DH+A12ndashndashRrsquo RndashDHndashA+ndashRrsquoΔpKa = pKAH(RDH) pKBH+(RrsquoA)
()CAHB is a proton sharing between two acids (HB donors)
RndashDndashHDrsquondashRrsquo [RDHDrsquoRrsquo] RDHDrsquoRrsquoΔpKa = pKAH(RDH) pKAH(RDH)
(+)CAHB is a proton sharing between two bases (HB acceptors)
R+AHArsquoRrsquo [RAHArsquoRrsquo]+ RAHArsquo+RrsquoΔpKa = pKBH+(RA) pKBH+(RrsquoArsquo)
Whenever () and (+)CAHBs are both homonuclear (D = Drsquo or A = Arsquo) and
homomolecular (R = Rrsquo) the matching condition ΔpKa= 0 will hold irrespective of the
actual pKarsquos of the two interacting moieties All HBs formed will be strong
Some Famous HBsSome Famous HBs
The NThe NHmiddotmiddotmiddotOOHmiddotmiddotmiddotOOHmiddotmiddotmiddotN System over the Full HmiddotmiddotmiddotN System over the Full ppKKaa Range Range
When evaluated from the pKa slide rule the total pKa range is extremely wide
ndash30 pa 60 So far we have been able to shown that the pKa equalization rule certainly holds in
a restricted interval around zero The problem is now Does this rule hold in the full pKa range
We will try to prove that by a full analysis the N-HmiddotmiddotmiddotOO-HmiddotmiddotmiddotN system
Procedure In a first CSD search functional groups of known pKa value and more frequently
implied in NHmiddotmiddotmiddotOOHmiddotmiddotmiddotN bonds were identified Finally 10 classes of donors and 11 of acceptors were selected and the search restarted for each separate donor-acceptor group Altogether 9078 different bonds were analyzed (4364 NHmiddotmiddotmiddotO 2289 OHmiddotmiddotmiddotN and
2425 OmiddotmiddotmiddotHN+) For each bond the NmiddotmiddotmiddotO distances were evaluated as dNH + dHO to account for the
N-H-O angle and for each group the shortest and average distances [dNmiddotmiddotmiddotO (min)
and dNmiddotmiddotmiddotO (mean)] were registered
These values were compared (see next slide) with the acid-base features of the donors (pKAH range) acceptors (pKBH+ range) and with their combinations
(pKa range)
pKa large amp positive
pKa largeamp negative
Increasing Acidity of the Protonated A H+ Acceptor Increasing Basicity of the A Acceptor
ppKKaa versusversus HB Geometry Correlation - Conclusions HB Geometry Correlation - Conclusions The PApKa Equalization Principle is therefore fully confirmed in its two forms All strong HBs correspond to very small pKa values
pKa values modulate the HB strength over the full pKa range These conclusions are of great practical importance in at least two respects pKa is definitively established as the driving force which controls the HB
strength by modulating the HB covalent contribution It is definitively established that an accurate analysis of structural crystal data
leads to the same conclusions suggested but never proved on a general base by thermodynamic and spectroscopic methods
References Huyskens and Zeegers-Huyskens 1964 Zeegers-Huyskens 1986 1988 Ault and Pimentel 1975 Ratajczak and Sobczyk 1969 Sobczyk et al 1982 Barnes 1983 Kebarle et al 1974-1979 Meot-Ner (Mautner) et al
1984-1988
Towards a General HB TheoryTowards a General HB Theory
The results so far obtained are not a True HB Theory but rather a Set of Empirical Rules (or an Empirical Natural Law) that is a great collection of HB experimental data neatly organized in tables which all together represent a General Taxonomy of the HB Phenomenon exactly as the Carl Linnaeusrsquo classification of plants A scientific theory is something different It is the casting of the empirical natural law into the frame of a theory which is more fundamental down to the reductionistic chain of the scientific disciplines For instance the kinetic gas theory is the casting of the empirical gas laws (the empirical natural law) into Newtonrsquos classical mechanics
How to make a HB TheoryHow to make a HB Theory
HB Properties = FF (HB Driving Variable)where
HB Driving Variable = PApKa and FF = Transition-State Theory
The Transition-State HB TheoryThe Transition-State HB Theory(Gilli et al JACS 2002 2005 Gilli et al J Mol Struct 2006)
Though it has taken us more than 12 years to develop it
the basic idea is very simpleAny DndashHmiddotmiddotmiddotA bond can be considered as a chemical reaction which is
bimolecular in both directions and proceeds via transition-state (TS) formation
AndashB + C AmiddotmiddotmiddotBmiddotmiddotmiddotC A + BndashCDndashHmiddotmiddotmiddotA DmiddotmiddotmiddotHmiddotmiddotmiddotA DmiddotmiddotmiddotHndashA
Changes of nomenclatureReaction Pathway PTPathwayActivation Energy DaggerE PTBarrierReaction Energy Er PApKa Transition State (TS) PTTS
Reaction Coordinate RC=[d(DH)ndashd(AH)] Experimentals Variable-Temperature X-allographyCalculations DFTEmulated PTPathwaysInterpretation Marcus Rate-Equilibrium Theory LefflerHammond Postulate
AcknowledgmentsAcknowledgments I have to thank my direct coworkers without whose help this work could have not been accomplished
Valerio BERTOLASI Paola GILLI
Valeria FERRETTI Loretta PRETTO
and the scientific institutions which made available to us the databases without which this work could not even be started
CCDCCambridge Crystallographic
Data Centrefor the use of the
Cambridge Structural Database
NIST National Institute of Standards and
Technologyfor the use of the
NIST Chemistry WebBook
Starting Again The Purely Empirical ApproachStarting Again The Purely Empirical Approach Fortunately we were realistic enough not to try to confute the Electrostatic
Paradigm On the other hand it was perfectly useless because too deeply rooted in the Weltanschaung of so many important and self-confident scientists
I have already given a short critical account of the very nature of these scientific paradigms at the ECM-2000 of Nancy based on the ideas of Thomas S Kuhn (The Structure of Scientific Revolutions The University of Chicago 1962 and 1970)
Anyway to get out of this impasse at the beginning of 1993 we decided to change approach and to restart to investigate the O-HO bond problem from the very beginning by adopting a purely empirical strategy
(i) suspend any previous ideas on the electrostatic or covalent nature of the HB (ii) define the OHmiddotmiddotmiddotO bond as a simple topological structure where a H atom is connected to two or more oxygen atoms(iii) collect all crystal structures having OHmiddotmiddotmiddotO bonds with d(OmiddotmiddotmiddotO) 270 Aring(iv) collect all available IR (O-H) and NMR (H) data of H-bonded protons(v) collect all available HB energy data from thermodynamic measurements in gas phase and non-polar solvents(vi) try to infer a conclusion on the very nature of the OHmiddotmiddotmiddotO bond from the ensemble of the data collected
A Full Classification of Strong HBsA Full Classification of Strong HBs
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs)CHARGE - ASSISTED HBs
PENTACHLOROPHENOL - p-TOLUIDINE
pKa = -070
12
12
N
CH3
O
ClCl
Cl
Cl
Cl
H25062 AringCL 1 (+ndash)CAHB SHB VSHB
Double Charge-Assisted HBDirect Acid-Base PApKa Matching
CL 2 (ndash)CAHB SHB VSHBNegative Charge-Assisted HB
Acid-Base PApKa Matching by Proton Loss R
OOH
R
O O24371 Aring
CARBOXYLIC ACID - CARBOXYLATE
CL 3 (+)CAHB SHB VSHBPositive Charge-Assisted HB
Acid-Base PApKa Matching by Proton Gain
O
HH H
O
HH
24303 Aring
WATER - HYDRONIUM
-BOND POLARIZATION - ASSISTED HBs
237-255 Aring
O OH
ArAr
DIBENZOYLMETHANE ENOLS
CL 4 RAHB SHB VSHB Resonance-Assisted or -Cooperative HB
PApKa Matching by -Conjugated-Bond Polarization
27501 Aring
OO
O
O O
WATER
CL 5 PAHB MHBPolarization-Assisted or -Cooperative HB(Partial) PApKa Matching by -Bond Polarization
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs) The most interesting aspect of a HB classification based on HB strength is that strong HBs belong only to a small number of chemical schemes that we have called Chemical Leitmotifs
The Alchemic Piper plays the Five Magic Tunes that make any Hydrogen Bond stronger The Chemical Leitmotifs
Symmetry and Covalency (1)Symmetry and Covalency (1)The covalent nature of the strong OHmiddotmiddotmiddotO bond was assessed by interpreting the
experimental results in terms of the Coulsonrsquos VB formalismWe cannot measure covalency but can evaluate molecular symmetry the
Coulsonrsquos model being the algorithm able to translate one concept into the other
In fact total symmetry across the HB implies energy equivalence between the two covalent VB forms ie E(ΨCOV1) = E(ΨCOV2) which is just the situation
associated with formation of the covalent HB
E E
NCT
CT
CTNCT
COV2
IONIC
COV1
IONIC
COV1 COV2
NCT
NCT
(a) Electrostatic HB (b) Covalent HB
Symmetry and Covalency (2)Symmetry and Covalency (2)
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 1
(+-)CAHBDouble Charge-Assisted HB
Direct Acid-Base PApKa Matching
R12DH+A12R
The role played by the PApKa equalization in HB strengthening
is self-evident for the (+-)CAHB chemical leitmotif
RDHARrsquo R12DH+A12Rrsquo RDHA+Rrsquo
which collects by definition all strong HBs formed by the acid-base pairs with a pKa matching within say ndash3 divide 3 pKa units
But what about the other leitmotifs Can we prove that
all chemical leitmotifs are simple artificesthat molecules can use to obliterate the normally
very large pKa between HB donor and acceptor atoms
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 2(-)CAHB
Negative Charge-Assisted HBAcid-Base PApKa Matching
by Proton Loss[R-DHA-R]-
Chemical Leitmotif 3(+)CAHB
Positive Charge-Assisted HBAcid-Base PApKa Matching
by Proton Gain[R-DHA-R]+
2II
2III
2IIa
2IIb
2IIIb
2IIIa
2VIa
pKa = pKAH(HO-H)-pKAH(HO-H) = 157 - 157 = 0
pKa = pKBH(H2O-H+)-pKBH(H2O-H
+) = -17 + 17 = 0
pKAH(HO-H) = 157
pKBH(H2O-H+) = -17
H
O H
H
O
H
(ndash)CAHB pKa = 00
VERYSTRONG~ 25-30 kcalmol
(+)CAHB pKa = 00
VERYSTRONG ~ 25-31 kcalmol
pKa = 175
OHB
WEAK ~ 4- 5kcalmol
ndash H+
+ H+
H
O H O
H
H
O H O
H
H
OHO
H
H
O
H
H
H
O
H
H
O
H
H
O
H
H H
O
H
H
H
O
H
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 4RAHB
Resonance-Assisted or -Bond Cooperative HBPApKa Matching by -Conjugated-Bond Polarization
R-D-HA=R R=DH-A-R
pKAH(RO-H) = 1518
pKBH(R2C=O-H+) = -(67)
O OH
O H O
R
R
R
Rn-RAHB pKa = ~ 21-25
WEAK ~ 4- 5kcalmol
EKO O
H
KEOO
H
pKa = 00
STRONG ~ 15-22 kcalmol
2IV
2IVa
2IVb
2VIb
OHB
The HB Empirical RulesThe HB Empirical Rules
The empirical analysis of experimental data joined with homeopathic doses of VB theory leads us to formulate two important HB Empirical Rules which have been called elsewhere ECHBM (Electrostatic-Covalent HB Model Gilli amp Gilli J Mol Struct 2000) and can be summarized as follows
Any given D-HA system may form HBs in a wide range of strengths lengths symmetries and proton locations the two extremes being represented
by the weak long dissymmetric and proton-out-centred HB of electrostatic nature
and by the very strong very short symmetric and proton-centred HB
classifiable as a true 3-center-4-electron covalent bond
The driving variable able to transform strong into weak HBs is dimensionally a free enthalpy corresponding to the difference between the Proton Affinities (PA) or related Acid-Base Dissociation Constants (pKa) of the Donor and Acceptor moieties
These rules have been verified beyond any reasonable doubt for the Conventional HBs of the following classification
Provisional Conclusions and New ControlsProvisional Conclusions and New Controls
We have so far established a sound set of empirical rules which include A full classification of all existing HBs A full classification of all strong HBs (The Chemical Leitmotifs) A plausible correlation between HB strengths and acid-base properties of the interacting molecules (The PApKa Equalization Principle)
To confirm this last point we have undertaken two years ago
a new research program aimed at assessing the Full Validity of the PApKa Equalization Principle
by comparing extended tables of pKa values arranged for chemical classes
withthe corresponding CSD-derived HB geometries
Hundreds of pKa were collected and more than 11000 crystal structures examined
The pThe pKKa Slide Rulea Slide Rule
It is a tool for the graphical evaluation of the difference
pKa = pKAH(DH) - pKBH+(AH+)
HB Acceptors on the left and HB Donors on the right
pKa values given for chemical class
Results expected
ΔpKagtgt0 DHmiddotmiddotmiddotmiddotA weak amp neutral
ΔpKa asymp 0 DmiddotmiddotmiddotHmiddotmiddotmiddotA strong amp
centeredΔpKa ltlt0DmiddotmiddotmiddotmiddotHA+ weak amp charged
pKa ranges of organic compounds
C-H acids -11 ltpKalt 53
Other Donors -1 ltpKalt 40
Acceptors -12 ltpKalt 16
All -15 ltpKalt 53
Water 0 ltpKalt 14
50
-10
0
10
20
30
40
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
ALDEHYDES
ETHERSALCOHOLS
AMIDES
NITRILES
ANILINES
CF3-SO3H
HClO4HI
HBrHCl
H2SO4
HSO4
HNO3
HBF4
H3PO4
H2PO4
HPO42
HF HNO2
HNNN
NH2OHH2CO3
HCO3
H2S
HS-
HCN H3BO3
H2BO3
H4SiO4
H2O2
HO
HSCN
H-H
SULFONICACIDS
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
OXIMES
ALCOHOLS
THIOLES
HB ACCEPTORS (A)pK BH+
HB DONORS (D-H)pK AH
C-H ACIDS pK AH
BE
TT
ER
HB
AC
CE
PT
OR
BE
TT
ER
BA
SE
BE
TT
ER
HB
DO
NO
R
BE
TT
ER
AC
ID
N-OXIDES
AMIDINES
UREA
THIOUREA
BARBITURICURIC ACID
MONO DIPHOSPHINES
TRIPHOSPHINES
TRINITROANILINES
AMINES
ANILINES
MONO DINITROANILINES
AMIDES
CARBOXYLIC ACIDS
HALOGENOANILINES
AZOCOMPS
TRINITROANILINES
PROTONSPONGES
ACIDSESTERS
H2O
H2O
MONODINITROANILINES
KETONES
SULFIDES
HALOGENCARB ACIDS
TRINITROPHENOLS
ENOLS
MONO DINITROPHENOLS
PHENOLSNAPHTHOLS
HALOGENOPHENOLS
HALOGENOALCOHOLS
SULFOXIDES
(NC)5-CYCLO
PENTADIENE
(NC)3CH
(O2N)2=CH2
HCCHNC-CH3
CH3-CO-CH3INDENE
O2N-CH3
(NC)2=CH2
(O2N)3CH
H2C=CH2
C6H6
CH4
CYCLOPENTADIENE
CYCLOPROPENE
Ar3CH
Ar2=CH2
Ar-CH3
NITROCOMPS
SELENOXIDES
AZOLES
AZINESDIAZINES
AMINES
Cl5-PHENOL
CH3-CH3
(CH3)3CH
NH3
NH3
51
53
51
53
Chemical Leitmotifs and PApChemical Leitmotifs and PApKKaa Equalization Rules Equalization Rules RAHB RAHB cannot be treated by pKa equalization methods because π-delocalization
modifies the pKarsquos of the donor and acceptor moieties (+)CAHB is a true proton transfer from an acid (HB donor) to a base (HB acceptor)
RndashDndashHAndashRrsquo Rndash12DH+A12ndashndashRrsquo RndashDHndashA+ndashRrsquoΔpKa = pKAH(RDH) pKBH+(RrsquoA)
()CAHB is a proton sharing between two acids (HB donors)
RndashDndashHDrsquondashRrsquo [RDHDrsquoRrsquo] RDHDrsquoRrsquoΔpKa = pKAH(RDH) pKAH(RDH)
(+)CAHB is a proton sharing between two bases (HB acceptors)
R+AHArsquoRrsquo [RAHArsquoRrsquo]+ RAHArsquo+RrsquoΔpKa = pKBH+(RA) pKBH+(RrsquoArsquo)
Whenever () and (+)CAHBs are both homonuclear (D = Drsquo or A = Arsquo) and
homomolecular (R = Rrsquo) the matching condition ΔpKa= 0 will hold irrespective of the
actual pKarsquos of the two interacting moieties All HBs formed will be strong
Some Famous HBsSome Famous HBs
The NThe NHmiddotmiddotmiddotOOHmiddotmiddotmiddotOOHmiddotmiddotmiddotN System over the Full HmiddotmiddotmiddotN System over the Full ppKKaa Range Range
When evaluated from the pKa slide rule the total pKa range is extremely wide
ndash30 pa 60 So far we have been able to shown that the pKa equalization rule certainly holds in
a restricted interval around zero The problem is now Does this rule hold in the full pKa range
We will try to prove that by a full analysis the N-HmiddotmiddotmiddotOO-HmiddotmiddotmiddotN system
Procedure In a first CSD search functional groups of known pKa value and more frequently
implied in NHmiddotmiddotmiddotOOHmiddotmiddotmiddotN bonds were identified Finally 10 classes of donors and 11 of acceptors were selected and the search restarted for each separate donor-acceptor group Altogether 9078 different bonds were analyzed (4364 NHmiddotmiddotmiddotO 2289 OHmiddotmiddotmiddotN and
2425 OmiddotmiddotmiddotHN+) For each bond the NmiddotmiddotmiddotO distances were evaluated as dNH + dHO to account for the
N-H-O angle and for each group the shortest and average distances [dNmiddotmiddotmiddotO (min)
and dNmiddotmiddotmiddotO (mean)] were registered
These values were compared (see next slide) with the acid-base features of the donors (pKAH range) acceptors (pKBH+ range) and with their combinations
(pKa range)
pKa large amp positive
pKa largeamp negative
Increasing Acidity of the Protonated A H+ Acceptor Increasing Basicity of the A Acceptor
ppKKaa versusversus HB Geometry Correlation - Conclusions HB Geometry Correlation - Conclusions The PApKa Equalization Principle is therefore fully confirmed in its two forms All strong HBs correspond to very small pKa values
pKa values modulate the HB strength over the full pKa range These conclusions are of great practical importance in at least two respects pKa is definitively established as the driving force which controls the HB
strength by modulating the HB covalent contribution It is definitively established that an accurate analysis of structural crystal data
leads to the same conclusions suggested but never proved on a general base by thermodynamic and spectroscopic methods
References Huyskens and Zeegers-Huyskens 1964 Zeegers-Huyskens 1986 1988 Ault and Pimentel 1975 Ratajczak and Sobczyk 1969 Sobczyk et al 1982 Barnes 1983 Kebarle et al 1974-1979 Meot-Ner (Mautner) et al
1984-1988
Towards a General HB TheoryTowards a General HB Theory
The results so far obtained are not a True HB Theory but rather a Set of Empirical Rules (or an Empirical Natural Law) that is a great collection of HB experimental data neatly organized in tables which all together represent a General Taxonomy of the HB Phenomenon exactly as the Carl Linnaeusrsquo classification of plants A scientific theory is something different It is the casting of the empirical natural law into the frame of a theory which is more fundamental down to the reductionistic chain of the scientific disciplines For instance the kinetic gas theory is the casting of the empirical gas laws (the empirical natural law) into Newtonrsquos classical mechanics
How to make a HB TheoryHow to make a HB Theory
HB Properties = FF (HB Driving Variable)where
HB Driving Variable = PApKa and FF = Transition-State Theory
The Transition-State HB TheoryThe Transition-State HB Theory(Gilli et al JACS 2002 2005 Gilli et al J Mol Struct 2006)
Though it has taken us more than 12 years to develop it
the basic idea is very simpleAny DndashHmiddotmiddotmiddotA bond can be considered as a chemical reaction which is
bimolecular in both directions and proceeds via transition-state (TS) formation
AndashB + C AmiddotmiddotmiddotBmiddotmiddotmiddotC A + BndashCDndashHmiddotmiddotmiddotA DmiddotmiddotmiddotHmiddotmiddotmiddotA DmiddotmiddotmiddotHndashA
Changes of nomenclatureReaction Pathway PTPathwayActivation Energy DaggerE PTBarrierReaction Energy Er PApKa Transition State (TS) PTTS
Reaction Coordinate RC=[d(DH)ndashd(AH)] Experimentals Variable-Temperature X-allographyCalculations DFTEmulated PTPathwaysInterpretation Marcus Rate-Equilibrium Theory LefflerHammond Postulate
AcknowledgmentsAcknowledgments I have to thank my direct coworkers without whose help this work could have not been accomplished
Valerio BERTOLASI Paola GILLI
Valeria FERRETTI Loretta PRETTO
and the scientific institutions which made available to us the databases without which this work could not even be started
CCDCCambridge Crystallographic
Data Centrefor the use of the
Cambridge Structural Database
NIST National Institute of Standards and
Technologyfor the use of the
NIST Chemistry WebBook
A Full Classification of Strong HBsA Full Classification of Strong HBs
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs)CHARGE - ASSISTED HBs
PENTACHLOROPHENOL - p-TOLUIDINE
pKa = -070
12
12
N
CH3
O
ClCl
Cl
Cl
Cl
H25062 AringCL 1 (+ndash)CAHB SHB VSHB
Double Charge-Assisted HBDirect Acid-Base PApKa Matching
CL 2 (ndash)CAHB SHB VSHBNegative Charge-Assisted HB
Acid-Base PApKa Matching by Proton Loss R
OOH
R
O O24371 Aring
CARBOXYLIC ACID - CARBOXYLATE
CL 3 (+)CAHB SHB VSHBPositive Charge-Assisted HB
Acid-Base PApKa Matching by Proton Gain
