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Bonds and interactions in crystals: Conformations and Chirality
Master of Crystallography and Crystallization – 2013
T01 – Mathematical, Physical and Chemical basis of Crystallography
Intermolecular Links
Are established between atoms electrically charged andbelonging to two different chemical species.
The chemical species are ions, or molecules. The electricalcharge comes from these species which are ions, or atomsinvolved in a permanent dipole or an induced dipole.
Play a crucial role in the Biocrystallography and Crystal
Engineering.
Intermolecular Forces or Van der Waals Forces
• Forces between permanent dipoles
• Hydrogen bond Forces
• Forces between induced dipoles (London Forces)
Van der Waals Intermolecular Forces
The basis of the forces of van der Waals is the existence of electric dipoles in molecules.
These dipoles may be permanent, short-lived o induced.
Permanent dipoles derive fromelectronic charge asymmetry.
+-
m
+ +
-
H H
O
The permanent dipolar moment is determined by spectroscopy (Stark effect) or by the dielectric constant.
In the water molecule, The O has 0.82 e- in excess and each H0.41 e- indefect.
Dipolar Moment (m)
m/D
CCl4 0
H2 0
H20 1.85
HCl 1.08
HI 0.42
D (Debye): 3.3 x 10-30 C/m(1 ecu/1A)
+ +
-
H H
O -+ + -
Interaction Ion-Dipole that helps the dissolution of ionic crystals in
water. Arrows indicate Ion-Dipole interactions.
Intermolecular Forces
Separation Distance (nm)
0 10 20 30 40 50
Inte
ract
ion
Fo
rce/
Rad
ius
(mN
/m)
-2
-1
0
1
2
3
4
5
6van der WaalsElectrostaticStericDepletionHydrophobicSolvation
Repulsive Forces (Above
X-axis)
Attractive Forces
(Below X-axis)
Intermolecular Forces:
The summation of all interaction energies of a molecule with all other molecules in
a spherical system with size L is:
3n
3n L1
3n
C4Energy
)(
This expression gives us the all important relation of n 3
= Molecular
diameter
L
n
2L
2 drr
r4Cdrr4rWEnergy )(
1L
Long distance contributions to Energy do not occur
ONLY when n 3Since
For n < 3, the size of the system is important (E.g. Gravity: Distant planets and stars
interact)
For n 3, intermolecular force potentials become important
It is also for this reason that:
- As we go to sub micron size distances, properties of material changes –
Intermolecular Forces Start Taking Over !
Intermolecular force potentials for n 3
It is for this reason that:
Bulk properties of material is size independent (unless in the domains of
intermolecular forces)
(Boiling point of water in a test tube = boiling point of water in a bucket)
van der Waals Forces
1873: To explain deviations from ideal gas behavior,
van der Waals proposed a modification to the gas law:
RTbVV
aP
2
Molecules have finite volume (accounted by “b”)
• Attractive forces between the molecules (accounted by “a”)
The relation predicted gas behavior across a larger pressure range
The attractive intermolecular forces between
gas molecules is now known as “ van der Waals forces ”
van der Waals Forces
The three components that constitute van der Waals Forces
The London component is the most dominant.
n = 6 indicates van der Waals forces are short range
Dipole – induced
dipole
Debye
Induced Dipole –
Induced Dipole
London
(Dispersion)
Dipole-dipole Keesom
EquationOrigin of
Interactions
Interaction
Component
6
21
21
2
o
2o1o
r
1
II
II
42
3rw
)()()(
62
ro
o
2
r
1
4
urw
)()(
6
B
2
ro
2
2
2
1
r
1
Tk43
uurw
)()(
- Dipole-dipole interactions are generally weak
- These weak dipole-dipole interactions becomes
significant when 2 interacting dipoles approach each other
closely. e.g. O–-H+, N–-H+, F–-H+
Keesom (dipole - dipole) component
ui (i = 1, 2): dipole moment, o : Permittivity of free space
r : Relative Permittivity, kB: Boltzmann’s constant,
r: distance between dipoles, T: Temperature
6
B
2
ro
2
2
2
1
r
1
Tk43
uurw
)()(
(These strong dipole-dipole interactions are the well known: Hydrogen Bond)
Debye (dipole–induced dipole) component
62
ro
o
2
r
1
4
urw
)()(
O: polarizability,
r: Relative Permittivity
r: distance between dipole and
induced dipole
- Interaction of a polarizable molecule with a dipole
- Polarizablility: Electron cloud of molecule responds to an
electric field by a localized shift
- Debye interactions are independent of temperature
London (Dispersion) component
6
21
21
2
o
2o1o
r
1
II
II
42
3rw
)()()(
Ii (i = 1,2): Ionization Potential
- The most important component of van der Waals interaction
- Keesom and Debye interactions require the presence of at
least 1 permanent dipole, but London interactions do not.