O
HH H
O
HH
24303 Aring
WATER - HYDRONIUM
-BOND POLARIZATION - ASSISTED HBs
237-255 Aring
O OH
ArAr
DIBENZOYLMETHANE ENOLS
CL 4 RAHB SHB VSHB Resonance-Assisted or -Cooperative HB
PApKa Matching by -Conjugated-Bond Polarization
27501 Aring
OO
O
O O
WATER
CL 5 PAHB MHBPolarization-Assisted or -Cooperative HB(Partial) PApKa Matching by -Bond Polarization
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs) The most interesting aspect of a HB classification based on HB strength is that strong HBs belong only to a small number of chemical schemes that we have called Chemical Leitmotifs
The Alchemic Piper plays the Five Magic Tunes that make any Hydrogen Bond stronger The Chemical Leitmotifs
Symmetry and Covalency (1)Symmetry and Covalency (1)The covalent nature of the strong OHmiddotmiddotmiddotO bond was assessed by interpreting the
experimental results in terms of the Coulsonrsquos VB formalismWe cannot measure covalency but can evaluate molecular symmetry the
Coulsonrsquos model being the algorithm able to translate one concept into the other
In fact total symmetry across the HB implies energy equivalence between the two covalent VB forms ie E(ΨCOV1) = E(ΨCOV2) which is just the situation
associated with formation of the covalent HB
E E
NCT
CT
CTNCT
COV2
IONIC
COV1
IONIC
COV1 COV2
NCT
NCT
(a) Electrostatic HB (b) Covalent HB
Symmetry and Covalency (2)Symmetry and Covalency (2)
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 1
(+-)CAHBDouble Charge-Assisted HB
Direct Acid-Base PApKa Matching
R12DH+A12R
The role played by the PApKa equalization in HB strengthening
is self-evident for the (+-)CAHB chemical leitmotif
RDHARrsquo R12DH+A12Rrsquo RDHA+Rrsquo
which collects by definition all strong HBs formed by the acid-base pairs with a pKa matching within say ndash3 divide 3 pKa units
But what about the other leitmotifs Can we prove that
all chemical leitmotifs are simple artificesthat molecules can use to obliterate the normally
very large pKa between HB donor and acceptor atoms
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 2(-)CAHB
Negative Charge-Assisted HBAcid-Base PApKa Matching
by Proton Loss[R-DHA-R]-
Chemical Leitmotif 3(+)CAHB
Positive Charge-Assisted HBAcid-Base PApKa Matching
by Proton Gain[R-DHA-R]+
2II
2III
2IIa
2IIb
2IIIb
2IIIa
2VIa
pKa = pKAH(HO-H)-pKAH(HO-H) = 157 - 157 = 0
pKa = pKBH(H2O-H+)-pKBH(H2O-H
+) = -17 + 17 = 0
pKAH(HO-H) = 157
pKBH(H2O-H+) = -17
H
O H
H
O
H
(ndash)CAHB pKa = 00
VERYSTRONG~ 25-30 kcalmol
(+)CAHB pKa = 00
VERYSTRONG ~ 25-31 kcalmol
pKa = 175
OHB
WEAK ~ 4- 5kcalmol
ndash H+
+ H+
H
O H O
H
H
O H O
H
H
OHO
H
H
O
H
H
H
O
H
H
O
H
H
O
H
H H
O
H
H
H
O
H
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 4RAHB
Resonance-Assisted or -Bond Cooperative HBPApKa Matching by -Conjugated-Bond Polarization
R-D-HA=R R=DH-A-R
pKAH(RO-H) = 1518
pKBH(R2C=O-H+) = -(67)
O OH
O H O
R
R
R
Rn-RAHB pKa = ~ 21-25
WEAK ~ 4- 5kcalmol
EKO O
H
KEOO
H
pKa = 00
STRONG ~ 15-22 kcalmol
2IV
2IVa
2IVb
2VIb
OHB
The HB Empirical RulesThe HB Empirical Rules
The empirical analysis of experimental data joined with homeopathic doses of VB theory leads us to formulate two important HB Empirical Rules which have been called elsewhere ECHBM (Electrostatic-Covalent HB Model Gilli amp Gilli J Mol Struct 2000) and can be summarized as follows
Any given D-HA system may form HBs in a wide range of strengths lengths symmetries and proton locations the two extremes being represented
by the weak long dissymmetric and proton-out-centred HB of electrostatic nature
and by the very strong very short symmetric and proton-centred HB
classifiable as a true 3-center-4-electron covalent bond
The driving variable able to transform strong into weak HBs is dimensionally a free enthalpy corresponding to the difference between the Proton Affinities (PA) or related Acid-Base Dissociation Constants (pKa) of the Donor and Acceptor moieties
These rules have been verified beyond any reasonable doubt for the Conventional HBs of the following classification
Provisional Conclusions and New ControlsProvisional Conclusions and New Controls
We have so far established a sound set of empirical rules which include A full classification of all existing HBs A full classification of all strong HBs (The Chemical Leitmotifs) A plausible correlation between HB strengths and acid-base properties of the interacting molecules (The PApKa Equalization Principle)
To confirm this last point we have undertaken two years ago
a new research program aimed at assessing the Full Validity of the PApKa Equalization Principle
by comparing extended tables of pKa values arranged for chemical classes
withthe corresponding CSD-derived HB geometries
Hundreds of pKa were collected and more than 11000 crystal structures examined
The pThe pKKa Slide Rulea Slide Rule
It is a tool for the graphical evaluation of the difference
pKa = pKAH(DH) - pKBH+(AH+)
HB Acceptors on the left and HB Donors on the right
pKa values given for chemical class
Results expected
ΔpKagtgt0 DHmiddotmiddotmiddotmiddotA weak amp neutral
ΔpKa asymp 0 DmiddotmiddotmiddotHmiddotmiddotmiddotA strong amp
centeredΔpKa ltlt0DmiddotmiddotmiddotmiddotHA+ weak amp charged
pKa ranges of organic compounds
C-H acids -11 ltpKalt 53
Other Donors -1 ltpKalt 40
Acceptors -12 ltpKalt 16
All -15 ltpKalt 53
Water 0 ltpKalt 14
50
-10
0
10
20
30
40
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
ALDEHYDES
ETHERSALCOHOLS
AMIDES
NITRILES
ANILINES
CF3-SO3H
HClO4HI
HBrHCl
H2SO4
HSO4
HNO3
HBF4
H3PO4
H2PO4
HPO42
HF HNO2
HNNN
NH2OHH2CO3
HCO3
H2S
HS-
HCN H3BO3
H2BO3
H4SiO4
H2O2
HO
HSCN
H-H
SULFONICACIDS
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
OXIMES
ALCOHOLS
THIOLES
HB ACCEPTORS (A)pK BH+
HB DONORS (D-H)pK AH
C-H ACIDS pK AH
BE
TT
ER
HB
AC
CE
PT
OR
BE
TT
ER
BA
SE
BE
TT
ER
HB
DO
NO
R
BE
TT
ER
AC
ID
N-OXIDES
AMIDINES
UREA
THIOUREA
BARBITURICURIC ACID
MONO DIPHOSPHINES
TRIPHOSPHINES
TRINITROANILINES
AMINES
ANILINES
MONO DINITROANILINES
AMIDES
CARBOXYLIC ACIDS
HALOGENOANILINES
AZOCOMPS
TRINITROANILINES
PROTONSPONGES
ACIDSESTERS
H2O
H2O
MONODINITROANILINES
KETONES
SULFIDES
HALOGENCARB ACIDS
TRINITROPHENOLS
ENOLS
MONO DINITROPHENOLS
PHENOLSNAPHTHOLS
HALOGENOPHENOLS
HALOGENOALCOHOLS
SULFOXIDES
(NC)5-CYCLO
PENTADIENE
(NC)3CH
(O2N)2=CH2
HCCHNC-CH3
CH3-CO-CH3INDENE
O2N-CH3
(NC)2=CH2
(O2N)3CH
H2C=CH2
C6H6
CH4
CYCLOPENTADIENE
CYCLOPROPENE
Ar3CH
Ar2=CH2
Ar-CH3
NITROCOMPS
SELENOXIDES
AZOLES
AZINESDIAZINES
AMINES
Cl5-PHENOL
CH3-CH3
(CH3)3CH
NH3
NH3
51
53
51
53
Chemical Leitmotifs and PApChemical Leitmotifs and PApKKaa Equalization Rules Equalization Rules RAHB RAHB cannot be treated by pKa equalization methods because π-delocalization
modifies the pKarsquos of the donor and acceptor moieties (+)CAHB is a true proton transfer from an acid (HB donor) to a base (HB acceptor)
RndashDndashHAndashRrsquo Rndash12DH+A12ndashndashRrsquo RndashDHndashA+ndashRrsquoΔpKa = pKAH(RDH) pKBH+(RrsquoA)
()CAHB is a proton sharing between two acids (HB donors)
RndashDndashHDrsquondashRrsquo [RDHDrsquoRrsquo] RDHDrsquoRrsquoΔpKa = pKAH(RDH) pKAH(RDH)
(+)CAHB is a proton sharing between two bases (HB acceptors)
R+AHArsquoRrsquo [RAHArsquoRrsquo]+ RAHArsquo+RrsquoΔpKa = pKBH+(RA) pKBH+(RrsquoArsquo)
Whenever () and (+)CAHBs are both homonuclear (D = Drsquo or A = Arsquo) and
homomolecular (R = Rrsquo) the matching condition ΔpKa= 0 will hold irrespective of the
actual pKarsquos of the two interacting moieties All HBs formed will be strong
Some Famous HBsSome Famous HBs
The NThe NHmiddotmiddotmiddotOOHmiddotmiddotmiddotOOHmiddotmiddotmiddotN System over the Full HmiddotmiddotmiddotN System over the Full ppKKaa Range Range
When evaluated from the pKa slide rule the total pKa range is extremely wide
ndash30 pa 60 So far we have been able to shown that the pKa equalization rule certainly holds in
a restricted interval around zero The problem is now Does this rule hold in the full pKa range
We will try to prove that by a full analysis the N-HmiddotmiddotmiddotOO-HmiddotmiddotmiddotN system
Procedure In a first CSD search functional groups of known pKa value and more frequently
implied in NHmiddotmiddotmiddotOOHmiddotmiddotmiddotN bonds were identified Finally 10 classes of donors and 11 of acceptors were selected and the search restarted for each separate donor-acceptor group Altogether 9078 different bonds were analyzed (4364 NHmiddotmiddotmiddotO 2289 OHmiddotmiddotmiddotN and
2425 OmiddotmiddotmiddotHN+) For each bond the NmiddotmiddotmiddotO distances were evaluated as dNH + dHO to account for the
N-H-O angle and for each group the shortest and average distances [dNmiddotmiddotmiddotO (min)
and dNmiddotmiddotmiddotO (mean)] were registered
These values were compared (see next slide) with the acid-base features of the donors (pKAH range) acceptors (pKBH+ range) and with their combinations
(pKa range)
pKa large amp positive
pKa largeamp negative
Increasing Acidity of the Protonated A H+ Acceptor Increasing Basicity of the A Acceptor
ppKKaa versusversus HB Geometry Correlation - Conclusions HB Geometry Correlation - Conclusions The PApKa Equalization Principle is therefore fully confirmed in its two forms All strong HBs correspond to very small pKa values
pKa values modulate the HB strength over the full pKa range These conclusions are of great practical importance in at least two respects pKa is definitively established as the driving force which controls the HB
strength by modulating the HB covalent contribution It is definitively established that an accurate analysis of structural crystal data
leads to the same conclusions suggested but never proved on a general base by thermodynamic and spectroscopic methods
References Huyskens and Zeegers-Huyskens 1964 Zeegers-Huyskens 1986 1988 Ault and Pimentel 1975 Ratajczak and Sobczyk 1969 Sobczyk et al 1982 Barnes 1983 Kebarle et al 1974-1979 Meot-Ner (Mautner) et al
1984-1988
Towards a General HB TheoryTowards a General HB Theory
The results so far obtained are not a True HB Theory but rather a Set of Empirical Rules (or an Empirical Natural Law) that is a great collection of HB experimental data neatly organized in tables which all together represent a General Taxonomy of the HB Phenomenon exactly as the Carl Linnaeusrsquo classification of plants A scientific theory is something different It is the casting of the empirical natural law into the frame of a theory which is more fundamental down to the reductionistic chain of the scientific disciplines For instance the kinetic gas theory is the casting of the empirical gas laws (the empirical natural law) into Newtonrsquos classical mechanics
How to make a HB TheoryHow to make a HB Theory
HB Properties = FF (HB Driving Variable)where
HB Driving Variable = PApKa and FF = Transition-State Theory
The Transition-State HB TheoryThe Transition-State HB Theory(Gilli et al JACS 2002 2005 Gilli et al J Mol Struct 2006)
Though it has taken us more than 12 years to develop it
the basic idea is very simpleAny DndashHmiddotmiddotmiddotA bond can be considered as a chemical reaction which is
bimolecular in both directions and proceeds via transition-state (TS) formation
AndashB + C AmiddotmiddotmiddotBmiddotmiddotmiddotC A + BndashCDndashHmiddotmiddotmiddotA DmiddotmiddotmiddotHmiddotmiddotmiddotA DmiddotmiddotmiddotHndashA
Changes of nomenclatureReaction Pathway PTPathwayActivation Energy DaggerE PTBarrierReaction Energy Er PApKa Transition State (TS) PTTS
Reaction Coordinate RC=[d(DH)ndashd(AH)] Experimentals Variable-Temperature X-allographyCalculations DFTEmulated PTPathwaysInterpretation Marcus Rate-Equilibrium Theory LefflerHammond Postulate
AcknowledgmentsAcknowledgments I have to thank my direct coworkers without whose help this work could have not been accomplished
Valerio BERTOLASI Paola GILLI
Valeria FERRETTI Loretta PRETTO
and the scientific institutions which made available to us the databases without which this work could not even be started
CCDCCambridge Crystallographic
Data Centrefor the use of the
Cambridge Structural Database
NIST National Institute of Standards and
Technologyfor the use of the
NIST Chemistry WebBook
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs)CHARGE - ASSISTED HBs
PENTACHLOROPHENOL - p-TOLUIDINE
pKa = -070
12
12
N
CH3
O
ClCl
Cl
Cl
Cl
H25062 AringCL 1 (+ndash)CAHB SHB VSHB
Double Charge-Assisted HBDirect Acid-Base PApKa Matching
CL 2 (ndash)CAHB SHB VSHBNegative Charge-Assisted HB
Acid-Base PApKa Matching by Proton Loss R
OOH
R
O O24371 Aring
CARBOXYLIC ACID - CARBOXYLATE
CL 3 (+)CAHB SHB VSHBPositive Charge-Assisted HB
Acid-Base PApKa Matching by Proton Gain
O
HH H
O
HH
24303 Aring
WATER - HYDRONIUM
-BOND POLARIZATION - ASSISTED HBs
237-255 Aring
O OH
ArAr
DIBENZOYLMETHANE ENOLS
CL 4 RAHB SHB VSHB Resonance-Assisted or -Cooperative HB
PApKa Matching by -Conjugated-Bond Polarization
27501 Aring
OO
O
O O
WATER
CL 5 PAHB MHBPolarization-Assisted or -Cooperative HB(Partial) PApKa Matching by -Bond Polarization
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs) The most interesting aspect of a HB classification based on HB strength is that strong HBs belong only to a small number of chemical schemes that we have called Chemical Leitmotifs
The Alchemic Piper plays the Five Magic Tunes that make any Hydrogen Bond stronger The Chemical Leitmotifs
Symmetry and Covalency (1)Symmetry and Covalency (1)The covalent nature of the strong OHmiddotmiddotmiddotO bond was assessed by interpreting the
experimental results in terms of the Coulsonrsquos VB formalismWe cannot measure covalency but can evaluate molecular symmetry the
Coulsonrsquos model being the algorithm able to translate one concept into the other
In fact total symmetry across the HB implies energy equivalence between the two covalent VB forms ie E(ΨCOV1) = E(ΨCOV2) which is just the situation
associated with formation of the covalent HB
E E
NCT
CT
CTNCT
COV2
IONIC
COV1
IONIC
COV1 COV2
NCT
NCT
(a) Electrostatic HB (b) Covalent HB
Symmetry and Covalency (2)Symmetry and Covalency (2)
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 1
(+-)CAHBDouble Charge-Assisted HB
Direct Acid-Base PApKa Matching
R12DH+A12R
The role played by the PApKa equalization in HB strengthening
is self-evident for the (+-)CAHB chemical leitmotif
RDHARrsquo R12DH+A12Rrsquo RDHA+Rrsquo
which collects by definition all strong HBs formed by the acid-base pairs with a pKa matching within say ndash3 divide 3 pKa units
But what about the other leitmotifs Can we prove that
all chemical leitmotifs are simple artificesthat molecules can use to obliterate the normally
very large pKa between HB donor and acceptor atoms
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 2(-)CAHB
Negative Charge-Assisted HBAcid-Base PApKa Matching
by Proton Loss[R-DHA-R]-
Chemical Leitmotif 3(+)CAHB
Positive Charge-Assisted HBAcid-Base PApKa Matching
by Proton Gain[R-DHA-R]+
2II
2III
2IIa
2IIb
2IIIb
2IIIa
2VIa
pKa = pKAH(HO-H)-pKAH(HO-H) = 157 - 157 = 0
pKa = pKBH(H2O-H+)-pKBH(H2O-H
+) = -17 + 17 = 0
pKAH(HO-H) = 157
pKBH(H2O-H+) = -17
H
O H
H
O
H
(ndash)CAHB pKa = 00
VERYSTRONG~ 25-30 kcalmol
(+)CAHB pKa = 00
VERYSTRONG ~ 25-31 kcalmol
pKa = 175
OHB
WEAK ~ 4- 5kcalmol
ndash H+
+ H+
H
O H O
H
H
O H O
H
H
OHO
H
H
O
H
H
H
O
H
H
O
H
H
O
H
H H
O
H
H
H
O
H
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 4RAHB
Resonance-Assisted or -Bond Cooperative HBPApKa Matching by -Conjugated-Bond Polarization
R-D-HA=R R=DH-A-R
pKAH(RO-H) = 1518
pKBH(R2C=O-H+) = -(67)
O OH
O H O
R
R
R
Rn-RAHB pKa = ~ 21-25
WEAK ~ 4- 5kcalmol
EKO O
H
KEOO
H
pKa = 00
STRONG ~ 15-22 kcalmol
2IV
2IVa
2IVb
2VIb
OHB
The HB Empirical RulesThe HB Empirical Rules
The empirical analysis of experimental data joined with homeopathic doses of VB theory leads us to formulate two important HB Empirical Rules which have been called elsewhere ECHBM (Electrostatic-Covalent HB Model Gilli amp Gilli J Mol Struct 2000) and can be summarized as follows
Any given D-HA system may form HBs in a wide range of strengths lengths symmetries and proton locations the two extremes being represented
by the weak long dissymmetric and proton-out-centred HB of electrostatic nature
and by the very strong very short symmetric and proton-centred HB
classifiable as a true 3-center-4-electron covalent bond
The driving variable able to transform strong into weak HBs is dimensionally a free enthalpy corresponding to the difference between the Proton Affinities (PA) or related Acid-Base Dissociation Constants (pKa) of the Donor and Acceptor moieties
These rules have been verified beyond any reasonable doubt for the Conventional HBs of the following classification
Provisional Conclusions and New ControlsProvisional Conclusions and New Controls
We have so far established a sound set of empirical rules which include A full classification of all existing HBs A full classification of all strong HBs (The Chemical Leitmotifs) A plausible correlation between HB strengths and acid-base properties of the interacting molecules (The PApKa Equalization Principle)
To confirm this last point we have undertaken two years ago
a new research program aimed at assessing the Full Validity of the PApKa Equalization Principle
by comparing extended tables of pKa values arranged for chemical classes
withthe corresponding CSD-derived HB geometries
Hundreds of pKa were collected and more than 11000 crystal structures examined
The pThe pKKa Slide Rulea Slide Rule
It is a tool for the graphical evaluation of the difference
pKa = pKAH(DH) - pKBH+(AH+)
HB Acceptors on the left and HB Donors on the right
pKa values given for chemical class
Results expected
ΔpKagtgt0 DHmiddotmiddotmiddotmiddotA weak amp neutral
ΔpKa asymp 0 DmiddotmiddotmiddotHmiddotmiddotmiddotA strong amp
centeredΔpKa ltlt0DmiddotmiddotmiddotmiddotHA+ weak amp charged
pKa ranges of organic compounds
C-H acids -11 ltpKalt 53
Other Donors -1 ltpKalt 40
Acceptors -12 ltpKalt 16
All -15 ltpKalt 53
Water 0 ltpKalt 14
50
-10
0
10
20
30
40
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
ALDEHYDES
ETHERSALCOHOLS
AMIDES
NITRILES
ANILINES
CF3-SO3H
HClO4HI
HBrHCl
H2SO4
HSO4
HNO3
HBF4
H3PO4
H2PO4
HPO42
HF HNO2
HNNN
NH2OHH2CO3
HCO3
H2S
HS-
HCN H3BO3
H2BO3
H4SiO4
H2O2
HO
HSCN
H-H
SULFONICACIDS
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
OXIMES
ALCOHOLS
THIOLES
HB ACCEPTORS (A)pK BH+
HB DONORS (D-H)pK AH
C-H ACIDS pK AH
BE
TT
ER
HB
AC
CE
PT
OR
BE
TT
ER
BA
SE
BE
TT
ER
HB
DO
NO
R
BE
TT
ER
AC
ID
N-OXIDES
AMIDINES
UREA
THIOUREA
BARBITURICURIC ACID
MONO DIPHOSPHINES
TRIPHOSPHINES
TRINITROANILINES
AMINES
ANILINES
MONO DINITROANILINES
AMIDES
CARBOXYLIC ACIDS
HALOGENOANILINES
AZOCOMPS
TRINITROANILINES
PROTONSPONGES
ACIDSESTERS
H2O
H2O
MONODINITROANILINES
KETONES
SULFIDES
HALOGENCARB ACIDS
TRINITROPHENOLS
ENOLS
MONO DINITROPHENOLS
PHENOLSNAPHTHOLS
HALOGENOPHENOLS
HALOGENOALCOHOLS
SULFOXIDES
(NC)5-CYCLO
PENTADIENE
(NC)3CH
(O2N)2=CH2
HCCHNC-CH3
CH3-CO-CH3INDENE
O2N-CH3
(NC)2=CH2
(O2N)3CH
H2C=CH2
C6H6
CH4
CYCLOPENTADIENE
CYCLOPROPENE
Ar3CH
Ar2=CH2
Ar-CH3
NITROCOMPS
SELENOXIDES
AZOLES
AZINESDIAZINES
AMINES
Cl5-PHENOL
CH3-CH3
(CH3)3CH
NH3
NH3
51
53
51
53
Chemical Leitmotifs and PApChemical Leitmotifs and PApKKaa Equalization Rules Equalization Rules RAHB RAHB cannot be treated by pKa equalization methods because π-delocalization
modifies the pKarsquos of the donor and acceptor moieties (+)CAHB is a true proton transfer from an acid (HB donor) to a base (HB acceptor)
RndashDndashHAndashRrsquo Rndash12DH+A12ndashndashRrsquo RndashDHndashA+ndashRrsquoΔpKa = pKAH(RDH) pKBH+(RrsquoA)
()CAHB is a proton sharing between two acids (HB donors)
RndashDndashHDrsquondashRrsquo [RDHDrsquoRrsquo] RDHDrsquoRrsquoΔpKa = pKAH(RDH) pKAH(RDH)
(+)CAHB is a proton sharing between two bases (HB acceptors)
R+AHArsquoRrsquo [RAHArsquoRrsquo]+ RAHArsquo+RrsquoΔpKa = pKBH+(RA) pKBH+(RrsquoArsquo)
Whenever () and (+)CAHBs are both homonuclear (D = Drsquo or A = Arsquo) and