- Hence, London interaction exist between all molecules
- The London interaction component was always known, but
evolved only after the development of quantum mechanics
- Provides molecular level reasoning that at room
temperature
Small molecules (Ar, He, CH4) are gases,
Bigger molecules (hexane, decane) are liquids,
Even bigger molecules (C35H71) are solids.
Intermolecular Van der Waals Forces
The van der Waals forces generate molecular interactionswithout perturbing the chemical reactivity of the involvedmolecules.
Recognized in XIX century as responsibles for thedesviations from the ideal behaviour of real gases ( P =[nRT/V - nb] - [n/V]2 ) and the cohesion of electricalyneutral (as Argon).
Electric charges interact among them and are responsablefor the cohesion of matter, especialy in liquid state andparticularly in biological systems.
• We call weak interactions (4-20 kJ/mol) in oposition to thecovalent unions (C-C: 350 kJ/mol y C-H: 410 kJ/mol) and theionic unions (Cl-/Na+: 785 kJ/mol).
INTERACTIONS• Ion-ion U(r) 1/r
• ion-dipole 1/r2
• dipole-dipole 1/r3
• London 1/r6
• H Bond
• 3/2kT (298K)
• 250 kJ mol-1
• 15 kJ mol-1
• 2 kJ mol-1
• 2 kJ mol-1
• 20 kJ mol-1
• 3.7 kJ mol-1
Intermolecular Van der Waals interactions at 30 °C
Interacction Type kJ/mol
Ion/dipole Na+ ... H2O 60
2 Permanent Dipoles H2O...H2O (structure of H2O) 20
2 Permanent Dipoles =CO...HN= (peptidic union ) 15
Dipoles: permanent and induced H2O...CH2= 10
2 Induced Dipoles =H2C...CH2= (London) 4
2 Induced Dipoles Ar...Ar (London) 4
2 Dipoles (in rotaction) Metane..Cl4C 2
Hydrogen Bond: When the hydrogen atom is
bonded to very electronegative atoms (F, O, N), becomespractically a proton. Being small, these “naked” hydrogenatom strongly attracts (short distance) zones of negative
charge of other molecules
HF
H2O
NH3
Crystals of
benzoic acid
contain pairs of
molecules
associated by
hydrogen
bonds. These
pairs are then
arranged at
levels that are
held together by
dispersion
forces.
Hydrogen Bonds in ADN
Stacking Bases
May 08, 2002 lecture 2/ MBB 222 02-2 4
Non-covalent Bonds
Much weaker than covalent bonds
- these bonds break and reform at
Room Temperature (RT)
‘Transient Bonds’
- however, cumulatively they are very
effective e.g. helix for proteins and
double helix for DNA
Enlaces de hidrógeno
Interiorhydrofobo
skeletondesoxiribose-Phosphate
Hydrogen bonds
Exterior hydrofilo
A: adeninaG: guaninaC: citosinaT: timina
Nitrogenated Bases
nitrogenadas
Electrostatic Repulsion
DNA structure: the double hélixWatson and Crick for DNA (1953)
What is an hydrogen bond?
“Under certain conditions an atom of hydrogen is attracted by rather strong
forces to two atoms instead of only one, so that it may be considered to be
acting as a bond between them” (Pauling, 1939).
D—H……..A
Other definitions of hydrogen bond, X–H…A
“A hydrogen bond is said to exist when (1) there is evidence of a bond,
and (2) there is evidence that this bond sterically involves a hydrogen
atom already bonded to another atom”
“Any cohesive interaction where H carries a positive charge and A a
negative charge (partial or full) and the charge on H is more positive than
on X”
Pimentel and McClellan (1960)
Steiner and Saenger (1993)
D—H……..A Very Strong
D—H………..A Strong
D—H……….….A Weak
Different types of Hydrogen Bonds
Hydrogen bond
Any cohesive
interaction X–H•••A
where H supports a
positive charge and A
one negative charge
(partial or complete)
and the charge on X
is more negative than
on H
O–H···O(-) O–H···O N–H···O
O–H···π N–H···π C–H···O
Os–H···O C–H···Ni C–H···π
Very Strong Strong Weak
[F–H…F]– N–H…O=C C–H…O
Energy (kcal/mol) –15 to –40 – 4 to – 15 < – 4
IR, νs >25% 5-25% <5%
∆(X–H), Å 0.05 to 0.2 0.01 to 0.05 < 0.01
H…A, Å 1.2 to1.5 1.5 to 2.2 2.0 to 3.0
Shorter than
van der Waals 100% ~100% 30-80%
Effect on
packing Pronounced Distinctive Variable
A complex interaction
Hydrogen Bond D—H……..A
A compose interaction which extend to a wide range of
geometries and energies.