homomolecular (R = Rrsquo) the matching condition ΔpKa= 0 will hold irrespective of the
actual pKarsquos of the two interacting moieties All HBs formed will be strong
Some Famous HBsSome Famous HBs
The NThe NHmiddotmiddotmiddotOOHmiddotmiddotmiddotOOHmiddotmiddotmiddotN System over the Full HmiddotmiddotmiddotN System over the Full ppKKaa Range Range
When evaluated from the pKa slide rule the total pKa range is extremely wide
ndash30 pa 60 So far we have been able to shown that the pKa equalization rule certainly holds in
a restricted interval around zero The problem is now Does this rule hold in the full pKa range
We will try to prove that by a full analysis the N-HmiddotmiddotmiddotOO-HmiddotmiddotmiddotN system
Procedure In a first CSD search functional groups of known pKa value and more frequently
implied in NHmiddotmiddotmiddotOOHmiddotmiddotmiddotN bonds were identified Finally 10 classes of donors and 11 of acceptors were selected and the search restarted for each separate donor-acceptor group Altogether 9078 different bonds were analyzed (4364 NHmiddotmiddotmiddotO 2289 OHmiddotmiddotmiddotN and
2425 OmiddotmiddotmiddotHN+) For each bond the NmiddotmiddotmiddotO distances were evaluated as dNH + dHO to account for the
N-H-O angle and for each group the shortest and average distances [dNmiddotmiddotmiddotO (min)
and dNmiddotmiddotmiddotO (mean)] were registered
These values were compared (see next slide) with the acid-base features of the donors (pKAH range) acceptors (pKBH+ range) and with their combinations
(pKa range)
pKa large amp positive
pKa largeamp negative
Increasing Acidity of the Protonated A H+ Acceptor Increasing Basicity of the A Acceptor
ppKKaa versusversus HB Geometry Correlation - Conclusions HB Geometry Correlation - Conclusions The PApKa Equalization Principle is therefore fully confirmed in its two forms All strong HBs correspond to very small pKa values
pKa values modulate the HB strength over the full pKa range These conclusions are of great practical importance in at least two respects pKa is definitively established as the driving force which controls the HB
strength by modulating the HB covalent contribution It is definitively established that an accurate analysis of structural crystal data
leads to the same conclusions suggested but never proved on a general base by thermodynamic and spectroscopic methods
References Huyskens and Zeegers-Huyskens 1964 Zeegers-Huyskens 1986 1988 Ault and Pimentel 1975 Ratajczak and Sobczyk 1969 Sobczyk et al 1982 Barnes 1983 Kebarle et al 1974-1979 Meot-Ner (Mautner) et al
1984-1988
Towards a General HB TheoryTowards a General HB Theory
The results so far obtained are not a True HB Theory but rather a Set of Empirical Rules (or an Empirical Natural Law) that is a great collection of HB experimental data neatly organized in tables which all together represent a General Taxonomy of the HB Phenomenon exactly as the Carl Linnaeusrsquo classification of plants A scientific theory is something different It is the casting of the empirical natural law into the frame of a theory which is more fundamental down to the reductionistic chain of the scientific disciplines For instance the kinetic gas theory is the casting of the empirical gas laws (the empirical natural law) into Newtonrsquos classical mechanics
How to make a HB TheoryHow to make a HB Theory
HB Properties = FF (HB Driving Variable)where
HB Driving Variable = PApKa and FF = Transition-State Theory
The Transition-State HB TheoryThe Transition-State HB Theory(Gilli et al JACS 2002 2005 Gilli et al J Mol Struct 2006)
Though it has taken us more than 12 years to develop it
the basic idea is very simpleAny DndashHmiddotmiddotmiddotA bond can be considered as a chemical reaction which is
bimolecular in both directions and proceeds via transition-state (TS) formation
AndashB + C AmiddotmiddotmiddotBmiddotmiddotmiddotC A + BndashCDndashHmiddotmiddotmiddotA DmiddotmiddotmiddotHmiddotmiddotmiddotA DmiddotmiddotmiddotHndashA
Changes of nomenclatureReaction Pathway PTPathwayActivation Energy DaggerE PTBarrierReaction Energy Er PApKa Transition State (TS) PTTS
Reaction Coordinate RC=[d(DH)ndashd(AH)] Experimentals Variable-Temperature X-allographyCalculations DFTEmulated PTPathwaysInterpretation Marcus Rate-Equilibrium Theory LefflerHammond Postulate
AcknowledgmentsAcknowledgments I have to thank my direct coworkers without whose help this work could have not been accomplished
Valerio BERTOLASI Paola GILLI
Valeria FERRETTI Loretta PRETTO
and the scientific institutions which made available to us the databases without which this work could not even be started
CCDCCambridge Crystallographic
Data Centrefor the use of the
Cambridge Structural Database
NIST National Institute of Standards and
Technologyfor the use of the
NIST Chemistry WebBook
The Five HB Chemical Leitmotifs (CLs)The Five HB Chemical Leitmotifs (CLs) The most interesting aspect of a HB classification based on HB strength is that strong HBs belong only to a small number of chemical schemes that we have called Chemical Leitmotifs
The Alchemic Piper plays the Five Magic Tunes that make any Hydrogen Bond stronger The Chemical Leitmotifs
Symmetry and Covalency (1)Symmetry and Covalency (1)The covalent nature of the strong OHmiddotmiddotmiddotO bond was assessed by interpreting the
experimental results in terms of the Coulsonrsquos VB formalismWe cannot measure covalency but can evaluate molecular symmetry the
Coulsonrsquos model being the algorithm able to translate one concept into the other
In fact total symmetry across the HB implies energy equivalence between the two covalent VB forms ie E(ΨCOV1) = E(ΨCOV2) which is just the situation
associated with formation of the covalent HB
E E
NCT
CT
CTNCT
COV2
IONIC
COV1
IONIC
COV1 COV2
NCT
NCT
(a) Electrostatic HB (b) Covalent HB
Symmetry and Covalency (2)Symmetry and Covalency (2)
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 1
(+-)CAHBDouble Charge-Assisted HB
Direct Acid-Base PApKa Matching
R12DH+A12R
The role played by the PApKa equalization in HB strengthening
is self-evident for the (+-)CAHB chemical leitmotif
RDHARrsquo R12DH+A12Rrsquo RDHA+Rrsquo
which collects by definition all strong HBs formed by the acid-base pairs with a pKa matching within say ndash3 divide 3 pKa units
But what about the other leitmotifs Can we prove that
all chemical leitmotifs are simple artificesthat molecules can use to obliterate the normally
very large pKa between HB donor and acceptor atoms
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 2(-)CAHB
Negative Charge-Assisted HBAcid-Base PApKa Matching
by Proton Loss[R-DHA-R]-
Chemical Leitmotif 3(+)CAHB
Positive Charge-Assisted HBAcid-Base PApKa Matching
by Proton Gain[R-DHA-R]+
2II
2III
2IIa
2IIb
2IIIb
2IIIa
2VIa
pKa = pKAH(HO-H)-pKAH(HO-H) = 157 - 157 = 0
pKa = pKBH(H2O-H+)-pKBH(H2O-H
+) = -17 + 17 = 0
pKAH(HO-H) = 157
pKBH(H2O-H+) = -17
H
O H
H
O
H
(ndash)CAHB pKa = 00
VERYSTRONG~ 25-30 kcalmol
(+)CAHB pKa = 00
VERYSTRONG ~ 25-31 kcalmol
pKa = 175
OHB
WEAK ~ 4- 5kcalmol
ndash H+
+ H+
H
O H O
H
H
O H O
H
H
OHO
H
H
O
H
H
H
O
H
H
O
H
H
O
H
H H
O
H
H
H
O
H
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 4RAHB
Resonance-Assisted or -Bond Cooperative HBPApKa Matching by -Conjugated-Bond Polarization
R-D-HA=R R=DH-A-R
pKAH(RO-H) = 1518
pKBH(R2C=O-H+) = -(67)
O OH
O H O
R
R
R
Rn-RAHB pKa = ~ 21-25
WEAK ~ 4- 5kcalmol
EKO O
H
KEOO
H
pKa = 00
STRONG ~ 15-22 kcalmol
2IV
2IVa
2IVb
2VIb
OHB
The HB Empirical RulesThe HB Empirical Rules
The empirical analysis of experimental data joined with homeopathic doses of VB theory leads us to formulate two important HB Empirical Rules which have been called elsewhere ECHBM (Electrostatic-Covalent HB Model Gilli amp Gilli J Mol Struct 2000) and can be summarized as follows
Any given D-HA system may form HBs in a wide range of strengths lengths symmetries and proton locations the two extremes being represented
by the weak long dissymmetric and proton-out-centred HB of electrostatic nature
and by the very strong very short symmetric and proton-centred HB
classifiable as a true 3-center-4-electron covalent bond
The driving variable able to transform strong into weak HBs is dimensionally a free enthalpy corresponding to the difference between the Proton Affinities (PA) or related Acid-Base Dissociation Constants (pKa) of the Donor and Acceptor moieties
These rules have been verified beyond any reasonable doubt for the Conventional HBs of the following classification
Provisional Conclusions and New ControlsProvisional Conclusions and New Controls
We have so far established a sound set of empirical rules which include A full classification of all existing HBs A full classification of all strong HBs (The Chemical Leitmotifs) A plausible correlation between HB strengths and acid-base properties of the interacting molecules (The PApKa Equalization Principle)
To confirm this last point we have undertaken two years ago
a new research program aimed at assessing the Full Validity of the PApKa Equalization Principle
by comparing extended tables of pKa values arranged for chemical classes
withthe corresponding CSD-derived HB geometries
Hundreds of pKa were collected and more than 11000 crystal structures examined
The pThe pKKa Slide Rulea Slide Rule
It is a tool for the graphical evaluation of the difference
pKa = pKAH(DH) - pKBH+(AH+)
HB Acceptors on the left and HB Donors on the right
pKa values given for chemical class
Results expected
ΔpKagtgt0 DHmiddotmiddotmiddotmiddotA weak amp neutral
ΔpKa asymp 0 DmiddotmiddotmiddotHmiddotmiddotmiddotA strong amp
centeredΔpKa ltlt0DmiddotmiddotmiddotmiddotHA+ weak amp charged
pKa ranges of organic compounds
C-H acids -11 ltpKalt 53
Other Donors -1 ltpKalt 40
Acceptors -12 ltpKalt 16
All -15 ltpKalt 53
Water 0 ltpKalt 14
50
-10
0
10
20
30
40
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
ALDEHYDES
ETHERSALCOHOLS
AMIDES
NITRILES
ANILINES
CF3-SO3H
HClO4HI
HBrHCl
H2SO4
HSO4
HNO3
HBF4
H3PO4
H2PO4
HPO42
HF HNO2
HNNN
NH2OHH2CO3
HCO3
H2S
HS-
HCN H3BO3
H2BO3
H4SiO4
H2O2
HO
HSCN
H-H
SULFONICACIDS
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
OXIMES
ALCOHOLS
THIOLES
HB ACCEPTORS (A)pK BH+
HB DONORS (D-H)pK AH
C-H ACIDS pK AH
BE
TT
ER
HB
AC
CE
PT
OR
BE
TT
ER
BA
SE
BE
TT
ER
HB
DO
NO
R
BE
TT
ER
AC
ID
N-OXIDES
AMIDINES
UREA
THIOUREA
BARBITURICURIC ACID
MONO DIPHOSPHINES
TRIPHOSPHINES
TRINITROANILINES
AMINES
ANILINES
MONO DINITROANILINES
AMIDES
CARBOXYLIC ACIDS
HALOGENOANILINES
AZOCOMPS
TRINITROANILINES
PROTONSPONGES
ACIDSESTERS
H2O
H2O
MONODINITROANILINES
KETONES
SULFIDES
HALOGENCARB ACIDS
TRINITROPHENOLS
ENOLS
MONO DINITROPHENOLS
PHENOLSNAPHTHOLS
HALOGENOPHENOLS
HALOGENOALCOHOLS
SULFOXIDES
(NC)5-CYCLO
PENTADIENE
(NC)3CH
(O2N)2=CH2
HCCHNC-CH3
CH3-CO-CH3INDENE
O2N-CH3
(NC)2=CH2
(O2N)3CH
H2C=CH2
C6H6
CH4
CYCLOPENTADIENE
CYCLOPROPENE
Ar3CH
Ar2=CH2
Ar-CH3
NITROCOMPS
SELENOXIDES
AZOLES
AZINESDIAZINES
AMINES
Cl5-PHENOL
CH3-CH3
(CH3)3CH
NH3
NH3
51
53
51
53
Chemical Leitmotifs and PApChemical Leitmotifs and PApKKaa Equalization Rules Equalization Rules RAHB RAHB cannot be treated by pKa equalization methods because π-delocalization
modifies the pKarsquos of the donor and acceptor moieties (+)CAHB is a true proton transfer from an acid (HB donor) to a base (HB acceptor)
RndashDndashHAndashRrsquo Rndash12DH+A12ndashndashRrsquo RndashDHndashA+ndashRrsquoΔpKa = pKAH(RDH) pKBH+(RrsquoA)
()CAHB is a proton sharing between two acids (HB donors)
RndashDndashHDrsquondashRrsquo [RDHDrsquoRrsquo] RDHDrsquoRrsquoΔpKa = pKAH(RDH) pKAH(RDH)
(+)CAHB is a proton sharing between two bases (HB acceptors)
R+AHArsquoRrsquo [RAHArsquoRrsquo]+ RAHArsquo+RrsquoΔpKa = pKBH+(RA) pKBH+(RrsquoArsquo)
Whenever () and (+)CAHBs are both homonuclear (D = Drsquo or A = Arsquo) and
homomolecular (R = Rrsquo) the matching condition ΔpKa= 0 will hold irrespective of the
actual pKarsquos of the two interacting moieties All HBs formed will be strong
Some Famous HBsSome Famous HBs
The NThe NHmiddotmiddotmiddotOOHmiddotmiddotmiddotOOHmiddotmiddotmiddotN System over the Full HmiddotmiddotmiddotN System over the Full ppKKaa Range Range
When evaluated from the pKa slide rule the total pKa range is extremely wide
ndash30 pa 60 So far we have been able to shown that the pKa equalization rule certainly holds in
a restricted interval around zero The problem is now Does this rule hold in the full pKa range
We will try to prove that by a full analysis the N-HmiddotmiddotmiddotOO-HmiddotmiddotmiddotN system
Procedure In a first CSD search functional groups of known pKa value and more frequently
implied in NHmiddotmiddotmiddotOOHmiddotmiddotmiddotN bonds were identified Finally 10 classes of donors and 11 of acceptors were selected and the search restarted for each separate donor-acceptor group Altogether 9078 different bonds were analyzed (4364 NHmiddotmiddotmiddotO 2289 OHmiddotmiddotmiddotN and
2425 OmiddotmiddotmiddotHN+) For each bond the NmiddotmiddotmiddotO distances were evaluated as dNH + dHO to account for the
N-H-O angle and for each group the shortest and average distances [dNmiddotmiddotmiddotO (min)
and dNmiddotmiddotmiddotO (mean)] were registered
These values were compared (see next slide) with the acid-base features of the donors (pKAH range) acceptors (pKBH+ range) and with their combinations
(pKa range)
pKa large amp positive
pKa largeamp negative
Increasing Acidity of the Protonated A H+ Acceptor Increasing Basicity of the A Acceptor
ppKKaa versusversus HB Geometry Correlation - Conclusions HB Geometry Correlation - Conclusions The PApKa Equalization Principle is therefore fully confirmed in its two forms All strong HBs correspond to very small pKa values
pKa values modulate the HB strength over the full pKa range These conclusions are of great practical importance in at least two respects pKa is definitively established as the driving force which controls the HB
strength by modulating the HB covalent contribution It is definitively established that an accurate analysis of structural crystal data
leads to the same conclusions suggested but never proved on a general base by thermodynamic and spectroscopic methods
References Huyskens and Zeegers-Huyskens 1964 Zeegers-Huyskens 1986 1988 Ault and Pimentel 1975 Ratajczak and Sobczyk 1969 Sobczyk et al 1982 Barnes 1983 Kebarle et al 1974-1979 Meot-Ner (Mautner) et al
1984-1988
Towards a General HB TheoryTowards a General HB Theory
The results so far obtained are not a True HB Theory but rather a Set of Empirical Rules (or an Empirical Natural Law) that is a great collection of HB experimental data neatly organized in tables which all together represent a General Taxonomy of the HB Phenomenon exactly as the Carl Linnaeusrsquo classification of plants A scientific theory is something different It is the casting of the empirical natural law into the frame of a theory which is more fundamental down to the reductionistic chain of the scientific disciplines For instance the kinetic gas theory is the casting of the empirical gas laws (the empirical natural law) into Newtonrsquos classical mechanics
How to make a HB TheoryHow to make a HB Theory
HB Properties = FF (HB Driving Variable)where
HB Driving Variable = PApKa and FF = Transition-State Theory
The Transition-State HB TheoryThe Transition-State HB Theory(Gilli et al JACS 2002 2005 Gilli et al J Mol Struct 2006)
Though it has taken us more than 12 years to develop it
the basic idea is very simpleAny DndashHmiddotmiddotmiddotA bond can be considered as a chemical reaction which is
bimolecular in both directions and proceeds via transition-state (TS) formation
AndashB + C AmiddotmiddotmiddotBmiddotmiddotmiddotC A + BndashCDndashHmiddotmiddotmiddotA DmiddotmiddotmiddotHmiddotmiddotmiddotA DmiddotmiddotmiddotHndashA
Changes of nomenclatureReaction Pathway PTPathwayActivation Energy DaggerE PTBarrierReaction Energy Er PApKa Transition State (TS) PTTS
Reaction Coordinate RC=[d(DH)ndashd(AH)] Experimentals Variable-Temperature X-allographyCalculations DFTEmulated PTPathwaysInterpretation Marcus Rate-Equilibrium Theory LefflerHammond Postulate
AcknowledgmentsAcknowledgments I have to thank my direct coworkers without whose help this work could have not been accomplished
Valerio BERTOLASI Paola GILLI
Valeria FERRETTI Loretta PRETTO
and the scientific institutions which made available to us the databases without which this work could not even be started
CCDCCambridge Crystallographic
Data Centrefor the use of the
Cambridge Structural Database
NIST National Institute of Standards and
Technologyfor the use of the
NIST Chemistry WebBook
Symmetry and Covalency (1)Symmetry and Covalency (1)The covalent nature of the strong OHmiddotmiddotmiddotO bond was assessed by interpreting the
experimental results in terms of the Coulsonrsquos VB formalismWe cannot measure covalency but can evaluate molecular symmetry the
Coulsonrsquos model being the algorithm able to translate one concept into the other
In fact total symmetry across the HB implies energy equivalence between the two covalent VB forms ie E(ΨCOV1) = E(ΨCOV2) which is just the situation
associated with formation of the covalent HB
E E
NCT
CT
CTNCT
COV2
IONIC
COV1
IONIC
COV1 COV2
NCT
NCT
(a) Electrostatic HB (b) Covalent HB
Symmetry and Covalency (2)Symmetry and Covalency (2)
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 1
(+-)CAHBDouble Charge-Assisted HB
Direct Acid-Base PApKa Matching
R12DH+A12R
The role played by the PApKa equalization in HB strengthening
is self-evident for the (+-)CAHB chemical leitmotif
RDHARrsquo R12DH+A12Rrsquo RDHA+Rrsquo
which collects by definition all strong HBs formed by the acid-base pairs with a pKa matching within say ndash3 divide 3 pKa units
But what about the other leitmotifs Can we prove that
all chemical leitmotifs are simple artificesthat molecules can use to obliterate the normally
very large pKa between HB donor and acceptor atoms
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 2(-)CAHB
Negative Charge-Assisted HBAcid-Base PApKa Matching
by Proton Loss[R-DHA-R]-
Chemical Leitmotif 3(+)CAHB
Positive Charge-Assisted HBAcid-Base PApKa Matching
by Proton Gain[R-DHA-R]+
2II
2III
2IIa
2IIb
2IIIb
2IIIa
2VIa
pKa = pKAH(HO-H)-pKAH(HO-H) = 157 - 157 = 0
pKa = pKBH(H2O-H+)-pKBH(H2O-H
+) = -17 + 17 = 0
pKAH(HO-H) = 157
pKBH(H2O-H+) = -17
H
O H
H
O
H
(ndash)CAHB pKa = 00
VERYSTRONG~ 25-30 kcalmol
(+)CAHB pKa = 00
VERYSTRONG ~ 25-31 kcalmol
pKa = 175
OHB
WEAK ~ 4- 5kcalmol
ndash H+
+ H+
H
O H O
H
H
O H O
H
H
OHO
H
H
O
H
H
H
O
H
H
O
H
H
O
H
H H
O
H
H
H
O
H
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 4RAHB
Resonance-Assisted or -Bond Cooperative HBPApKa Matching by -Conjugated-Bond Polarization
R-D-HA=R R=DH-A-R
pKAH(RO-H) = 1518
pKBH(R2C=O-H+) = -(67)
O OH
O H O
R
R
R
Rn-RAHB pKa = ~ 21-25
WEAK ~ 4- 5kcalmol
EKO O
H
KEOO
H
pKa = 00
STRONG ~ 15-22 kcalmol
2IV
2IVa
2IVb
2VIb
OHB
The HB Empirical RulesThe HB Empirical Rules
The empirical analysis of experimental data joined with homeopathic doses of VB theory leads us to formulate two important HB Empirical Rules which have been called elsewhere ECHBM (Electrostatic-Covalent HB Model Gilli amp Gilli J Mol Struct 2000) and can be summarized as follows
Any given D-HA system may form HBs in a wide range of strengths lengths symmetries and proton locations the two extremes being represented
by the weak long dissymmetric and proton-out-centred HB of electrostatic nature
and by the very strong very short symmetric and proton-centred HB
classifiable as a true 3-center-4-electron covalent bond
The driving variable able to transform strong into weak HBs is dimensionally a free enthalpy corresponding to the difference between the Proton Affinities (PA) or related Acid-Base Dissociation Constants (pKa) of the Donor and Acceptor moieties
These rules have been verified beyond any reasonable doubt for the Conventional HBs of the following classification