Large chemical choice among the groups donor D—H and
acceptor A
Nevertheless, all Hydrogen Bonds have many common
characteristics.
Mainly, their effect on both Structure and Crystal Packing.
Dispersion ForcesOccur between all molecules and are the result of the net attraction force arising between molecules and originates from imbalances in induced charges.
The magnitude of the dispersion forces is dependent on the ease of the electronic cloud distortion. As more voluminous is the molecule greatest are the Dispersion forces.
induced-dipoles (London Forces)
The alkanes boiling point increases with the carbon chain length. Long chain alkanes have more high dispersion forces due to the increase of polarizability of its more extensive electronic cloud.
Liquid Crystals
IntermolecularVan der Waals interactionsImportance in biologic systems
Hydrogen Bonds
Nucleic Acids
Proteins
In the cells of living organisms the weak intermolecular Van der Waals interactions define the physical state
(semi-solid/semi-liquid).
Hydrophobic Union
Lipids and proteinhydrophobic domains
Hydratation of Solutes
Organic Metabolites
Ions
Structure of the living organisms
Water is 75 % of the weight of the cells.
Hydrogen bridges confer on the water itsextraordinary properties (PF: 0 ° C; PE 100 ° C;heat of vaporization: 2.26 J/g).
Hydrogen bridges have a very short half-life (1 x10-9 seg) (“flickering clusters”)
In the liquid water, each molecule forms hydrogenbridges with other 3.4 molecules and ice with 4molecules
Structure of water in living organisms
Water electrostaticaly interacts with the chargedsolutes: amino (+) or carboxyl (-) groups and ions(ion/dipole interaction).
Water form hydrogen bonds with organic soluteswith polar groups: alcohol (-OH), carbonyls (= O),Phosphonyls (= P = O), imino (= NH).
Intracellular water has a high degree oforganization called "structure of water". Anestimated 30-40 % of "fixed water".
The denaturing or fusion of DNA
The process is reversible, adjustable by temperature.
PCR (Polymerase Chain Reaction) technique is based on the denaturationand DNA copy.
The denaturing or fusion of DNA
The fusion temperatureis different for differentDNA (red or blue). Thefusion (temperature ofthe average height ofthe curve) pointdepends on the ionicstrength, pH and thecomposition of DNAbases.
The Hydrophobic union
Long chain fatty acidshave hydrophobic alkylchains, which to beintroduced into thewater, surrounded byhighly ordered watermolecules.
When fatty acid molecules are grouped laterally decreases the number of “ordered" water molecules
Similarly to grouped into micelles, fatty acids expose a hydrophilic surface and minimize the ordering of water molecules system . The micelle stabilizes due to the entropic effect of increasing unordered water.
The Hidrophobic union
Top view generation of a hydrophobic Union each hydrocarbon chain (of 9 C) issurrounded by 4 columns 6 water molecules each of the “solvent cell”
G = H – T S H = H2 –H1 y S = S2 – S1
H calculation (for the described molecular complex):
Break of 12 unions H2O/CH2= + 120 kJFormation of 9 unions =H2C/H2C= - 36 kJFormation of 6 unions H2O/H2O - 120 kJ
H = - 36 kJ
S calculation: Asumming the change water (s) => water (l)
S = 22 J/K . mol of water and 12 moles of water(22 J/K x 12 x 300 K) = 79.2 kJ TS = - 79 kJ
Domains (spaces) hydrophobic shared between molecules, which exclude water molecules are referred to as hydrophobic union.
In reality, there is not a hydrophobic union, but a number of attractions van der Waals type and London type together with the hydrogen bridges of the solvent (water). Hydrophobic unions are responsible for the formation of micelles, biological membranes,
lipid monolayers and bilayers and protein folds.
G = H – T SG = - 36 kJ – 79 kJ
G = - 115 kJEspontaneous Process
Biologic MembranesFormed by a double layer of phospholipids and internal
and peripheral proteins (Singer y Nicholson, 1961)
“It seems to me that experimental study of the scattered radiation, in particular from light atoms, should get more attention, since along this way it should be possible to determine the arrangement of the electrons in the atoms”
P. Debye, Ann. Phys, 1915, 48, 809.
Electron density by x-ray diffraction studies
“Any attempt to determine the state of ionization of atoms in a crystal is likely to fail, since scattering factor curves will differ appreciably only
at angles for which no spectra exist”
R.W. James, The optical principles of X-ray diffaction, 1948
“It would be desirable to base X-ray structure refinements on a more appropriate model, taking proper account of the asymmetry of the several atomic charge clouds and of the modification of the free atom densities due to chemical bonding”
F. L. Hirshfeld, Israel J. Chem. , 1964, 2, 87.
Spherical and non Spherical Atomic ModelsSpheric Diffusion
Same diffusion at the same q Different diffusion at the same q
Spherical atomic modeladopted as routine to solve and refine
Crystal Structures
Non spherical atomic modelNon conventional approximation to the refinement of crystal structures and to
study the chemical bonds.