Provisional Conclusions and New ControlsProvisional Conclusions and New Controls
We have so far established a sound set of empirical rules which include A full classification of all existing HBs A full classification of all strong HBs (The Chemical Leitmotifs) A plausible correlation between HB strengths and acid-base properties of the interacting molecules (The PApKa Equalization Principle)
To confirm this last point we have undertaken two years ago
a new research program aimed at assessing the Full Validity of the PApKa Equalization Principle
by comparing extended tables of pKa values arranged for chemical classes
withthe corresponding CSD-derived HB geometries
Hundreds of pKa were collected and more than 11000 crystal structures examined
The pThe pKKa Slide Rulea Slide Rule
It is a tool for the graphical evaluation of the difference
pKa = pKAH(DH) - pKBH+(AH+)
HB Acceptors on the left and HB Donors on the right
pKa values given for chemical class
Results expected
ΔpKagtgt0 DHmiddotmiddotmiddotmiddotA weak amp neutral
ΔpKa asymp 0 DmiddotmiddotmiddotHmiddotmiddotmiddotA strong amp
centeredΔpKa ltlt0DmiddotmiddotmiddotmiddotHA+ weak amp charged
pKa ranges of organic compounds
C-H acids -11 ltpKalt 53
Other Donors -1 ltpKalt 40
Acceptors -12 ltpKalt 16
All -15 ltpKalt 53
Water 0 ltpKalt 14
50
-10
0
10
20
30
40
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
ALDEHYDES
ETHERSALCOHOLS
AMIDES
NITRILES
ANILINES
CF3-SO3H
HClO4HI
HBrHCl
H2SO4
HSO4
HNO3
HBF4
H3PO4
H2PO4
HPO42
HF HNO2
HNNN
NH2OHH2CO3
HCO3
H2S
HS-
HCN H3BO3
H2BO3
H4SiO4
H2O2
HO
HSCN
H-H
SULFONICACIDS
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
OXIMES
ALCOHOLS
THIOLES
HB ACCEPTORS (A)pK BH+
HB DONORS (D-H)pK AH
C-H ACIDS pK AH
BE
TT
ER
HB
AC
CE
PT
OR
BE
TT
ER
BA
SE
BE
TT
ER
HB
DO
NO
R
BE
TT
ER
AC
ID
N-OXIDES
AMIDINES
UREA
THIOUREA
BARBITURICURIC ACID
MONO DIPHOSPHINES
TRIPHOSPHINES
TRINITROANILINES
AMINES
ANILINES
MONO DINITROANILINES
AMIDES
CARBOXYLIC ACIDS
HALOGENOANILINES
AZOCOMPS
TRINITROANILINES
PROTONSPONGES
ACIDSESTERS
H2O
H2O
MONODINITROANILINES
KETONES
SULFIDES
HALOGENCARB ACIDS
TRINITROPHENOLS
ENOLS
MONO DINITROPHENOLS
PHENOLSNAPHTHOLS
HALOGENOPHENOLS
HALOGENOALCOHOLS
SULFOXIDES
(NC)5-CYCLO
PENTADIENE
(NC)3CH
(O2N)2=CH2
HCCHNC-CH3
CH3-CO-CH3INDENE
O2N-CH3
(NC)2=CH2
(O2N)3CH
H2C=CH2
C6H6
CH4
CYCLOPENTADIENE
CYCLOPROPENE
Ar3CH
Ar2=CH2
Ar-CH3
NITROCOMPS
SELENOXIDES
AZOLES
AZINESDIAZINES
AMINES
Cl5-PHENOL
CH3-CH3
(CH3)3CH
NH3
NH3
51
53
51
53
Chemical Leitmotifs and PApChemical Leitmotifs and PApKKaa Equalization Rules Equalization Rules RAHB RAHB cannot be treated by pKa equalization methods because π-delocalization
modifies the pKarsquos of the donor and acceptor moieties (+)CAHB is a true proton transfer from an acid (HB donor) to a base (HB acceptor)
RndashDndashHAndashRrsquo Rndash12DH+A12ndashndashRrsquo RndashDHndashA+ndashRrsquoΔpKa = pKAH(RDH) pKBH+(RrsquoA)
()CAHB is a proton sharing between two acids (HB donors)
RndashDndashHDrsquondashRrsquo [RDHDrsquoRrsquo] RDHDrsquoRrsquoΔpKa = pKAH(RDH) pKAH(RDH)
(+)CAHB is a proton sharing between two bases (HB acceptors)
R+AHArsquoRrsquo [RAHArsquoRrsquo]+ RAHArsquo+RrsquoΔpKa = pKBH+(RA) pKBH+(RrsquoArsquo)
Whenever () and (+)CAHBs are both homonuclear (D = Drsquo or A = Arsquo) and
homomolecular (R = Rrsquo) the matching condition ΔpKa= 0 will hold irrespective of the
actual pKarsquos of the two interacting moieties All HBs formed will be strong
Some Famous HBsSome Famous HBs
The NThe NHmiddotmiddotmiddotOOHmiddotmiddotmiddotOOHmiddotmiddotmiddotN System over the Full HmiddotmiddotmiddotN System over the Full ppKKaa Range Range
When evaluated from the pKa slide rule the total pKa range is extremely wide
ndash30 pa 60 So far we have been able to shown that the pKa equalization rule certainly holds in
a restricted interval around zero The problem is now Does this rule hold in the full pKa range
We will try to prove that by a full analysis the N-HmiddotmiddotmiddotOO-HmiddotmiddotmiddotN system
Procedure In a first CSD search functional groups of known pKa value and more frequently
implied in NHmiddotmiddotmiddotOOHmiddotmiddotmiddotN bonds were identified Finally 10 classes of donors and 11 of acceptors were selected and the search restarted for each separate donor-acceptor group Altogether 9078 different bonds were analyzed (4364 NHmiddotmiddotmiddotO 2289 OHmiddotmiddotmiddotN and
2425 OmiddotmiddotmiddotHN+) For each bond the NmiddotmiddotmiddotO distances were evaluated as dNH + dHO to account for the
N-H-O angle and for each group the shortest and average distances [dNmiddotmiddotmiddotO (min)
and dNmiddotmiddotmiddotO (mean)] were registered
These values were compared (see next slide) with the acid-base features of the donors (pKAH range) acceptors (pKBH+ range) and with their combinations
(pKa range)
pKa large amp positive
pKa largeamp negative
Increasing Acidity of the Protonated A H+ Acceptor Increasing Basicity of the A Acceptor
ppKKaa versusversus HB Geometry Correlation - Conclusions HB Geometry Correlation - Conclusions The PApKa Equalization Principle is therefore fully confirmed in its two forms All strong HBs correspond to very small pKa values
pKa values modulate the HB strength over the full pKa range These conclusions are of great practical importance in at least two respects pKa is definitively established as the driving force which controls the HB
strength by modulating the HB covalent contribution It is definitively established that an accurate analysis of structural crystal data
leads to the same conclusions suggested but never proved on a general base by thermodynamic and spectroscopic methods
References Huyskens and Zeegers-Huyskens 1964 Zeegers-Huyskens 1986 1988 Ault and Pimentel 1975 Ratajczak and Sobczyk 1969 Sobczyk et al 1982 Barnes 1983 Kebarle et al 1974-1979 Meot-Ner (Mautner) et al
1984-1988
Towards a General HB TheoryTowards a General HB Theory
The results so far obtained are not a True HB Theory but rather a Set of Empirical Rules (or an Empirical Natural Law) that is a great collection of HB experimental data neatly organized in tables which all together represent a General Taxonomy of the HB Phenomenon exactly as the Carl Linnaeusrsquo classification of plants A scientific theory is something different It is the casting of the empirical natural law into the frame of a theory which is more fundamental down to the reductionistic chain of the scientific disciplines For instance the kinetic gas theory is the casting of the empirical gas laws (the empirical natural law) into Newtonrsquos classical mechanics
How to make a HB TheoryHow to make a HB Theory
HB Properties = FF (HB Driving Variable)where
HB Driving Variable = PApKa and FF = Transition-State Theory
The Transition-State HB TheoryThe Transition-State HB Theory(Gilli et al JACS 2002 2005 Gilli et al J Mol Struct 2006)
Though it has taken us more than 12 years to develop it
the basic idea is very simpleAny DndashHmiddotmiddotmiddotA bond can be considered as a chemical reaction which is
bimolecular in both directions and proceeds via transition-state (TS) formation
AndashB + C AmiddotmiddotmiddotBmiddotmiddotmiddotC A + BndashCDndashHmiddotmiddotmiddotA DmiddotmiddotmiddotHmiddotmiddotmiddotA DmiddotmiddotmiddotHndashA
Changes of nomenclatureReaction Pathway PTPathwayActivation Energy DaggerE PTBarrierReaction Energy Er PApKa Transition State (TS) PTTS
Reaction Coordinate RC=[d(DH)ndashd(AH)] Experimentals Variable-Temperature X-allographyCalculations DFTEmulated PTPathwaysInterpretation Marcus Rate-Equilibrium Theory LefflerHammond Postulate
AcknowledgmentsAcknowledgments I have to thank my direct coworkers without whose help this work could have not been accomplished
Valerio BERTOLASI Paola GILLI
Valeria FERRETTI Loretta PRETTO
and the scientific institutions which made available to us the databases without which this work could not even be started
CCDCCambridge Crystallographic
Data Centrefor the use of the
Cambridge Structural Database
NIST National Institute of Standards and
Technologyfor the use of the
NIST Chemistry WebBook
Symmetry and Covalency (2)Symmetry and Covalency (2)
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 1
(+-)CAHBDouble Charge-Assisted HB
Direct Acid-Base PApKa Matching
R12DH+A12R
The role played by the PApKa equalization in HB strengthening
is self-evident for the (+-)CAHB chemical leitmotif
RDHARrsquo R12DH+A12Rrsquo RDHA+Rrsquo
which collects by definition all strong HBs formed by the acid-base pairs with a pKa matching within say ndash3 divide 3 pKa units
But what about the other leitmotifs Can we prove that
all chemical leitmotifs are simple artificesthat molecules can use to obliterate the normally
very large pKa between HB donor and acceptor atoms
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 2(-)CAHB
Negative Charge-Assisted HBAcid-Base PApKa Matching
by Proton Loss[R-DHA-R]-
Chemical Leitmotif 3(+)CAHB
Positive Charge-Assisted HBAcid-Base PApKa Matching
by Proton Gain[R-DHA-R]+
2II
2III
2IIa
2IIb
2IIIb
2IIIa
2VIa
pKa = pKAH(HO-H)-pKAH(HO-H) = 157 - 157 = 0
pKa = pKBH(H2O-H+)-pKBH(H2O-H
+) = -17 + 17 = 0
pKAH(HO-H) = 157
pKBH(H2O-H+) = -17
H
O H
H
O
H
(ndash)CAHB pKa = 00
VERYSTRONG~ 25-30 kcalmol
(+)CAHB pKa = 00
VERYSTRONG ~ 25-31 kcalmol
pKa = 175
OHB
WEAK ~ 4- 5kcalmol
ndash H+
+ H+
H
O H O
H
H
O H O
H
H
OHO
H
H
O
H
H
H
O
H
H
O
H
H
O
H
H H
O
H
H
H
O
H
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 4RAHB
Resonance-Assisted or -Bond Cooperative HBPApKa Matching by -Conjugated-Bond Polarization
R-D-HA=R R=DH-A-R
pKAH(RO-H) = 1518
pKBH(R2C=O-H+) = -(67)
O OH
O H O
R
R
R
Rn-RAHB pKa = ~ 21-25
WEAK ~ 4- 5kcalmol
EKO O
H
KEOO
H
pKa = 00
STRONG ~ 15-22 kcalmol
2IV
2IVa
2IVb
2VIb
OHB
The HB Empirical RulesThe HB Empirical Rules
The empirical analysis of experimental data joined with homeopathic doses of VB theory leads us to formulate two important HB Empirical Rules which have been called elsewhere ECHBM (Electrostatic-Covalent HB Model Gilli amp Gilli J Mol Struct 2000) and can be summarized as follows
Any given D-HA system may form HBs in a wide range of strengths lengths symmetries and proton locations the two extremes being represented
by the weak long dissymmetric and proton-out-centred HB of electrostatic nature
and by the very strong very short symmetric and proton-centred HB
classifiable as a true 3-center-4-electron covalent bond
The driving variable able to transform strong into weak HBs is dimensionally a free enthalpy corresponding to the difference between the Proton Affinities (PA) or related Acid-Base Dissociation Constants (pKa) of the Donor and Acceptor moieties
These rules have been verified beyond any reasonable doubt for the Conventional HBs of the following classification
Provisional Conclusions and New ControlsProvisional Conclusions and New Controls
We have so far established a sound set of empirical rules which include A full classification of all existing HBs A full classification of all strong HBs (The Chemical Leitmotifs) A plausible correlation between HB strengths and acid-base properties of the interacting molecules (The PApKa Equalization Principle)
To confirm this last point we have undertaken two years ago
a new research program aimed at assessing the Full Validity of the PApKa Equalization Principle
by comparing extended tables of pKa values arranged for chemical classes
withthe corresponding CSD-derived HB geometries
Hundreds of pKa were collected and more than 11000 crystal structures examined
The pThe pKKa Slide Rulea Slide Rule
It is a tool for the graphical evaluation of the difference
pKa = pKAH(DH) - pKBH+(AH+)
HB Acceptors on the left and HB Donors on the right
pKa values given for chemical class
Results expected
ΔpKagtgt0 DHmiddotmiddotmiddotmiddotA weak amp neutral
ΔpKa asymp 0 DmiddotmiddotmiddotHmiddotmiddotmiddotA strong amp
centeredΔpKa ltlt0DmiddotmiddotmiddotmiddotHA+ weak amp charged
pKa ranges of organic compounds
C-H acids -11 ltpKalt 53
Other Donors -1 ltpKalt 40
Acceptors -12 ltpKalt 16
All -15 ltpKalt 53
Water 0 ltpKalt 14
50
-10
0
10
20
30
40
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
ALDEHYDES
ETHERSALCOHOLS
AMIDES
NITRILES
ANILINES
CF3-SO3H
HClO4HI
HBrHCl
H2SO4
HSO4
HNO3
HBF4
H3PO4
H2PO4
HPO42
HF HNO2
HNNN
NH2OHH2CO3
HCO3
H2S
HS-
HCN H3BO3
H2BO3
H4SiO4
H2O2
HO
HSCN
H-H
SULFONICACIDS
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
OXIMES
ALCOHOLS
THIOLES
HB ACCEPTORS (A)pK BH+
HB DONORS (D-H)pK AH
C-H ACIDS pK AH
BE
TT
ER
HB
AC
CE
PT
OR
BE
TT
ER
BA
SE
BE
TT
ER
HB
DO
NO
R
BE
TT
ER
AC
ID
N-OXIDES
AMIDINES
UREA
THIOUREA
BARBITURICURIC ACID
MONO DIPHOSPHINES
TRIPHOSPHINES
TRINITROANILINES
AMINES
ANILINES
MONO DINITROANILINES
AMIDES
CARBOXYLIC ACIDS
HALOGENOANILINES
AZOCOMPS
TRINITROANILINES
PROTONSPONGES
ACIDSESTERS
H2O
H2O
MONODINITROANILINES
KETONES
SULFIDES
HALOGENCARB ACIDS
TRINITROPHENOLS
ENOLS
MONO DINITROPHENOLS
PHENOLSNAPHTHOLS
HALOGENOPHENOLS
HALOGENOALCOHOLS
SULFOXIDES
(NC)5-CYCLO
PENTADIENE
(NC)3CH
(O2N)2=CH2
HCCHNC-CH3
CH3-CO-CH3INDENE
O2N-CH3
(NC)2=CH2
(O2N)3CH
H2C=CH2
C6H6
CH4
CYCLOPENTADIENE
CYCLOPROPENE
Ar3CH
Ar2=CH2
Ar-CH3
NITROCOMPS
SELENOXIDES
AZOLES
AZINESDIAZINES
AMINES
Cl5-PHENOL
CH3-CH3
(CH3)3CH
NH3
NH3
51
53
51
53
Chemical Leitmotifs and PApChemical Leitmotifs and PApKKaa Equalization Rules Equalization Rules RAHB RAHB cannot be treated by pKa equalization methods because π-delocalization
modifies the pKarsquos of the donor and acceptor moieties (+)CAHB is a true proton transfer from an acid (HB donor) to a base (HB acceptor)
RndashDndashHAndashRrsquo Rndash12DH+A12ndashndashRrsquo RndashDHndashA+ndashRrsquoΔpKa = pKAH(RDH) pKBH+(RrsquoA)
()CAHB is a proton sharing between two acids (HB donors)
RndashDndashHDrsquondashRrsquo [RDHDrsquoRrsquo] RDHDrsquoRrsquoΔpKa = pKAH(RDH) pKAH(RDH)
(+)CAHB is a proton sharing between two bases (HB acceptors)
R+AHArsquoRrsquo [RAHArsquoRrsquo]+ RAHArsquo+RrsquoΔpKa = pKBH+(RA) pKBH+(RrsquoArsquo)
Whenever () and (+)CAHBs are both homonuclear (D = Drsquo or A = Arsquo) and
homomolecular (R = Rrsquo) the matching condition ΔpKa= 0 will hold irrespective of the
actual pKarsquos of the two interacting moieties All HBs formed will be strong
Some Famous HBsSome Famous HBs
The NThe NHmiddotmiddotmiddotOOHmiddotmiddotmiddotOOHmiddotmiddotmiddotN System over the Full HmiddotmiddotmiddotN System over the Full ppKKaa Range Range
When evaluated from the pKa slide rule the total pKa range is extremely wide
ndash30 pa 60 So far we have been able to shown that the pKa equalization rule certainly holds in
a restricted interval around zero The problem is now Does this rule hold in the full pKa range
We will try to prove that by a full analysis the N-HmiddotmiddotmiddotOO-HmiddotmiddotmiddotN system
Procedure In a first CSD search functional groups of known pKa value and more frequently
implied in NHmiddotmiddotmiddotOOHmiddotmiddotmiddotN bonds were identified Finally 10 classes of donors and 11 of acceptors were selected and the search restarted for each separate donor-acceptor group Altogether 9078 different bonds were analyzed (4364 NHmiddotmiddotmiddotO 2289 OHmiddotmiddotmiddotN and
2425 OmiddotmiddotmiddotHN+) For each bond the NmiddotmiddotmiddotO distances were evaluated as dNH + dHO to account for the
N-H-O angle and for each group the shortest and average distances [dNmiddotmiddotmiddotO (min)
and dNmiddotmiddotmiddotO (mean)] were registered
These values were compared (see next slide) with the acid-base features of the donors (pKAH range) acceptors (pKBH+ range) and with their combinations
(pKa range)
pKa large amp positive
pKa largeamp negative
Increasing Acidity of the Protonated A H+ Acceptor Increasing Basicity of the A Acceptor
ppKKaa versusversus HB Geometry Correlation - Conclusions HB Geometry Correlation - Conclusions The PApKa Equalization Principle is therefore fully confirmed in its two forms All strong HBs correspond to very small pKa values
pKa values modulate the HB strength over the full pKa range These conclusions are of great practical importance in at least two respects pKa is definitively established as the driving force which controls the HB
strength by modulating the HB covalent contribution It is definitively established that an accurate analysis of structural crystal data
leads to the same conclusions suggested but never proved on a general base by thermodynamic and spectroscopic methods
References Huyskens and Zeegers-Huyskens 1964 Zeegers-Huyskens 1986 1988 Ault and Pimentel 1975 Ratajczak and Sobczyk 1969 Sobczyk et al 1982 Barnes 1983 Kebarle et al 1974-1979 Meot-Ner (Mautner) et al
1984-1988
Towards a General HB TheoryTowards a General HB Theory
The results so far obtained are not a True HB Theory but rather a Set of Empirical Rules (or an Empirical Natural Law) that is a great collection of HB experimental data neatly organized in tables which all together represent a General Taxonomy of the HB Phenomenon exactly as the Carl Linnaeusrsquo classification of plants A scientific theory is something different It is the casting of the empirical natural law into the frame of a theory which is more fundamental down to the reductionistic chain of the scientific disciplines For instance the kinetic gas theory is the casting of the empirical gas laws (the empirical natural law) into Newtonrsquos classical mechanics
How to make a HB TheoryHow to make a HB Theory
HB Properties = FF (HB Driving Variable)where
HB Driving Variable = PApKa and FF = Transition-State Theory
The Transition-State HB TheoryThe Transition-State HB Theory(Gilli et al JACS 2002 2005 Gilli et al J Mol Struct 2006)
Though it has taken us more than 12 years to develop it
the basic idea is very simpleAny DndashHmiddotmiddotmiddotA bond can be considered as a chemical reaction which is
bimolecular in both directions and proceeds via transition-state (TS) formation
AndashB + C AmiddotmiddotmiddotBmiddotmiddotmiddotC A + BndashCDndashHmiddotmiddotmiddotA DmiddotmiddotmiddotHmiddotmiddotmiddotA DmiddotmiddotmiddotHndashA
Changes of nomenclatureReaction Pathway PTPathwayActivation Energy DaggerE PTBarrierReaction Energy Er PApKa Transition State (TS) PTTS
Reaction Coordinate RC=[d(DH)ndashd(AH)] Experimentals Variable-Temperature X-allographyCalculations DFTEmulated PTPathwaysInterpretation Marcus Rate-Equilibrium Theory LefflerHammond Postulate
AcknowledgmentsAcknowledgments I have to thank my direct coworkers without whose help this work could have not been accomplished
Valerio BERTOLASI Paola GILLI
Valeria FERRETTI Loretta PRETTO
and the scientific institutions which made available to us the databases without which this work could not even be started
CCDCCambridge Crystallographic
Data Centrefor the use of the
Cambridge Structural Database
NIST National Institute of Standards and
Technologyfor the use of the
NIST Chemistry WebBook
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 1
(+-)CAHBDouble Charge-Assisted HB
Direct Acid-Base PApKa Matching
R12DH+A12R
The role played by the PApKa equalization in HB strengthening
is self-evident for the (+-)CAHB chemical leitmotif
RDHARrsquo R12DH+A12Rrsquo RDHA+Rrsquo
which collects by definition all strong HBs formed by the acid-base pairs with a pKa matching within say ndash3 divide 3 pKa units
But what about the other leitmotifs Can we prove that
all chemical leitmotifs are simple artificesthat molecules can use to obliterate the normally
very large pKa between HB donor and acceptor atoms
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 2(-)CAHB
Negative Charge-Assisted HBAcid-Base PApKa Matching
by Proton Loss[R-DHA-R]-
Chemical Leitmotif 3(+)CAHB
Positive Charge-Assisted HBAcid-Base PApKa Matching
by Proton Gain[R-DHA-R]+
2II
2III
2IIa
2IIb
2IIIb
2IIIa
2VIa
pKa = pKAH(HO-H)-pKAH(HO-H) = 157 - 157 = 0
pKa = pKBH(H2O-H+)-pKBH(H2O-H
+) = -17 + 17 = 0
pKAH(HO-H) = 157
pKBH(H2O-H+) = -17
H
O H
H
O
H
(ndash)CAHB pKa = 00
VERYSTRONG~ 25-30 kcalmol
(+)CAHB pKa = 00
VERYSTRONG ~ 25-31 kcalmol
pKa = 175
OHB
WEAK ~ 4- 5kcalmol
ndash H+
+ H+
H
O H O
H
H
O H O
H
H
OHO
H
H
O
H
H
H
O
H
H
O
H
H
O
H
H H
O
H
H
H
O
H
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 4RAHB
Resonance-Assisted or -Bond Cooperative HBPApKa Matching by -Conjugated-Bond Polarization
R-D-HA=R R=DH-A-R
pKAH(RO-H) = 1518
pKBH(R2C=O-H+) = -(67)
O OH
O H O
R
R
R
Rn-RAHB pKa = ~ 21-25
WEAK ~ 4- 5kcalmol
EKO O
H
KEOO
H
pKa = 00
STRONG ~ 15-22 kcalmol
2IV
2IVa
2IVb
2VIb
OHB
The HB Empirical RulesThe HB Empirical Rules
The empirical analysis of experimental data joined with homeopathic doses of VB theory leads us to formulate two important HB Empirical Rules which have been called elsewhere ECHBM (Electrostatic-Covalent HB Model Gilli amp Gilli J Mol Struct 2000) and can be summarized as follows
Any given D-HA system may form HBs in a wide range of strengths lengths symmetries and proton locations the two extremes being represented
by the weak long dissymmetric and proton-out-centred HB of electrostatic nature
and by the very strong very short symmetric and proton-centred HB
classifiable as a true 3-center-4-electron covalent bond
The driving variable able to transform strong into weak HBs is dimensionally a free enthalpy corresponding to the difference between the Proton Affinities (PA) or related Acid-Base Dissociation Constants (pKa) of the Donor and Acceptor moieties
These rules have been verified beyond any reasonable doubt for the Conventional HBs of the following classification
Provisional Conclusions and New ControlsProvisional Conclusions and New Controls
We have so far established a sound set of empirical rules which include A full classification of all existing HBs A full classification of all strong HBs (The Chemical Leitmotifs) A plausible correlation between HB strengths and acid-base properties of the interacting molecules (The PApKa Equalization Principle)
To confirm this last point we have undertaken two years ago
a new research program aimed at assessing the Full Validity of the PApKa Equalization Principle
by comparing extended tables of pKa values arranged for chemical classes
withthe corresponding CSD-derived HB geometries
Hundreds of pKa were collected and more than 11000 crystal structures examined
The pThe pKKa Slide Rulea Slide Rule
It is a tool for the graphical evaluation of the difference
pKa = pKAH(DH) - pKBH+(AH+)
HB Acceptors on the left and HB Donors on the right
pKa values given for chemical class
Results expected
ΔpKagtgt0 DHmiddotmiddotmiddotmiddotA weak amp neutral
ΔpKa asymp 0 DmiddotmiddotmiddotHmiddotmiddotmiddotA strong amp
centeredΔpKa ltlt0DmiddotmiddotmiddotmiddotHA+ weak amp charged
pKa ranges of organic compounds
C-H acids -11 ltpKalt 53
Other Donors -1 ltpKalt 40
Acceptors -12 ltpKalt 16
All -15 ltpKalt 53
Water 0 ltpKalt 14
50
-10
0
10
20
30
40
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
ALDEHYDES
ETHERSALCOHOLS
AMIDES
NITRILES
ANILINES
CF3-SO3H
HClO4HI
HBrHCl
H2SO4
HSO4
HNO3
HBF4
H3PO4
H2PO4
HPO42
HF HNO2
HNNN
NH2OHH2CO3
HCO3
H2S
HS-
HCN H3BO3
H2BO3
H4SiO4
H2O2
HO
HSCN
H-H
SULFONICACIDS
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
OXIMES
ALCOHOLS
THIOLES
HB ACCEPTORS (A)pK BH+
HB DONORS (D-H)pK AH
C-H ACIDS pK AH
BE
TT
ER
HB
AC
CE
PT
OR
BE
TT
ER
BA
SE
BE
TT
ER
HB
DO
NO
R
BE
TT
ER
AC
ID
N-OXIDES
AMIDINES
UREA
THIOUREA
BARBITURICURIC ACID
MONO DIPHOSPHINES
TRIPHOSPHINES
TRINITROANILINES
AMINES
ANILINES
MONO DINITROANILINES
AMIDES
CARBOXYLIC ACIDS
HALOGENOANILINES
AZOCOMPS
TRINITROANILINES
PROTONSPONGES
ACIDSESTERS
H2O
H2O
MONODINITROANILINES
KETONES
SULFIDES
HALOGENCARB ACIDS
TRINITROPHENOLS
ENOLS
MONO DINITROPHENOLS
PHENOLSNAPHTHOLS
HALOGENOPHENOLS
HALOGENOALCOHOLS
SULFOXIDES
(NC)5-CYCLO
PENTADIENE
(NC)3CH
(O2N)2=CH2
HCCHNC-CH3
CH3-CO-CH3INDENE
O2N-CH3
(NC)2=CH2
(O2N)3CH
H2C=CH2
C6H6
CH4
CYCLOPENTADIENE
CYCLOPROPENE
Ar3CH
Ar2=CH2
Ar-CH3
NITROCOMPS
SELENOXIDES
AZOLES
AZINESDIAZINES
AMINES
Cl5-PHENOL
CH3-CH3
(CH3)3CH
NH3
NH3
51
53
51
53
Chemical Leitmotifs and PApChemical Leitmotifs and PApKKaa Equalization Rules Equalization Rules RAHB RAHB cannot be treated by pKa equalization methods because π-delocalization
modifies the pKarsquos of the donor and acceptor moieties (+)CAHB is a true proton transfer from an acid (HB donor) to a base (HB acceptor)
RndashDndashHAndashRrsquo Rndash12DH+A12ndashndashRrsquo RndashDHndashA+ndashRrsquoΔpKa = pKAH(RDH) pKBH+(RrsquoA)
()CAHB is a proton sharing between two acids (HB donors)
RndashDndashHDrsquondashRrsquo [RDHDrsquoRrsquo] RDHDrsquoRrsquoΔpKa = pKAH(RDH) pKAH(RDH)
(+)CAHB is a proton sharing between two bases (HB acceptors)
R+AHArsquoRrsquo [RAHArsquoRrsquo]+ RAHArsquo+RrsquoΔpKa = pKBH+(RA) pKBH+(RrsquoArsquo)
Whenever () and (+)CAHBs are both homonuclear (D = Drsquo or A = Arsquo) and
homomolecular (R = Rrsquo) the matching condition ΔpKa= 0 will hold irrespective of the
actual pKarsquos of the two interacting moieties All HBs formed will be strong
Some Famous HBsSome Famous HBs
The NThe NHmiddotmiddotmiddotOOHmiddotmiddotmiddotOOHmiddotmiddotmiddotN System over the Full HmiddotmiddotmiddotN System over the Full ppKKaa Range Range
When evaluated from the pKa slide rule the total pKa range is extremely wide
ndash30 pa 60 So far we have been able to shown that the pKa equalization rule certainly holds in
a restricted interval around zero The problem is now Does this rule hold in the full pKa range
We will try to prove that by a full analysis the N-HmiddotmiddotmiddotOO-HmiddotmiddotmiddotN system
Procedure In a first CSD search functional groups of known pKa value and more frequently
implied in NHmiddotmiddotmiddotOOHmiddotmiddotmiddotN bonds were identified Finally 10 classes of donors and 11 of acceptors were selected and the search restarted for each separate donor-acceptor group Altogether 9078 different bonds were analyzed (4364 NHmiddotmiddotmiddotO 2289 OHmiddotmiddotmiddotN and
2425 OmiddotmiddotmiddotHN+) For each bond the NmiddotmiddotmiddotO distances were evaluated as dNH + dHO to account for the
N-H-O angle and for each group the shortest and average distances [dNmiddotmiddotmiddotO (min)
and dNmiddotmiddotmiddotO (mean)] were registered
These values were compared (see next slide) with the acid-base features of the donors (pKAH range) acceptors (pKBH+ range) and with their combinations
(pKa range)
pKa large amp positive
pKa largeamp negative
Increasing Acidity of the Protonated A H+ Acceptor Increasing Basicity of the A Acceptor
ppKKaa versusversus HB Geometry Correlation - Conclusions HB Geometry Correlation - Conclusions The PApKa Equalization Principle is therefore fully confirmed in its two forms All strong HBs correspond to very small pKa values
pKa values modulate the HB strength over the full pKa range These conclusions are of great practical importance in at least two respects pKa is definitively established as the driving force which controls the HB
strength by modulating the HB covalent contribution It is definitively established that an accurate analysis of structural crystal data
leads to the same conclusions suggested but never proved on a general base by thermodynamic and spectroscopic methods
References Huyskens and Zeegers-Huyskens 1964 Zeegers-Huyskens 1986 1988 Ault and Pimentel 1975 Ratajczak and Sobczyk 1969 Sobczyk et al 1982 Barnes 1983 Kebarle et al 1974-1979 Meot-Ner (Mautner) et al
1984-1988
Towards a General HB TheoryTowards a General HB Theory
The results so far obtained are not a True HB Theory but rather a Set of Empirical Rules (or an Empirical Natural Law) that is a great collection of HB experimental data neatly organized in tables which all together represent a General Taxonomy of the HB Phenomenon exactly as the Carl Linnaeusrsquo classification of plants A scientific theory is something different It is the casting of the empirical natural law into the frame of a theory which is more fundamental down to the reductionistic chain of the scientific disciplines For instance the kinetic gas theory is the casting of the empirical gas laws (the empirical natural law) into Newtonrsquos classical mechanics
How to make a HB TheoryHow to make a HB Theory
HB Properties = FF (HB Driving Variable)where
HB Driving Variable = PApKa and FF = Transition-State Theory
The Transition-State HB TheoryThe Transition-State HB Theory(Gilli et al JACS 2002 2005 Gilli et al J Mol Struct 2006)
Though it has taken us more than 12 years to develop it
the basic idea is very simpleAny DndashHmiddotmiddotmiddotA bond can be considered as a chemical reaction which is
bimolecular in both directions and proceeds via transition-state (TS) formation
AndashB + C AmiddotmiddotmiddotBmiddotmiddotmiddotC A + BndashCDndashHmiddotmiddotmiddotA DmiddotmiddotmiddotHmiddotmiddotmiddotA DmiddotmiddotmiddotHndashA
Changes of nomenclatureReaction Pathway PTPathwayActivation Energy DaggerE PTBarrierReaction Energy Er PApKa Transition State (TS) PTTS
Reaction Coordinate RC=[d(DH)ndashd(AH)] Experimentals Variable-Temperature X-allographyCalculations DFTEmulated PTPathwaysInterpretation Marcus Rate-Equilibrium Theory LefflerHammond Postulate
AcknowledgmentsAcknowledgments I have to thank my direct coworkers without whose help this work could have not been accomplished
Valerio BERTOLASI Paola GILLI
Valeria FERRETTI Loretta PRETTO
and the scientific institutions which made available to us the databases without which this work could not even be started
CCDCCambridge Crystallographic
Data Centrefor the use of the
Cambridge Structural Database
NIST National Institute of Standards and
Technologyfor the use of the
NIST Chemistry WebBook
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 2(-)CAHB
Negative Charge-Assisted HBAcid-Base PApKa Matching
by Proton Loss[R-DHA-R]-
Chemical Leitmotif 3(+)CAHB
Positive Charge-Assisted HBAcid-Base PApKa Matching
by Proton Gain[R-DHA-R]+
2II
2III
2IIa
2IIb
2IIIb
2IIIa
2VIa
pKa = pKAH(HO-H)-pKAH(HO-H) = 157 - 157 = 0
pKa = pKBH(H2O-H+)-pKBH(H2O-H
+) = -17 + 17 = 0
pKAH(HO-H) = 157
pKBH(H2O-H+) = -17
H
O H
H
O
H
(ndash)CAHB pKa = 00
VERYSTRONG~ 25-30 kcalmol
(+)CAHB pKa = 00
VERYSTRONG ~ 25-31 kcalmol
pKa = 175
OHB
WEAK ~ 4- 5kcalmol
ndash H+
+ H+
H
O H O
H
H
O H O
H
H
OHO
H
H
O
H
H
H
O
H
H
O
H
H
O
H
H H
O
H
H
H
O
H
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 4RAHB
Resonance-Assisted or -Bond Cooperative HBPApKa Matching by -Conjugated-Bond Polarization
R-D-HA=R R=DH-A-R
pKAH(RO-H) = 1518
pKBH(R2C=O-H+) = -(67)
O OH
O H O
R
R
R
Rn-RAHB pKa = ~ 21-25
WEAK ~ 4- 5kcalmol
EKO O
H
KEOO
H
pKa = 00
STRONG ~ 15-22 kcalmol
2IV
2IVa
2IVb
2VIb
OHB
The HB Empirical RulesThe HB Empirical Rules
The empirical analysis of experimental data joined with homeopathic doses of VB theory leads us to formulate two important HB Empirical Rules which have been called elsewhere ECHBM (Electrostatic-Covalent HB Model Gilli amp Gilli J Mol Struct 2000) and can be summarized as follows
Any given D-HA system may form HBs in a wide range of strengths lengths symmetries and proton locations the two extremes being represented
by the weak long dissymmetric and proton-out-centred HB of electrostatic nature
and by the very strong very short symmetric and proton-centred HB
classifiable as a true 3-center-4-electron covalent bond
The driving variable able to transform strong into weak HBs is dimensionally a free enthalpy corresponding to the difference between the Proton Affinities (PA) or related Acid-Base Dissociation Constants (pKa) of the Donor and Acceptor moieties
These rules have been verified beyond any reasonable doubt for the Conventional HBs of the following classification
Provisional Conclusions and New ControlsProvisional Conclusions and New Controls
We have so far established a sound set of empirical rules which include A full classification of all existing HBs A full classification of all strong HBs (The Chemical Leitmotifs) A plausible correlation between HB strengths and acid-base properties of the interacting molecules (The PApKa Equalization Principle)
To confirm this last point we have undertaken two years ago
a new research program aimed at assessing the Full Validity of the PApKa Equalization Principle
by comparing extended tables of pKa values arranged for chemical classes
withthe corresponding CSD-derived HB geometries
Hundreds of pKa were collected and more than 11000 crystal structures examined
The pThe pKKa Slide Rulea Slide Rule
It is a tool for the graphical evaluation of the difference
pKa = pKAH(DH) - pKBH+(AH+)
HB Acceptors on the left and HB Donors on the right
pKa values given for chemical class
Results expected
ΔpKagtgt0 DHmiddotmiddotmiddotmiddotA weak amp neutral
ΔpKa asymp 0 DmiddotmiddotmiddotHmiddotmiddotmiddotA strong amp
centeredΔpKa ltlt0DmiddotmiddotmiddotmiddotHA+ weak amp charged
pKa ranges of organic compounds
C-H acids -11 ltpKalt 53
Other Donors -1 ltpKalt 40
Acceptors -12 ltpKalt 16
All -15 ltpKalt 53
Water 0 ltpKalt 14
50
-10
0
10
20
30
40
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
ALDEHYDES
ETHERSALCOHOLS
AMIDES
NITRILES
ANILINES
CF3-SO3H
HClO4HI
HBrHCl
H2SO4
HSO4
HNO3
HBF4
H3PO4
H2PO4
HPO42
HF HNO2
HNNN
NH2OHH2CO3
HCO3
H2S
HS-
HCN H3BO3
H2BO3
H4SiO4
H2O2
HO
HSCN
H-H
SULFONICACIDS
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
OXIMES
ALCOHOLS
THIOLES
HB ACCEPTORS (A)pK BH+
HB DONORS (D-H)pK AH
C-H ACIDS pK AH
BE
TT
ER
HB
AC
CE
PT
OR
BE
TT
ER
BA
SE
BE
TT
ER
HB
DO
NO
R
BE
TT
ER
AC
ID
N-OXIDES
AMIDINES
UREA
THIOUREA
BARBITURICURIC ACID
MONO DIPHOSPHINES
TRIPHOSPHINES
TRINITROANILINES
AMINES
ANILINES
MONO DINITROANILINES
AMIDES
CARBOXYLIC ACIDS
HALOGENOANILINES
AZOCOMPS
TRINITROANILINES
PROTONSPONGES
ACIDSESTERS
H2O
H2O
MONODINITROANILINES
KETONES
SULFIDES
HALOGENCARB ACIDS
TRINITROPHENOLS
ENOLS
MONO DINITROPHENOLS
PHENOLSNAPHTHOLS
HALOGENOPHENOLS
HALOGENOALCOHOLS
SULFOXIDES
(NC)5-CYCLO
PENTADIENE
(NC)3CH
(O2N)2=CH2
HCCHNC-CH3
CH3-CO-CH3INDENE
O2N-CH3
(NC)2=CH2
(O2N)3CH
H2C=CH2
C6H6
CH4
CYCLOPENTADIENE
CYCLOPROPENE
Ar3CH
Ar2=CH2
Ar-CH3
NITROCOMPS
SELENOXIDES
AZOLES
AZINESDIAZINES
AMINES
Cl5-PHENOL
CH3-CH3
(CH3)3CH
NH3
NH3
51
53
51
53
Chemical Leitmotifs and PApChemical Leitmotifs and PApKKaa Equalization Rules Equalization Rules RAHB RAHB cannot be treated by pKa equalization methods because π-delocalization
modifies the pKarsquos of the donor and acceptor moieties (+)CAHB is a true proton transfer from an acid (HB donor) to a base (HB acceptor)
RndashDndashHAndashRrsquo Rndash12DH+A12ndashndashRrsquo RndashDHndashA+ndashRrsquoΔpKa = pKAH(RDH) pKBH+(RrsquoA)
()CAHB is a proton sharing between two acids (HB donors)
RndashDndashHDrsquondashRrsquo [RDHDrsquoRrsquo] RDHDrsquoRrsquoΔpKa = pKAH(RDH) pKAH(RDH)
(+)CAHB is a proton sharing between two bases (HB acceptors)
R+AHArsquoRrsquo [RAHArsquoRrsquo]+ RAHArsquo+RrsquoΔpKa = pKBH+(RA) pKBH+(RrsquoArsquo)
Whenever () and (+)CAHBs are both homonuclear (D = Drsquo or A = Arsquo) and
homomolecular (R = Rrsquo) the matching condition ΔpKa= 0 will hold irrespective of the
actual pKarsquos of the two interacting moieties All HBs formed will be strong
Some Famous HBsSome Famous HBs
The NThe NHmiddotmiddotmiddotOOHmiddotmiddotmiddotOOHmiddotmiddotmiddotN System over the Full HmiddotmiddotmiddotN System over the Full ppKKaa Range Range
When evaluated from the pKa slide rule the total pKa range is extremely wide
ndash30 pa 60 So far we have been able to shown that the pKa equalization rule certainly holds in
a restricted interval around zero The problem is now Does this rule hold in the full pKa range
We will try to prove that by a full analysis the N-HmiddotmiddotmiddotOO-HmiddotmiddotmiddotN system
Procedure In a first CSD search functional groups of known pKa value and more frequently
implied in NHmiddotmiddotmiddotOOHmiddotmiddotmiddotN bonds were identified Finally 10 classes of donors and 11 of acceptors were selected and the search restarted for each separate donor-acceptor group Altogether 9078 different bonds were analyzed (4364 NHmiddotmiddotmiddotO 2289 OHmiddotmiddotmiddotN and
2425 OmiddotmiddotmiddotHN+) For each bond the NmiddotmiddotmiddotO distances were evaluated as dNH + dHO to account for the
N-H-O angle and for each group the shortest and average distances [dNmiddotmiddotmiddotO (min)
and dNmiddotmiddotmiddotO (mean)] were registered
These values were compared (see next slide) with the acid-base features of the donors (pKAH range) acceptors (pKBH+ range) and with their combinations
(pKa range)
pKa large amp positive
pKa largeamp negative
Increasing Acidity of the Protonated A H+ Acceptor Increasing Basicity of the A Acceptor
ppKKaa versusversus HB Geometry Correlation - Conclusions HB Geometry Correlation - Conclusions The PApKa Equalization Principle is therefore fully confirmed in its two forms All strong HBs correspond to very small pKa values
pKa values modulate the HB strength over the full pKa range These conclusions are of great practical importance in at least two respects pKa is definitively established as the driving force which controls the HB
strength by modulating the HB covalent contribution It is definitively established that an accurate analysis of structural crystal data
leads to the same conclusions suggested but never proved on a general base by thermodynamic and spectroscopic methods
References Huyskens and Zeegers-Huyskens 1964 Zeegers-Huyskens 1986 1988 Ault and Pimentel 1975 Ratajczak and Sobczyk 1969 Sobczyk et al 1982 Barnes 1983 Kebarle et al 1974-1979 Meot-Ner (Mautner) et al
1984-1988
Towards a General HB TheoryTowards a General HB Theory
The results so far obtained are not a True HB Theory but rather a Set of Empirical Rules (or an Empirical Natural Law) that is a great collection of HB experimental data neatly organized in tables which all together represent a General Taxonomy of the HB Phenomenon exactly as the Carl Linnaeusrsquo classification of plants A scientific theory is something different It is the casting of the empirical natural law into the frame of a theory which is more fundamental down to the reductionistic chain of the scientific disciplines For instance the kinetic gas theory is the casting of the empirical gas laws (the empirical natural law) into Newtonrsquos classical mechanics
How to make a HB TheoryHow to make a HB Theory
HB Properties = FF (HB Driving Variable)where
HB Driving Variable = PApKa and FF = Transition-State Theory
The Transition-State HB TheoryThe Transition-State HB Theory(Gilli et al JACS 2002 2005 Gilli et al J Mol Struct 2006)
Though it has taken us more than 12 years to develop it
the basic idea is very simpleAny DndashHmiddotmiddotmiddotA bond can be considered as a chemical reaction which is
bimolecular in both directions and proceeds via transition-state (TS) formation
AndashB + C AmiddotmiddotmiddotBmiddotmiddotmiddotC A + BndashCDndashHmiddotmiddotmiddotA DmiddotmiddotmiddotHmiddotmiddotmiddotA DmiddotmiddotmiddotHndashA
Changes of nomenclatureReaction Pathway PTPathwayActivation Energy DaggerE PTBarrierReaction Energy Er PApKa Transition State (TS) PTTS
Reaction Coordinate RC=[d(DH)ndashd(AH)] Experimentals Variable-Temperature X-allographyCalculations DFTEmulated PTPathwaysInterpretation Marcus Rate-Equilibrium Theory LefflerHammond Postulate
AcknowledgmentsAcknowledgments I have to thank my direct coworkers without whose help this work could have not been accomplished
Valerio BERTOLASI Paola GILLI
Valeria FERRETTI Loretta PRETTO
and the scientific institutions which made available to us the databases without which this work could not even be started
CCDCCambridge Crystallographic
Data Centrefor the use of the
Cambridge Structural Database
NIST National Institute of Standards and
Technologyfor the use of the
NIST Chemistry WebBook
The Origin of the Chemical Leitmotifs The Origin of the Chemical Leitmotifs The PApThe PApKKaa Equalization Principle Equalization Principle
Chemical Leitmotif 4RAHB
Resonance-Assisted or -Bond Cooperative HBPApKa Matching by -Conjugated-Bond Polarization
R-D-HA=R R=DH-A-R
pKAH(RO-H) = 1518
pKBH(R2C=O-H+) = -(67)
O OH
O H O
R
R
R
Rn-RAHB pKa = ~ 21-25
WEAK ~ 4- 5kcalmol
EKO O
H
KEOO
H
pKa = 00
STRONG ~ 15-22 kcalmol
2IV
2IVa
2IVb
2VIb
OHB
The HB Empirical RulesThe HB Empirical Rules
The empirical analysis of experimental data joined with homeopathic doses of VB theory leads us to formulate two important HB Empirical Rules which have been called elsewhere ECHBM (Electrostatic-Covalent HB Model Gilli amp Gilli J Mol Struct 2000) and can be summarized as follows
Any given D-HA system may form HBs in a wide range of strengths lengths symmetries and proton locations the two extremes being represented
by the weak long dissymmetric and proton-out-centred HB of electrostatic nature
and by the very strong very short symmetric and proton-centred HB
classifiable as a true 3-center-4-electron covalent bond
The driving variable able to transform strong into weak HBs is dimensionally a free enthalpy corresponding to the difference between the Proton Affinities (PA) or related Acid-Base Dissociation Constants (pKa) of the Donor and Acceptor moieties
These rules have been verified beyond any reasonable doubt for the Conventional HBs of the following classification
Provisional Conclusions and New ControlsProvisional Conclusions and New Controls
We have so far established a sound set of empirical rules which include A full classification of all existing HBs A full classification of all strong HBs (The Chemical Leitmotifs) A plausible correlation between HB strengths and acid-base properties of the interacting molecules (The PApKa Equalization Principle)
To confirm this last point we have undertaken two years ago
a new research program aimed at assessing the Full Validity of the PApKa Equalization Principle
by comparing extended tables of pKa values arranged for chemical classes
withthe corresponding CSD-derived HB geometries
Hundreds of pKa were collected and more than 11000 crystal structures examined
The pThe pKKa Slide Rulea Slide Rule
It is a tool for the graphical evaluation of the difference
pKa = pKAH(DH) - pKBH+(AH+)
HB Acceptors on the left and HB Donors on the right
pKa values given for chemical class
Results expected
ΔpKagtgt0 DHmiddotmiddotmiddotmiddotA weak amp neutral
ΔpKa asymp 0 DmiddotmiddotmiddotHmiddotmiddotmiddotA strong amp
centeredΔpKa ltlt0DmiddotmiddotmiddotmiddotHA+ weak amp charged
pKa ranges of organic compounds
C-H acids -11 ltpKalt 53
Other Donors -1 ltpKalt 40
Acceptors -12 ltpKalt 16
All -15 ltpKalt 53
Water 0 ltpKalt 14
50
-10
0
10
20
30
40
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
ALDEHYDES
ETHERSALCOHOLS
AMIDES
NITRILES
ANILINES
CF3-SO3H
HClO4HI
HBrHCl
H2SO4
HSO4
HNO3
HBF4
H3PO4
H2PO4
HPO42
HF HNO2
HNNN
NH2OHH2CO3
HCO3
H2S
HS-
HCN H3BO3
H2BO3
H4SiO4
H2O2
HO
HSCN
H-H
SULFONICACIDS
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
OXIMES
ALCOHOLS
THIOLES
HB ACCEPTORS (A)pK BH+
HB DONORS (D-H)pK AH
C-H ACIDS pK AH
BE
TT
ER
HB
AC
CE
PT
OR
BE
TT
ER
BA
SE
BE
TT
ER
HB
DO
NO
R
BE
TT
ER
AC
ID
N-OXIDES
AMIDINES
UREA
THIOUREA
BARBITURICURIC ACID
MONO DIPHOSPHINES
TRIPHOSPHINES
TRINITROANILINES
AMINES
ANILINES
MONO DINITROANILINES
AMIDES
CARBOXYLIC ACIDS
HALOGENOANILINES
AZOCOMPS
TRINITROANILINES
PROTONSPONGES
ACIDSESTERS
H2O
H2O
MONODINITROANILINES
KETONES
SULFIDES
HALOGENCARB ACIDS
TRINITROPHENOLS
ENOLS
MONO DINITROPHENOLS
PHENOLSNAPHTHOLS
HALOGENOPHENOLS
HALOGENOALCOHOLS
SULFOXIDES
(NC)5-CYCLO
PENTADIENE
(NC)3CH
(O2N)2=CH2
HCCHNC-CH3
CH3-CO-CH3INDENE
O2N-CH3
(NC)2=CH2
(O2N)3CH
H2C=CH2
C6H6
CH4
CYCLOPENTADIENE
CYCLOPROPENE
Ar3CH
Ar2=CH2
Ar-CH3
NITROCOMPS
SELENOXIDES
AZOLES
AZINESDIAZINES
AMINES
Cl5-PHENOL
CH3-CH3
(CH3)3CH
NH3
NH3
51
53
51
53
Chemical Leitmotifs and PApChemical Leitmotifs and PApKKaa Equalization Rules Equalization Rules RAHB RAHB cannot be treated by pKa equalization methods because π-delocalization
modifies the pKarsquos of the donor and acceptor moieties (+)CAHB is a true proton transfer from an acid (HB donor) to a base (HB acceptor)
RndashDndashHAndashRrsquo Rndash12DH+A12ndashndashRrsquo RndashDHndashA+ndashRrsquoΔpKa = pKAH(RDH) pKBH+(RrsquoA)
()CAHB is a proton sharing between two acids (HB donors)
RndashDndashHDrsquondashRrsquo [RDHDrsquoRrsquo] RDHDrsquoRrsquoΔpKa = pKAH(RDH) pKAH(RDH)
(+)CAHB is a proton sharing between two bases (HB acceptors)
R+AHArsquoRrsquo [RAHArsquoRrsquo]+ RAHArsquo+RrsquoΔpKa = pKBH+(RA) pKBH+(RrsquoArsquo)
Whenever () and (+)CAHBs are both homonuclear (D = Drsquo or A = Arsquo) and
homomolecular (R = Rrsquo) the matching condition ΔpKa= 0 will hold irrespective of the
actual pKarsquos of the two interacting moieties All HBs formed will be strong
Some Famous HBsSome Famous HBs
The NThe NHmiddotmiddotmiddotOOHmiddotmiddotmiddotOOHmiddotmiddotmiddotN System over the Full HmiddotmiddotmiddotN System over the Full ppKKaa Range Range
When evaluated from the pKa slide rule the total pKa range is extremely wide
ndash30 pa 60 So far we have been able to shown that the pKa equalization rule certainly holds in
a restricted interval around zero The problem is now Does this rule hold in the full pKa range
We will try to prove that by a full analysis the N-HmiddotmiddotmiddotOO-HmiddotmiddotmiddotN system
Procedure In a first CSD search functional groups of known pKa value and more frequently
implied in NHmiddotmiddotmiddotOOHmiddotmiddotmiddotN bonds were identified Finally 10 classes of donors and 11 of acceptors were selected and the search restarted for each separate donor-acceptor group Altogether 9078 different bonds were analyzed (4364 NHmiddotmiddotmiddotO 2289 OHmiddotmiddotmiddotN and
2425 OmiddotmiddotmiddotHN+) For each bond the NmiddotmiddotmiddotO distances were evaluated as dNH + dHO to account for the
N-H-O angle and for each group the shortest and average distances [dNmiddotmiddotmiddotO (min)
and dNmiddotmiddotmiddotO (mean)] were registered
These values were compared (see next slide) with the acid-base features of the donors (pKAH range) acceptors (pKBH+ range) and with their combinations
(pKa range)
pKa large amp positive
pKa largeamp negative
Increasing Acidity of the Protonated A H+ Acceptor Increasing Basicity of the A Acceptor
ppKKaa versusversus HB Geometry Correlation - Conclusions HB Geometry Correlation - Conclusions The PApKa Equalization Principle is therefore fully confirmed in its two forms All strong HBs correspond to very small pKa values
pKa values modulate the HB strength over the full pKa range These conclusions are of great practical importance in at least two respects pKa is definitively established as the driving force which controls the HB
strength by modulating the HB covalent contribution It is definitively established that an accurate analysis of structural crystal data
leads to the same conclusions suggested but never proved on a general base by thermodynamic and spectroscopic methods
References Huyskens and Zeegers-Huyskens 1964 Zeegers-Huyskens 1986 1988 Ault and Pimentel 1975 Ratajczak and Sobczyk 1969 Sobczyk et al 1982 Barnes 1983 Kebarle et al 1974-1979 Meot-Ner (Mautner) et al
1984-1988
Towards a General HB TheoryTowards a General HB Theory
The results so far obtained are not a True HB Theory but rather a Set of Empirical Rules (or an Empirical Natural Law) that is a great collection of HB experimental data neatly organized in tables which all together represent a General Taxonomy of the HB Phenomenon exactly as the Carl Linnaeusrsquo classification of plants A scientific theory is something different It is the casting of the empirical natural law into the frame of a theory which is more fundamental down to the reductionistic chain of the scientific disciplines For instance the kinetic gas theory is the casting of the empirical gas laws (the empirical natural law) into Newtonrsquos classical mechanics
How to make a HB TheoryHow to make a HB Theory
HB Properties = FF (HB Driving Variable)where
HB Driving Variable = PApKa and FF = Transition-State Theory
The Transition-State HB TheoryThe Transition-State HB Theory(Gilli et al JACS 2002 2005 Gilli et al J Mol Struct 2006)
Though it has taken us more than 12 years to develop it
the basic idea is very simpleAny DndashHmiddotmiddotmiddotA bond can be considered as a chemical reaction which is
bimolecular in both directions and proceeds via transition-state (TS) formation
AndashB + C AmiddotmiddotmiddotBmiddotmiddotmiddotC A + BndashCDndashHmiddotmiddotmiddotA DmiddotmiddotmiddotHmiddotmiddotmiddotA DmiddotmiddotmiddotHndashA
Changes of nomenclatureReaction Pathway PTPathwayActivation Energy DaggerE PTBarrierReaction Energy Er PApKa Transition State (TS) PTTS
Reaction Coordinate RC=[d(DH)ndashd(AH)] Experimentals Variable-Temperature X-allographyCalculations DFTEmulated PTPathwaysInterpretation Marcus Rate-Equilibrium Theory LefflerHammond Postulate
AcknowledgmentsAcknowledgments I have to thank my direct coworkers without whose help this work could have not been accomplished
Valerio BERTOLASI Paola GILLI
Valeria FERRETTI Loretta PRETTO
and the scientific institutions which made available to us the databases without which this work could not even be started
CCDCCambridge Crystallographic
Data Centrefor the use of the
Cambridge Structural Database
NIST National Institute of Standards and
Technologyfor the use of the
NIST Chemistry WebBook
The HB Empirical RulesThe HB Empirical Rules
The empirical analysis of experimental data joined with homeopathic doses of VB theory leads us to formulate two important HB Empirical Rules which have been called elsewhere ECHBM (Electrostatic-Covalent HB Model Gilli amp Gilli J Mol Struct 2000) and can be summarized as follows
Any given D-HA system may form HBs in a wide range of strengths lengths symmetries and proton locations the two extremes being represented
by the weak long dissymmetric and proton-out-centred HB of electrostatic nature
and by the very strong very short symmetric and proton-centred HB
classifiable as a true 3-center-4-electron covalent bond
The driving variable able to transform strong into weak HBs is dimensionally a free enthalpy corresponding to the difference between the Proton Affinities (PA) or related Acid-Base Dissociation Constants (pKa) of the Donor and Acceptor moieties
These rules have been verified beyond any reasonable doubt for the Conventional HBs of the following classification
Provisional Conclusions and New ControlsProvisional Conclusions and New Controls
We have so far established a sound set of empirical rules which include A full classification of all existing HBs A full classification of all strong HBs (The Chemical Leitmotifs) A plausible correlation between HB strengths and acid-base properties of the interacting molecules (The PApKa Equalization Principle)
To confirm this last point we have undertaken two years ago
a new research program aimed at assessing the Full Validity of the PApKa Equalization Principle
by comparing extended tables of pKa values arranged for chemical classes
withthe corresponding CSD-derived HB geometries
Hundreds of pKa were collected and more than 11000 crystal structures examined
The pThe pKKa Slide Rulea Slide Rule
It is a tool for the graphical evaluation of the difference
pKa = pKAH(DH) - pKBH+(AH+)
HB Acceptors on the left and HB Donors on the right
pKa values given for chemical class
Results expected
ΔpKagtgt0 DHmiddotmiddotmiddotmiddotA weak amp neutral
ΔpKa asymp 0 DmiddotmiddotmiddotHmiddotmiddotmiddotA strong amp
centeredΔpKa ltlt0DmiddotmiddotmiddotmiddotHA+ weak amp charged
pKa ranges of organic compounds
C-H acids -11 ltpKalt 53
Other Donors -1 ltpKalt 40
Acceptors -12 ltpKalt 16
All -15 ltpKalt 53
Water 0 ltpKalt 14
50
-10
0
10
20
30
40
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
ALDEHYDES
ETHERSALCOHOLS
AMIDES
NITRILES
ANILINES
CF3-SO3H
HClO4HI
HBrHCl
H2SO4
HSO4
HNO3
HBF4
H3PO4
H2PO4
HPO42
HF HNO2
HNNN
NH2OHH2CO3
HCO3
H2S
HS-
HCN H3BO3
H2BO3
H4SiO4
H2O2
HO
HSCN
H-H
SULFONICACIDS
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
OXIMES
ALCOHOLS
THIOLES
HB ACCEPTORS (A)pK BH+
HB DONORS (D-H)pK AH
C-H ACIDS pK AH
BE
TT
ER
HB
AC
CE
PT
OR
BE
TT
ER
BA
SE
BE
TT
ER
HB
DO
NO
R
BE
TT
ER
AC
ID
N-OXIDES
AMIDINES
UREA
THIOUREA
BARBITURICURIC ACID
MONO DIPHOSPHINES
TRIPHOSPHINES
TRINITROANILINES
AMINES
ANILINES
MONO DINITROANILINES
AMIDES
CARBOXYLIC ACIDS
HALOGENOANILINES
AZOCOMPS
TRINITROANILINES
PROTONSPONGES
ACIDSESTERS
H2O
H2O
MONODINITROANILINES
KETONES
SULFIDES
HALOGENCARB ACIDS
TRINITROPHENOLS
ENOLS
MONO DINITROPHENOLS
PHENOLSNAPHTHOLS
HALOGENOPHENOLS
HALOGENOALCOHOLS
SULFOXIDES
(NC)5-CYCLO
PENTADIENE
(NC)3CH
(O2N)2=CH2
HCCHNC-CH3
CH3-CO-CH3INDENE
O2N-CH3
(NC)2=CH2
(O2N)3CH
H2C=CH2
C6H6
CH4
CYCLOPENTADIENE
CYCLOPROPENE
Ar3CH
Ar2=CH2
Ar-CH3
NITROCOMPS
SELENOXIDES
AZOLES
AZINESDIAZINES
AMINES
Cl5-PHENOL
CH3-CH3
(CH3)3CH
NH3
NH3
51
53
51
53
Chemical Leitmotifs and PApChemical Leitmotifs and PApKKaa Equalization Rules Equalization Rules RAHB RAHB cannot be treated by pKa equalization methods because π-delocalization
modifies the pKarsquos of the donor and acceptor moieties (+)CAHB is a true proton transfer from an acid (HB donor) to a base (HB acceptor)
RndashDndashHAndashRrsquo Rndash12DH+A12ndashndashRrsquo RndashDHndashA+ndashRrsquoΔpKa = pKAH(RDH) pKBH+(RrsquoA)
()CAHB is a proton sharing between two acids (HB donors)
RndashDndashHDrsquondashRrsquo [RDHDrsquoRrsquo] RDHDrsquoRrsquoΔpKa = pKAH(RDH) pKAH(RDH)
(+)CAHB is a proton sharing between two bases (HB acceptors)
R+AHArsquoRrsquo [RAHArsquoRrsquo]+ RAHArsquo+RrsquoΔpKa = pKBH+(RA) pKBH+(RrsquoArsquo)
Whenever () and (+)CAHBs are both homonuclear (D = Drsquo or A = Arsquo) and
homomolecular (R = Rrsquo) the matching condition ΔpKa= 0 will hold irrespective of the
actual pKarsquos of the two interacting moieties All HBs formed will be strong
Some Famous HBsSome Famous HBs
The NThe NHmiddotmiddotmiddotOOHmiddotmiddotmiddotOOHmiddotmiddotmiddotN System over the Full HmiddotmiddotmiddotN System over the Full ppKKaa Range Range
When evaluated from the pKa slide rule the total pKa range is extremely wide
ndash30 pa 60 So far we have been able to shown that the pKa equalization rule certainly holds in
a restricted interval around zero The problem is now Does this rule hold in the full pKa range
We will try to prove that by a full analysis the N-HmiddotmiddotmiddotOO-HmiddotmiddotmiddotN system
Procedure In a first CSD search functional groups of known pKa value and more frequently
implied in NHmiddotmiddotmiddotOOHmiddotmiddotmiddotN bonds were identified Finally 10 classes of donors and 11 of acceptors were selected and the search restarted for each separate donor-acceptor group Altogether 9078 different bonds were analyzed (4364 NHmiddotmiddotmiddotO 2289 OHmiddotmiddotmiddotN and
2425 OmiddotmiddotmiddotHN+) For each bond the NmiddotmiddotmiddotO distances were evaluated as dNH + dHO to account for the
N-H-O angle and for each group the shortest and average distances [dNmiddotmiddotmiddotO (min)
and dNmiddotmiddotmiddotO (mean)] were registered
These values were compared (see next slide) with the acid-base features of the donors (pKAH range) acceptors (pKBH+ range) and with their combinations
(pKa range)
pKa large amp positive
pKa largeamp negative
Increasing Acidity of the Protonated A H+ Acceptor Increasing Basicity of the A Acceptor
ppKKaa versusversus HB Geometry Correlation - Conclusions HB Geometry Correlation - Conclusions The PApKa Equalization Principle is therefore fully confirmed in its two forms All strong HBs correspond to very small pKa values
pKa values modulate the HB strength over the full pKa range These conclusions are of great practical importance in at least two respects pKa is definitively established as the driving force which controls the HB
strength by modulating the HB covalent contribution It is definitively established that an accurate analysis of structural crystal data
leads to the same conclusions suggested but never proved on a general base by thermodynamic and spectroscopic methods
References Huyskens and Zeegers-Huyskens 1964 Zeegers-Huyskens 1986 1988 Ault and Pimentel 1975 Ratajczak and Sobczyk 1969 Sobczyk et al 1982 Barnes 1983 Kebarle et al 1974-1979 Meot-Ner (Mautner) et al
1984-1988
Towards a General HB TheoryTowards a General HB Theory
The results so far obtained are not a True HB Theory but rather a Set of Empirical Rules (or an Empirical Natural Law) that is a great collection of HB experimental data neatly organized in tables which all together represent a General Taxonomy of the HB Phenomenon exactly as the Carl Linnaeusrsquo classification of plants A scientific theory is something different It is the casting of the empirical natural law into the frame of a theory which is more fundamental down to the reductionistic chain of the scientific disciplines For instance the kinetic gas theory is the casting of the empirical gas laws (the empirical natural law) into Newtonrsquos classical mechanics
How to make a HB TheoryHow to make a HB Theory
HB Properties = FF (HB Driving Variable)where
HB Driving Variable = PApKa and FF = Transition-State Theory
The Transition-State HB TheoryThe Transition-State HB Theory(Gilli et al JACS 2002 2005 Gilli et al J Mol Struct 2006)
Though it has taken us more than 12 years to develop it
the basic idea is very simpleAny DndashHmiddotmiddotmiddotA bond can be considered as a chemical reaction which is
bimolecular in both directions and proceeds via transition-state (TS) formation
AndashB + C AmiddotmiddotmiddotBmiddotmiddotmiddotC A + BndashCDndashHmiddotmiddotmiddotA DmiddotmiddotmiddotHmiddotmiddotmiddotA DmiddotmiddotmiddotHndashA
Changes of nomenclatureReaction Pathway PTPathwayActivation Energy DaggerE PTBarrierReaction Energy Er PApKa Transition State (TS) PTTS
Reaction Coordinate RC=[d(DH)ndashd(AH)] Experimentals Variable-Temperature X-allographyCalculations DFTEmulated PTPathwaysInterpretation Marcus Rate-Equilibrium Theory LefflerHammond Postulate
AcknowledgmentsAcknowledgments I have to thank my direct coworkers without whose help this work could have not been accomplished
Valerio BERTOLASI Paola GILLI
Valeria FERRETTI Loretta PRETTO
and the scientific institutions which made available to us the databases without which this work could not even be started
CCDCCambridge Crystallographic
Data Centrefor the use of the
Cambridge Structural Database
NIST National Institute of Standards and
Technologyfor the use of the
NIST Chemistry WebBook
Provisional Conclusions and New ControlsProvisional Conclusions and New Controls
We have so far established a sound set of empirical rules which include A full classification of all existing HBs A full classification of all strong HBs (The Chemical Leitmotifs) A plausible correlation between HB strengths and acid-base properties of the interacting molecules (The PApKa Equalization Principle)
To confirm this last point we have undertaken two years ago
a new research program aimed at assessing the Full Validity of the PApKa Equalization Principle
by comparing extended tables of pKa values arranged for chemical classes
withthe corresponding CSD-derived HB geometries
Hundreds of pKa were collected and more than 11000 crystal structures examined
The pThe pKKa Slide Rulea Slide Rule
It is a tool for the graphical evaluation of the difference
pKa = pKAH(DH) - pKBH+(AH+)
HB Acceptors on the left and HB Donors on the right
pKa values given for chemical class
Results expected
ΔpKagtgt0 DHmiddotmiddotmiddotmiddotA weak amp neutral
ΔpKa asymp 0 DmiddotmiddotmiddotHmiddotmiddotmiddotA strong amp
centeredΔpKa ltlt0DmiddotmiddotmiddotmiddotHA+ weak amp charged
pKa ranges of organic compounds
C-H acids -11 ltpKalt 53
Other Donors -1 ltpKalt 40
Acceptors -12 ltpKalt 16
All -15 ltpKalt 53
Water 0 ltpKalt 14
50
-10
0
10
20
30
40
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
ALDEHYDES
ETHERSALCOHOLS
AMIDES
NITRILES
ANILINES
CF3-SO3H
HClO4HI
HBrHCl
H2SO4
HSO4
HNO3
HBF4
H3PO4
H2PO4
HPO42
HF HNO2
HNNN
NH2OHH2CO3
HCO3
H2S
HS-
HCN H3BO3
H2BO3
H4SiO4
H2O2
HO
HSCN
H-H
SULFONICACIDS
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
OXIMES
ALCOHOLS
THIOLES
HB ACCEPTORS (A)pK BH+
HB DONORS (D-H)pK AH
C-H ACIDS pK AH
BE
TT
ER
HB
AC
CE
PT
OR
BE
TT
ER
BA
SE
BE
TT
ER
HB
DO
NO
R
BE
TT
ER
AC
ID
N-OXIDES
AMIDINES
UREA
THIOUREA
BARBITURICURIC ACID
MONO DIPHOSPHINES
TRIPHOSPHINES
TRINITROANILINES
AMINES
ANILINES
MONO DINITROANILINES
AMIDES
CARBOXYLIC ACIDS
HALOGENOANILINES
AZOCOMPS
TRINITROANILINES
PROTONSPONGES
ACIDSESTERS
H2O
H2O
MONODINITROANILINES
KETONES
SULFIDES
HALOGENCARB ACIDS
TRINITROPHENOLS
ENOLS
MONO DINITROPHENOLS
PHENOLSNAPHTHOLS
HALOGENOPHENOLS
HALOGENOALCOHOLS
SULFOXIDES
(NC)5-CYCLO
PENTADIENE
(NC)3CH
(O2N)2=CH2
HCCHNC-CH3
CH3-CO-CH3INDENE
O2N-CH3
(NC)2=CH2
(O2N)3CH
H2C=CH2
C6H6
CH4
CYCLOPENTADIENE
CYCLOPROPENE
Ar3CH
Ar2=CH2
Ar-CH3
NITROCOMPS
SELENOXIDES
AZOLES
AZINESDIAZINES
AMINES
Cl5-PHENOL
CH3-CH3
(CH3)3CH
NH3
NH3
51
53
51
53
Chemical Leitmotifs and PApChemical Leitmotifs and PApKKaa Equalization Rules Equalization Rules RAHB RAHB cannot be treated by pKa equalization methods because π-delocalization
modifies the pKarsquos of the donor and acceptor moieties (+)CAHB is a true proton transfer from an acid (HB donor) to a base (HB acceptor)
RndashDndashHAndashRrsquo Rndash12DH+A12ndashndashRrsquo RndashDHndashA+ndashRrsquoΔpKa = pKAH(RDH) pKBH+(RrsquoA)
()CAHB is a proton sharing between two acids (HB donors)
RndashDndashHDrsquondashRrsquo [RDHDrsquoRrsquo] RDHDrsquoRrsquoΔpKa = pKAH(RDH) pKAH(RDH)
(+)CAHB is a proton sharing between two bases (HB acceptors)
R+AHArsquoRrsquo [RAHArsquoRrsquo]+ RAHArsquo+RrsquoΔpKa = pKBH+(RA) pKBH+(RrsquoArsquo)
Whenever () and (+)CAHBs are both homonuclear (D = Drsquo or A = Arsquo) and
homomolecular (R = Rrsquo) the matching condition ΔpKa= 0 will hold irrespective of the
actual pKarsquos of the two interacting moieties All HBs formed will be strong
Some Famous HBsSome Famous HBs
The NThe NHmiddotmiddotmiddotOOHmiddotmiddotmiddotOOHmiddotmiddotmiddotN System over the Full HmiddotmiddotmiddotN System over the Full ppKKaa Range Range
When evaluated from the pKa slide rule the total pKa range is extremely wide
ndash30 pa 60 So far we have been able to shown that the pKa equalization rule certainly holds in
a restricted interval around zero The problem is now Does this rule hold in the full pKa range
We will try to prove that by a full analysis the N-HmiddotmiddotmiddotOO-HmiddotmiddotmiddotN system
Procedure In a first CSD search functional groups of known pKa value and more frequently
implied in NHmiddotmiddotmiddotOOHmiddotmiddotmiddotN bonds were identified Finally 10 classes of donors and 11 of acceptors were selected and the search restarted for each separate donor-acceptor group Altogether 9078 different bonds were analyzed (4364 NHmiddotmiddotmiddotO 2289 OHmiddotmiddotmiddotN and
2425 OmiddotmiddotmiddotHN+) For each bond the NmiddotmiddotmiddotO distances were evaluated as dNH + dHO to account for the
N-H-O angle and for each group the shortest and average distances [dNmiddotmiddotmiddotO (min)
and dNmiddotmiddotmiddotO (mean)] were registered
These values were compared (see next slide) with the acid-base features of the donors (pKAH range) acceptors (pKBH+ range) and with their combinations
(pKa range)
pKa large amp positive
pKa largeamp negative
Increasing Acidity of the Protonated A H+ Acceptor Increasing Basicity of the A Acceptor
ppKKaa versusversus HB Geometry Correlation - Conclusions HB Geometry Correlation - Conclusions The PApKa Equalization Principle is therefore fully confirmed in its two forms All strong HBs correspond to very small pKa values
pKa values modulate the HB strength over the full pKa range These conclusions are of great practical importance in at least two respects pKa is definitively established as the driving force which controls the HB
strength by modulating the HB covalent contribution It is definitively established that an accurate analysis of structural crystal data
leads to the same conclusions suggested but never proved on a general base by thermodynamic and spectroscopic methods
References Huyskens and Zeegers-Huyskens 1964 Zeegers-Huyskens 1986 1988 Ault and Pimentel 1975 Ratajczak and Sobczyk 1969 Sobczyk et al 1982 Barnes 1983 Kebarle et al 1974-1979 Meot-Ner (Mautner) et al
1984-1988
Towards a General HB TheoryTowards a General HB Theory
The results so far obtained are not a True HB Theory but rather a Set of Empirical Rules (or an Empirical Natural Law) that is a great collection of HB experimental data neatly organized in tables which all together represent a General Taxonomy of the HB Phenomenon exactly as the Carl Linnaeusrsquo classification of plants A scientific theory is something different It is the casting of the empirical natural law into the frame of a theory which is more fundamental down to the reductionistic chain of the scientific disciplines For instance the kinetic gas theory is the casting of the empirical gas laws (the empirical natural law) into Newtonrsquos classical mechanics
How to make a HB TheoryHow to make a HB Theory
HB Properties = FF (HB Driving Variable)where
HB Driving Variable = PApKa and FF = Transition-State Theory
The Transition-State HB TheoryThe Transition-State HB Theory(Gilli et al JACS 2002 2005 Gilli et al J Mol Struct 2006)
Though it has taken us more than 12 years to develop it
the basic idea is very simpleAny DndashHmiddotmiddotmiddotA bond can be considered as a chemical reaction which is
bimolecular in both directions and proceeds via transition-state (TS) formation
AndashB + C AmiddotmiddotmiddotBmiddotmiddotmiddotC A + BndashCDndashHmiddotmiddotmiddotA DmiddotmiddotmiddotHmiddotmiddotmiddotA DmiddotmiddotmiddotHndashA
Changes of nomenclatureReaction Pathway PTPathwayActivation Energy DaggerE PTBarrierReaction Energy Er PApKa Transition State (TS) PTTS
Reaction Coordinate RC=[d(DH)ndashd(AH)] Experimentals Variable-Temperature X-allographyCalculations DFTEmulated PTPathwaysInterpretation Marcus Rate-Equilibrium Theory LefflerHammond Postulate
AcknowledgmentsAcknowledgments I have to thank my direct coworkers without whose help this work could have not been accomplished
Valerio BERTOLASI Paola GILLI
Valeria FERRETTI Loretta PRETTO
and the scientific institutions which made available to us the databases without which this work could not even be started
CCDCCambridge Crystallographic
Data Centrefor the use of the
Cambridge Structural Database
NIST National Institute of Standards and
Technologyfor the use of the
NIST Chemistry WebBook
The pThe pKKa Slide Rulea Slide Rule
It is a tool for the graphical evaluation of the difference
pKa = pKAH(DH) - pKBH+(AH+)
HB Acceptors on the left and HB Donors on the right
pKa values given for chemical class
Results expected
ΔpKagtgt0 DHmiddotmiddotmiddotmiddotA weak amp neutral
ΔpKa asymp 0 DmiddotmiddotmiddotHmiddotmiddotmiddotA strong amp
centeredΔpKa ltlt0DmiddotmiddotmiddotmiddotHA+ weak amp charged
pKa ranges of organic compounds
C-H acids -11 ltpKalt 53
Other Donors -1 ltpKalt 40
Acceptors -12 ltpKalt 16
All -15 ltpKalt 53
Water 0 ltpKalt 14
50
-10
0
10
20
30
40
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
ALDEHYDES
ETHERSALCOHOLS
AMIDES
NITRILES
ANILINES
CF3-SO3H
HClO4HI
HBrHCl
H2SO4
HSO4
HNO3
HBF4
H3PO4
H2PO4
HPO42
HF HNO2
HNNN
NH2OHH2CO3
HCO3
H2S
HS-
HCN H3BO3
H2BO3
H4SiO4
H2O2
HO
HSCN
H-H
SULFONICACIDS
49
47
45
41
39
50
37
35
33
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
-1
-3
-5
-7
43
-9
-11
-13
-15
-10
0
10
20
30
40
OXIMES
ALCOHOLS
THIOLES
HB ACCEPTORS (A)pK BH+
HB DONORS (D-H)pK AH
C-H ACIDS pK AH
BE
TT
ER
HB
AC
CE
PT
OR
BE
TT
ER
BA
SE
BE
TT
ER
HB
DO
NO
R
BE
TT
ER
AC
ID
N-OXIDES
AMIDINES
UREA
THIOUREA
BARBITURICURIC ACID
MONO DIPHOSPHINES
TRIPHOSPHINES
TRINITROANILINES
AMINES
ANILINES
MONO DINITROANILINES
AMIDES
CARBOXYLIC ACIDS
HALOGENOANILINES
AZOCOMPS
TRINITROANILINES
PROTONSPONGES
ACIDSESTERS
H2O
H2O
MONODINITROANILINES
KETONES
SULFIDES
HALOGENCARB ACIDS
TRINITROPHENOLS
ENOLS
MONO DINITROPHENOLS
PHENOLSNAPHTHOLS
HALOGENOPHENOLS
HALOGENOALCOHOLS
SULFOXIDES
(NC)5-CYCLO
PENTADIENE
(NC)3CH
(O2N)2=CH2
HCCHNC-CH3
CH3-CO-CH3INDENE
O2N-CH3
(NC)2=CH2
(O2N)3CH
H2C=CH2
C6H6
CH4
CYCLOPENTADIENE
CYCLOPROPENE
Ar3CH
Ar2=CH2
Ar-CH3
NITROCOMPS
SELENOXIDES
AZOLES
AZINESDIAZINES
AMINES
Cl5-PHENOL
CH3-CH3
(CH3)3CH
NH3
NH3
51
53
51
53
Chemical Leitmotifs and PApChemical Leitmotifs and PApKKaa Equalization Rules Equalization Rules RAHB RAHB cannot be treated by pKa equalization methods because π-delocalization
modifies the pKarsquos of the donor and acceptor moieties (+)CAHB is a true proton transfer from an acid (HB donor) to a base (HB acceptor)
RndashDndashHAndashRrsquo Rndash12DH+A12ndashndashRrsquo RndashDHndashA+ndashRrsquoΔpKa = pKAH(RDH) pKBH+(RrsquoA)
()CAHB is a proton sharing between two acids (HB donors)
RndashDndashHDrsquondashRrsquo [RDHDrsquoRrsquo] RDHDrsquoRrsquoΔpKa = pKAH(RDH) pKAH(RDH)
(+)CAHB is a proton sharing between two bases (HB acceptors)
R+AHArsquoRrsquo [RAHArsquoRrsquo]+ RAHArsquo+RrsquoΔpKa = pKBH+(RA) pKBH+(RrsquoArsquo)
Whenever () and (+)CAHBs are both homonuclear (D = Drsquo or A = Arsquo) and
homomolecular (R = Rrsquo) the matching condition ΔpKa= 0 will hold irrespective of the
actual pKarsquos of the two interacting moieties All HBs formed will be strong
Some Famous HBsSome Famous HBs
The NThe NHmiddotmiddotmiddotOOHmiddotmiddotmiddotOOHmiddotmiddotmiddotN System over the Full HmiddotmiddotmiddotN System over the Full ppKKaa Range Range
When evaluated from the pKa slide rule the total pKa range is extremely wide
ndash30 pa 60 So far we have been able to shown that the pKa equalization rule certainly holds in
a restricted interval around zero The problem is now Does this rule hold in the full pKa range
We will try to prove that by a full analysis the N-HmiddotmiddotmiddotOO-HmiddotmiddotmiddotN system
Procedure In a first CSD search functional groups of known pKa value and more frequently
implied in NHmiddotmiddotmiddotOOHmiddotmiddotmiddotN bonds were identified Finally 10 classes of donors and 11 of acceptors were selected and the search restarted for each separate donor-acceptor group Altogether 9078 different bonds were analyzed (4364 NHmiddotmiddotmiddotO 2289 OHmiddotmiddotmiddotN and
2425 OmiddotmiddotmiddotHN+) For each bond the NmiddotmiddotmiddotO distances were evaluated as dNH + dHO to account for the
N-H-O angle and for each group the shortest and average distances [dNmiddotmiddotmiddotO (min)
and dNmiddotmiddotmiddotO (mean)] were registered
These values were compared (see next slide) with the acid-base features of the donors (pKAH range) acceptors (pKBH+ range) and with their combinations
(pKa range)
pKa large amp positive
pKa largeamp negative
Increasing Acidity of the Protonated A H+ Acceptor Increasing Basicity of the A Acceptor
ppKKaa versusversus HB Geometry Correlation - Conclusions HB Geometry Correlation - Conclusions The PApKa Equalization Principle is therefore fully confirmed in its two forms All strong HBs correspond to very small pKa values
pKa values modulate the HB strength over the full pKa range These conclusions are of great practical importance in at least two respects pKa is definitively established as the driving force which controls the HB
strength by modulating the HB covalent contribution It is definitively established that an accurate analysis of structural crystal data
leads to the same conclusions suggested but never proved on a general base by thermodynamic and spectroscopic methods
References Huyskens and Zeegers-Huyskens 1964 Zeegers-Huyskens 1986 1988 Ault and Pimentel 1975 Ratajczak and Sobczyk 1969 Sobczyk et al 1982 Barnes 1983 Kebarle et al 1974-1979 Meot-Ner (Mautner) et al
1984-1988
Towards a General HB TheoryTowards a General HB Theory
The results so far obtained are not a True HB Theory but rather a Set of Empirical Rules (or an Empirical Natural Law) that is a great collection of HB experimental data neatly organized in tables which all together represent a General Taxonomy of the HB Phenomenon exactly as the Carl Linnaeusrsquo classification of plants A scientific theory is something different It is the casting of the empirical natural law into the frame of a theory which is more fundamental down to the reductionistic chain of the scientific disciplines For instance the kinetic gas theory is the casting of the empirical gas laws (the empirical natural law) into Newtonrsquos classical mechanics
How to make a HB TheoryHow to make a HB Theory
HB Properties = FF (HB Driving Variable)where
HB Driving Variable = PApKa and FF = Transition-State Theory
The Transition-State HB TheoryThe Transition-State HB Theory(Gilli et al JACS 2002 2005 Gilli et al J Mol Struct 2006)
Though it has taken us more than 12 years to develop it
the basic idea is very simpleAny DndashHmiddotmiddotmiddotA bond can be considered as a chemical reaction which is
bimolecular in both directions and proceeds via transition-state (TS) formation
AndashB + C AmiddotmiddotmiddotBmiddotmiddotmiddotC A + BndashCDndashHmiddotmiddotmiddotA DmiddotmiddotmiddotHmiddotmiddotmiddotA DmiddotmiddotmiddotHndashA
Changes of nomenclatureReaction Pathway PTPathwayActivation Energy DaggerE PTBarrierReaction Energy Er PApKa Transition State (TS) PTTS
Reaction Coordinate RC=[d(DH)ndashd(AH)] Experimentals Variable-Temperature X-allographyCalculations DFTEmulated PTPathwaysInterpretation Marcus Rate-Equilibrium Theory LefflerHammond Postulate
AcknowledgmentsAcknowledgments I have to thank my direct coworkers without whose help this work could have not been accomplished
Valerio BERTOLASI Paola GILLI
Valeria FERRETTI Loretta PRETTO
and the scientific institutions which made available to us the databases without which this work could not even be started
CCDCCambridge Crystallographic
Data Centrefor the use of the
Cambridge Structural Database
NIST National Institute of Standards and
Technologyfor the use of the
NIST Chemistry WebBook
Chemical Leitmotifs and PApChemical Leitmotifs and PApKKaa Equalization Rules Equalization Rules RAHB RAHB cannot be treated by pKa equalization methods because π-delocalization
modifies the pKarsquos of the donor and acceptor moieties (+)CAHB is a true proton transfer from an acid (HB donor) to a base (HB acceptor)
RndashDndashHAndashRrsquo Rndash12DH+A12ndashndashRrsquo RndashDHndashA+ndashRrsquoΔpKa = pKAH(RDH) pKBH+(RrsquoA)
()CAHB is a proton sharing between two acids (HB donors)
RndashDndashHDrsquondashRrsquo [RDHDrsquoRrsquo] RDHDrsquoRrsquoΔpKa = pKAH(RDH) pKAH(RDH)
(+)CAHB is a proton sharing between two bases (HB acceptors)
R+AHArsquoRrsquo [RAHArsquoRrsquo]+ RAHArsquo+RrsquoΔpKa = pKBH+(RA) pKBH+(RrsquoArsquo)
Whenever () and (+)CAHBs are both homonuclear (D = Drsquo or A = Arsquo) and
homomolecular (R = Rrsquo) the matching condition ΔpKa= 0 will hold irrespective of the
actual pKarsquos of the two interacting moieties All HBs formed will be strong
Some Famous HBsSome Famous HBs
The NThe NHmiddotmiddotmiddotOOHmiddotmiddotmiddotOOHmiddotmiddotmiddotN System over the Full HmiddotmiddotmiddotN System over the Full ppKKaa Range Range
When evaluated from the pKa slide rule the total pKa range is extremely wide
ndash30 pa 60 So far we have been able to shown that the pKa equalization rule certainly holds in
a restricted interval around zero The problem is now Does this rule hold in the full pKa range
We will try to prove that by a full analysis the N-HmiddotmiddotmiddotOO-HmiddotmiddotmiddotN system
Procedure In a first CSD search functional groups of known pKa value and more frequently
implied in NHmiddotmiddotmiddotOOHmiddotmiddotmiddotN bonds were identified Finally 10 classes of donors and 11 of acceptors were selected and the search restarted for each separate donor-acceptor group Altogether 9078 different bonds were analyzed (4364 NHmiddotmiddotmiddotO 2289 OHmiddotmiddotmiddotN and
2425 OmiddotmiddotmiddotHN+) For each bond the NmiddotmiddotmiddotO distances were evaluated as dNH + dHO to account for the
N-H-O angle and for each group the shortest and average distances [dNmiddotmiddotmiddotO (min)
and dNmiddotmiddotmiddotO (mean)] were registered
These values were compared (see next slide) with the acid-base features of the donors (pKAH range) acceptors (pKBH+ range) and with their combinations
(pKa range)
pKa large amp positive
pKa largeamp negative
Increasing Acidity of the Protonated A H+ Acceptor Increasing Basicity of the A Acceptor
ppKKaa versusversus HB Geometry Correlation - Conclusions HB Geometry Correlation - Conclusions The PApKa Equalization Principle is therefore fully confirmed in its two forms All strong HBs correspond to very small pKa values
pKa values modulate the HB strength over the full pKa range These conclusions are of great practical importance in at least two respects pKa is definitively established as the driving force which controls the HB
strength by modulating the HB covalent contribution It is definitively established that an accurate analysis of structural crystal data
leads to the same conclusions suggested but never proved on a general base by thermodynamic and spectroscopic methods
References Huyskens and Zeegers-Huyskens 1964 Zeegers-Huyskens 1986 1988 Ault and Pimentel 1975 Ratajczak and Sobczyk 1969 Sobczyk et al 1982 Barnes 1983 Kebarle et al 1974-1979 Meot-Ner (Mautner) et al
1984-1988
Towards a General HB TheoryTowards a General HB Theory
The results so far obtained are not a True HB Theory but rather a Set of Empirical Rules (or an Empirical Natural Law) that is a great collection of HB experimental data neatly organized in tables which all together represent a General Taxonomy of the HB Phenomenon exactly as the Carl Linnaeusrsquo classification of plants A scientific theory is something different It is the casting of the empirical natural law into the frame of a theory which is more fundamental down to the reductionistic chain of the scientific disciplines For instance the kinetic gas theory is the casting of the empirical gas laws (the empirical natural law) into Newtonrsquos classical mechanics
How to make a HB TheoryHow to make a HB Theory
HB Properties = FF (HB Driving Variable)where
HB Driving Variable = PApKa and FF = Transition-State Theory
The Transition-State HB TheoryThe Transition-State HB Theory(Gilli et al JACS 2002 2005 Gilli et al J Mol Struct 2006)
Though it has taken us more than 12 years to develop it
the basic idea is very simpleAny DndashHmiddotmiddotmiddotA bond can be considered as a chemical reaction which is
bimolecular in both directions and proceeds via transition-state (TS) formation
AndashB + C AmiddotmiddotmiddotBmiddotmiddotmiddotC A + BndashCDndashHmiddotmiddotmiddotA DmiddotmiddotmiddotHmiddotmiddotmiddotA DmiddotmiddotmiddotHndashA
Changes of nomenclatureReaction Pathway PTPathwayActivation Energy DaggerE PTBarrierReaction Energy Er PApKa Transition State (TS) PTTS
Reaction Coordinate RC=[d(DH)ndashd(AH)] Experimentals Variable-Temperature X-allographyCalculations DFTEmulated PTPathwaysInterpretation Marcus Rate-Equilibrium Theory LefflerHammond Postulate
AcknowledgmentsAcknowledgments I have to thank my direct coworkers without whose help this work could have not been accomplished
Valerio BERTOLASI Paola GILLI
Valeria FERRETTI Loretta PRETTO
and the scientific institutions which made available to us the databases without which this work could not even be started
CCDCCambridge Crystallographic
Data Centrefor the use of the
Cambridge Structural Database
NIST National Institute of Standards and
Technologyfor the use of the
NIST Chemistry WebBook
Some Famous HBsSome Famous HBs
The NThe NHmiddotmiddotmiddotOOHmiddotmiddotmiddotOOHmiddotmiddotmiddotN System over the Full HmiddotmiddotmiddotN System over the Full ppKKaa Range Range
When evaluated from the pKa slide rule the total pKa range is extremely wide
ndash30 pa 60 So far we have been able to shown that the pKa equalization rule certainly holds in
a restricted interval around zero The problem is now Does this rule hold in the full pKa range
We will try to prove that by a full analysis the N-HmiddotmiddotmiddotOO-HmiddotmiddotmiddotN system
Procedure In a first CSD search functional groups of known pKa value and more frequently
implied in NHmiddotmiddotmiddotOOHmiddotmiddotmiddotN bonds were identified Finally 10 classes of donors and 11 of acceptors were selected and the search restarted for each separate donor-acceptor group Altogether 9078 different bonds were analyzed (4364 NHmiddotmiddotmiddotO 2289 OHmiddotmiddotmiddotN and
2425 OmiddotmiddotmiddotHN+) For each bond the NmiddotmiddotmiddotO distances were evaluated as dNH + dHO to account for the
N-H-O angle and for each group the shortest and average distances [dNmiddotmiddotmiddotO (min)
and dNmiddotmiddotmiddotO (mean)] were registered
These values were compared (see next slide) with the acid-base features of the donors (pKAH range) acceptors (pKBH+ range) and with their combinations
(pKa range)
pKa large amp positive
pKa largeamp negative
Increasing Acidity of the Protonated A H+ Acceptor Increasing Basicity of the A Acceptor
ppKKaa versusversus HB Geometry Correlation - Conclusions HB Geometry Correlation - Conclusions The PApKa Equalization Principle is therefore fully confirmed in its two forms All strong HBs correspond to very small pKa values
pKa values modulate the HB strength over the full pKa range These conclusions are of great practical importance in at least two respects pKa is definitively established as the driving force which controls the HB
strength by modulating the HB covalent contribution It is definitively established that an accurate analysis of structural crystal data
leads to the same conclusions suggested but never proved on a general base by thermodynamic and spectroscopic methods
References Huyskens and Zeegers-Huyskens 1964 Zeegers-Huyskens 1986 1988 Ault and Pimentel 1975 Ratajczak and Sobczyk 1969 Sobczyk et al 1982 Barnes 1983 Kebarle et al 1974-1979 Meot-Ner (Mautner) et al
1984-1988
Towards a General HB TheoryTowards a General HB Theory
The results so far obtained are not a True HB Theory but rather a Set of Empirical Rules (or an Empirical Natural Law) that is a great collection of HB experimental data neatly organized in tables which all together represent a General Taxonomy of the HB Phenomenon exactly as the Carl Linnaeusrsquo classification of plants A scientific theory is something different It is the casting of the empirical natural law into the frame of a theory which is more fundamental down to the reductionistic chain of the scientific disciplines For instance the kinetic gas theory is the casting of the empirical gas laws (the empirical natural law) into Newtonrsquos classical mechanics
How to make a HB TheoryHow to make a HB Theory
HB Properties = FF (HB Driving Variable)where
HB Driving Variable = PApKa and FF = Transition-State Theory
The Transition-State HB TheoryThe Transition-State HB Theory(Gilli et al JACS 2002 2005 Gilli et al J Mol Struct 2006)
Though it has taken us more than 12 years to develop it
the basic idea is very simpleAny DndashHmiddotmiddotmiddotA bond can be considered as a chemical reaction which is
bimolecular in both directions and proceeds via transition-state (TS) formation
AndashB + C AmiddotmiddotmiddotBmiddotmiddotmiddotC A + BndashCDndashHmiddotmiddotmiddotA DmiddotmiddotmiddotHmiddotmiddotmiddotA DmiddotmiddotmiddotHndashA
Changes of nomenclatureReaction Pathway PTPathwayActivation Energy DaggerE PTBarrierReaction Energy Er PApKa Transition State (TS) PTTS
Reaction Coordinate RC=[d(DH)ndashd(AH)] Experimentals Variable-Temperature X-allographyCalculations DFTEmulated PTPathwaysInterpretation Marcus Rate-Equilibrium Theory LefflerHammond Postulate
AcknowledgmentsAcknowledgments I have to thank my direct coworkers without whose help this work could have not been accomplished
Valerio BERTOLASI Paola GILLI
Valeria FERRETTI Loretta PRETTO
and the scientific institutions which made available to us the databases without which this work could not even be started
CCDCCambridge Crystallographic
Data Centrefor the use of the
Cambridge Structural Database
NIST National Institute of Standards and
Technologyfor the use of the
NIST Chemistry WebBook
The NThe NHmiddotmiddotmiddotOOHmiddotmiddotmiddotOOHmiddotmiddotmiddotN System over the Full HmiddotmiddotmiddotN System over the Full ppKKaa Range Range
When evaluated from the pKa slide rule the total pKa range is extremely wide
ndash30 pa 60 So far we have been able to shown that the pKa equalization rule certainly holds in
a restricted interval around zero The problem is now Does this rule hold in the full pKa range
We will try to prove that by a full analysis the N-HmiddotmiddotmiddotOO-HmiddotmiddotmiddotN system
Procedure In a first CSD search functional groups of known pKa value and more frequently
implied in NHmiddotmiddotmiddotOOHmiddotmiddotmiddotN bonds were identified Finally 10 classes of donors and 11 of acceptors were selected and the search restarted for each separate donor-acceptor group Altogether 9078 different bonds were analyzed (4364 NHmiddotmiddotmiddotO 2289 OHmiddotmiddotmiddotN and
2425 OmiddotmiddotmiddotHN+) For each bond the NmiddotmiddotmiddotO distances were evaluated as dNH + dHO to account for the
N-H-O angle and for each group the shortest and average distances [dNmiddotmiddotmiddotO (min)
and dNmiddotmiddotmiddotO (mean)] were registered
These values were compared (see next slide) with the acid-base features of the donors (pKAH range) acceptors (pKBH+ range) and with their combinations
(pKa range)
pKa large amp positive
pKa largeamp negative
Increasing Acidity of the Protonated A H+ Acceptor Increasing Basicity of the A Acceptor
ppKKaa versusversus HB Geometry Correlation - Conclusions HB Geometry Correlation - Conclusions The PApKa Equalization Principle is therefore fully confirmed in its two forms All strong HBs correspond to very small pKa values
pKa values modulate the HB strength over the full pKa range These conclusions are of great practical importance in at least two respects pKa is definitively established as the driving force which controls the HB
strength by modulating the HB covalent contribution It is definitively established that an accurate analysis of structural crystal data
leads to the same conclusions suggested but never proved on a general base by thermodynamic and spectroscopic methods
References Huyskens and Zeegers-Huyskens 1964 Zeegers-Huyskens 1986 1988 Ault and Pimentel 1975 Ratajczak and Sobczyk 1969 Sobczyk et al 1982 Barnes 1983 Kebarle et al 1974-1979 Meot-Ner (Mautner) et al
1984-1988
Towards a General HB TheoryTowards a General HB Theory
The results so far obtained are not a True HB Theory but rather a Set of Empirical Rules (or an Empirical Natural Law) that is a great collection of HB experimental data neatly organized in tables which all together represent a General Taxonomy of the HB Phenomenon exactly as the Carl Linnaeusrsquo classification of plants A scientific theory is something different It is the casting of the empirical natural law into the frame of a theory which is more fundamental down to the reductionistic chain of the scientific disciplines For instance the kinetic gas theory is the casting of the empirical gas laws (the empirical natural law) into Newtonrsquos classical mechanics
How to make a HB TheoryHow to make a HB Theory
HB Properties = FF (HB Driving Variable)where
HB Driving Variable = PApKa and FF = Transition-State Theory
The Transition-State HB TheoryThe Transition-State HB Theory(Gilli et al JACS 2002 2005 Gilli et al J Mol Struct 2006)
Though it has taken us more than 12 years to develop it
the basic idea is very simpleAny DndashHmiddotmiddotmiddotA bond can be considered as a chemical reaction which is
bimolecular in both directions and proceeds via transition-state (TS) formation
AndashB + C AmiddotmiddotmiddotBmiddotmiddotmiddotC A + BndashCDndashHmiddotmiddotmiddotA DmiddotmiddotmiddotHmiddotmiddotmiddotA DmiddotmiddotmiddotHndashA
Changes of nomenclatureReaction Pathway PTPathwayActivation Energy DaggerE PTBarrierReaction Energy Er PApKa Transition State (TS) PTTS
Reaction Coordinate RC=[d(DH)ndashd(AH)] Experimentals Variable-Temperature X-allographyCalculations DFTEmulated PTPathwaysInterpretation Marcus Rate-Equilibrium Theory LefflerHammond Postulate
AcknowledgmentsAcknowledgments I have to thank my direct coworkers without whose help this work could have not been accomplished
Valerio BERTOLASI Paola GILLI
Valeria FERRETTI Loretta PRETTO
and the scientific institutions which made available to us the databases without which this work could not even be started
CCDCCambridge Crystallographic
Data Centrefor the use of the
Cambridge Structural Database
NIST National Institute of Standards and
Technologyfor the use of the
NIST Chemistry WebBook
pKa large amp positive
pKa largeamp negative
Increasing Acidity of the Protonated A H+ Acceptor Increasing Basicity of the A Acceptor
ppKKaa versusversus HB Geometry Correlation - Conclusions HB Geometry Correlation - Conclusions The PApKa Equalization Principle is therefore fully confirmed in its two forms All strong HBs correspond to very small pKa values
pKa values modulate the HB strength over the full pKa range These conclusions are of great practical importance in at least two respects pKa is definitively established as the driving force which controls the HB
strength by modulating the HB covalent contribution It is definitively established that an accurate analysis of structural crystal data
leads to the same conclusions suggested but never proved on a general base by thermodynamic and spectroscopic methods
References Huyskens and Zeegers-Huyskens 1964 Zeegers-Huyskens 1986 1988 Ault and Pimentel 1975 Ratajczak and Sobczyk 1969 Sobczyk et al 1982 Barnes 1983 Kebarle et al 1974-1979 Meot-Ner (Mautner) et al
1984-1988
Towards a General HB TheoryTowards a General HB Theory
The results so far obtained are not a True HB Theory but rather a Set of Empirical Rules (or an Empirical Natural Law) that is a great collection of HB experimental data neatly organized in tables which all together represent a General Taxonomy of the HB Phenomenon exactly as the Carl Linnaeusrsquo classification of plants A scientific theory is something different It is the casting of the empirical natural law into the frame of a theory which is more fundamental down to the reductionistic chain of the scientific disciplines For instance the kinetic gas theory is the casting of the empirical gas laws (the empirical natural law) into Newtonrsquos classical mechanics
How to make a HB TheoryHow to make a HB Theory
HB Properties = FF (HB Driving Variable)where
HB Driving Variable = PApKa and FF = Transition-State Theory
The Transition-State HB TheoryThe Transition-State HB Theory(Gilli et al JACS 2002 2005 Gilli et al J Mol Struct 2006)
Though it has taken us more than 12 years to develop it
the basic idea is very simpleAny DndashHmiddotmiddotmiddotA bond can be considered as a chemical reaction which is
bimolecular in both directions and proceeds via transition-state (TS) formation
AndashB + C AmiddotmiddotmiddotBmiddotmiddotmiddotC A + BndashCDndashHmiddotmiddotmiddotA DmiddotmiddotmiddotHmiddotmiddotmiddotA DmiddotmiddotmiddotHndashA
Changes of nomenclatureReaction Pathway PTPathwayActivation Energy DaggerE PTBarrierReaction Energy Er PApKa Transition State (TS) PTTS
Reaction Coordinate RC=[d(DH)ndashd(AH)] Experimentals Variable-Temperature X-allographyCalculations DFTEmulated PTPathwaysInterpretation Marcus Rate-Equilibrium Theory LefflerHammond Postulate
AcknowledgmentsAcknowledgments I have to thank my direct coworkers without whose help this work could have not been accomplished
Valerio BERTOLASI Paola GILLI
Valeria FERRETTI Loretta PRETTO
and the scientific institutions which made available to us the databases without which this work could not even be started
CCDCCambridge Crystallographic
Data Centrefor the use of the
Cambridge Structural Database
NIST National Institute of Standards and
Technologyfor the use of the
NIST Chemistry WebBook
ppKKaa versusversus HB Geometry Correlation - Conclusions HB Geometry Correlation - Conclusions The PApKa Equalization Principle is therefore fully confirmed in its two forms All strong HBs correspond to very small pKa values
pKa values modulate the HB strength over the full pKa range These conclusions are of great practical importance in at least two respects pKa is definitively established as the driving force which controls the HB
strength by modulating the HB covalent contribution It is definitively established that an accurate analysis of structural crystal data
leads to the same conclusions suggested but never proved on a general base by thermodynamic and spectroscopic methods
References Huyskens and Zeegers-Huyskens 1964 Zeegers-Huyskens 1986 1988 Ault and Pimentel 1975 Ratajczak and Sobczyk 1969 Sobczyk et al 1982 Barnes 1983 Kebarle et al 1974-1979 Meot-Ner (Mautner) et al
1984-1988
Towards a General HB TheoryTowards a General HB Theory
The results so far obtained are not a True HB Theory but rather a Set of Empirical Rules (or an Empirical Natural Law) that is a great collection of HB experimental data neatly organized in tables which all together represent a General Taxonomy of the HB Phenomenon exactly as the Carl Linnaeusrsquo classification of plants A scientific theory is something different It is the casting of the empirical natural law into the frame of a theory which is more fundamental down to the reductionistic chain of the scientific disciplines For instance the kinetic gas theory is the casting of the empirical gas laws (the empirical natural law) into Newtonrsquos classical mechanics
How to make a HB TheoryHow to make a HB Theory
HB Properties = FF (HB Driving Variable)where
HB Driving Variable = PApKa and FF = Transition-State Theory
The Transition-State HB TheoryThe Transition-State HB Theory(Gilli et al JACS 2002 2005 Gilli et al J Mol Struct 2006)
Though it has taken us more than 12 years to develop it
the basic idea is very simpleAny DndashHmiddotmiddotmiddotA bond can be considered as a chemical reaction which is
bimolecular in both directions and proceeds via transition-state (TS) formation
AndashB + C AmiddotmiddotmiddotBmiddotmiddotmiddotC A + BndashCDndashHmiddotmiddotmiddotA DmiddotmiddotmiddotHmiddotmiddotmiddotA DmiddotmiddotmiddotHndashA
Changes of nomenclatureReaction Pathway PTPathwayActivation Energy DaggerE PTBarrierReaction Energy Er PApKa Transition State (TS) PTTS
Reaction Coordinate RC=[d(DH)ndashd(AH)] Experimentals Variable-Temperature X-allographyCalculations DFTEmulated PTPathwaysInterpretation Marcus Rate-Equilibrium Theory LefflerHammond Postulate
AcknowledgmentsAcknowledgments I have to thank my direct coworkers without whose help this work could have not been accomplished
Valerio BERTOLASI Paola GILLI
Valeria FERRETTI Loretta PRETTO
and the scientific institutions which made available to us the databases without which this work could not even be started
CCDCCambridge Crystallographic
Data Centrefor the use of the
Cambridge Structural Database
NIST National Institute of Standards and
Technologyfor the use of the
NIST Chemistry WebBook
Towards a General HB TheoryTowards a General HB Theory
The results so far obtained are not a True HB Theory but rather a Set of Empirical Rules (or an Empirical Natural Law) that is a great collection of HB experimental data neatly organized in tables which all together represent a General Taxonomy of the HB Phenomenon exactly as the Carl Linnaeusrsquo classification of plants A scientific theory is something different It is the casting of the empirical natural law into the frame of a theory which is more fundamental down to the reductionistic chain of the scientific disciplines For instance the kinetic gas theory is the casting of the empirical gas laws (the empirical natural law) into Newtonrsquos classical mechanics
How to make a HB TheoryHow to make a HB Theory
HB Properties = FF (HB Driving Variable)where
HB Driving Variable = PApKa and FF = Transition-State Theory
The Transition-State HB TheoryThe Transition-State HB Theory(Gilli et al JACS 2002 2005 Gilli et al J Mol Struct 2006)
Though it has taken us more than 12 years to develop it
the basic idea is very simpleAny DndashHmiddotmiddotmiddotA bond can be considered as a chemical reaction which is
bimolecular in both directions and proceeds via transition-state (TS) formation
AndashB + C AmiddotmiddotmiddotBmiddotmiddotmiddotC A + BndashCDndashHmiddotmiddotmiddotA DmiddotmiddotmiddotHmiddotmiddotmiddotA DmiddotmiddotmiddotHndashA
Changes of nomenclatureReaction Pathway PTPathwayActivation Energy DaggerE PTBarrierReaction Energy Er PApKa Transition State (TS) PTTS
Reaction Coordinate RC=[d(DH)ndashd(AH)] Experimentals Variable-Temperature X-allographyCalculations DFTEmulated PTPathwaysInterpretation Marcus Rate-Equilibrium Theory LefflerHammond Postulate
AcknowledgmentsAcknowledgments I have to thank my direct coworkers without whose help this work could have not been accomplished
Valerio BERTOLASI Paola GILLI
Valeria FERRETTI Loretta PRETTO
and the scientific institutions which made available to us the databases without which this work could not even be started
CCDCCambridge Crystallographic
Data Centrefor the use of the
Cambridge Structural Database
NIST National Institute of Standards and
Technologyfor the use of the
NIST Chemistry WebBook
The Transition-State HB TheoryThe Transition-State HB Theory(Gilli et al JACS 2002 2005 Gilli et al J Mol Struct 2006)
Though it has taken us more than 12 years to develop it
the basic idea is very simpleAny DndashHmiddotmiddotmiddotA bond can be considered as a chemical reaction which is
bimolecular in both directions and proceeds via transition-state (TS) formation
AndashB + C AmiddotmiddotmiddotBmiddotmiddotmiddotC A + BndashCDndashHmiddotmiddotmiddotA DmiddotmiddotmiddotHmiddotmiddotmiddotA DmiddotmiddotmiddotHndashA
Changes of nomenclatureReaction Pathway PTPathwayActivation Energy DaggerE PTBarrierReaction Energy Er PApKa Transition State (TS) PTTS
Reaction Coordinate RC=[d(DH)ndashd(AH)] Experimentals Variable-Temperature X-allographyCalculations DFTEmulated PTPathwaysInterpretation Marcus Rate-Equilibrium Theory LefflerHammond Postulate
AcknowledgmentsAcknowledgments I have to thank my direct coworkers without whose help this work could have not been accomplished
Valerio BERTOLASI Paola GILLI
Valeria FERRETTI Loretta PRETTO
and the scientific institutions which made available to us the databases without which this work could not even be started
CCDCCambridge Crystallographic
Data Centrefor the use of the
Cambridge Structural Database
NIST National Institute of Standards and
Technologyfor the use of the
NIST Chemistry WebBook
AcknowledgmentsAcknowledgments I have to thank my direct coworkers without whose help this work could have not been accomplished
Valerio BERTOLASI Paola GILLI
Valeria FERRETTI Loretta PRETTO
and the scientific institutions which made available to us the databases without which this work could not even be started
CCDCCambridge Crystallographic
Data Centrefor the use of the
Cambridge Structural Database
NIST National Institute of Standards and
Technologyfor the use of the
NIST Chemistry WebBook