MODELING
Non Spheric Diffusion
Spherical
Harmonics
Original from the
Atomic Orbitals
May be contracted
or expanded
Non Spherical Atomic Model(multipolar)
Orbital Function
< | >
Orbital Density
+
=
Properties of the Spherical Harmonic functions
problem: density “multi-centric”??
Approximate in terms of linear combination of multicentric base functions
Orbitals vs. multipoles
New properties from the studies of electron density
Atomic, Charges/Moleculars, multipolar moments
Interaction Energies between “building blocks” in crystals
(→ Lattice Energies and lattice properties)
Investigation of the chemical bond:Analysis of deformation densities.Topological Analysis.
Electrostatic Potential
Empirical Analysis of theOrbital populations
ρ (r)
New properties from the studies of electron density
• Analysis of static electron density and electrostatic potential; • Analysis of interatomic interactions; • “atoms in crystals” topology;• Interaction Energies in crystals; • Distributions of energy density;
LiAl(SiO3)2 : Electrostatic Potential Map and evaluation of the electric potential on the atomic positions.
Applications
Electrostatic Interactions
Crystal Energies
Volkov, A.; King, H. F.; Coppens, P.; Macchi, P.
EP
aMM
mMM
Total bond Energy in the Crystal :
-------------------------------------------------
Exchange-Repulsion = 433.18131 kJ/mol
Dispersion = -205.60893 kJ/mol
-------------------------------------------------
Exch.-Rep. + Disp. = 227.57239 kJ/mol
Electrostatic = -334.77971 kJ/mol
-------------------------------------------------
Total de Interaction Energy = -107.20732 kJ/mol
-------------------------------------------------
Molecular multipoles
Exact potential
Distributed atomic multipoles
ICE VIII
Bond length
Conformational Parameters – Form Descriptors
Conformation: The structure or outline of an item or entity, determined by the
arrangement of its parts.
Bond (valence) angle
Dihedral (torsional) angle
The C-O-H plane is rotated counterclockwise about the C-O bond from
the H-C-O plane.
Improper dihedral (torsional) angle
Bond length calculation
jizzyyxxd ijijijij 222
xi yi
zi
xj
zj
xj
jkji
jkij
jkjijkjijkji
ijk
jk
jk
ji
ji
jkji
jkji
dd
zzzzyyyyxxxx
uu ˆˆ
cos
ijk
i
j
k
Bond angle calculation
i
j
k
l
bijkl
a
b
ba
Dihedral angle calculation
jklijkkljkij
ijkl
jklijk
jklijk
klij
ijkl
ddd
jkklji
dd
klji
b
b
sinsinsin
sinsin
coscos
cos
ba
ba
Conformation of the proteins
All proteins have a NATIVE state, a characteristic tridimensionalform known as CONFORMATION.
The conformation can be described interms of different structural levels
1ry, 2ry, 3ry and 4ry structures
Tridimensional Ordering
Concerns the ordering of the covalentskeleton of the polypeptidic chain,
GIVEN BY THE SEQUENCE OF aminoacids
1ry Structure
Will be determining the tridimensional ordering to be adopted by the protein
Different forces participate in the estabilization of the peptidic skeleton in order to reach the
tridimensional conformation
Hydrogen bonds
Hidrofobic interactions
Electroestatic atraction
NON COVALENT
COVALENT S-S Bidges
2ry, 3ry and 4ry Structures
• - helix (like a cylinder)
• b - sheet (fold)
• Turns (, b, )
• Random coil (desordered)
Different spacial dispositions or 2ry
structures
Conformation -helix
link C=O of rn
with N-H of rn+4
ALL RESIDUES GET BONDED by H-bond in thesame polipeptidic chain
Conformation b
- Sheet fold
Antiparallel
Parallel
b - Sheet fully extended !
H bond between the NH and CO groups of different polipeptidicchains
Turns
1/3 of the aminoacids are found on turns orloops where the CHAINS INVERT the their
direction
b turns
The C=O group of one residue n bonded by H bondwith the NH groupof residue (n+3)
3ry Structure
Concerns the way in which the polipeptidicchain folds or curvs itself to
produce the folded o compact structureof the soluble proteins
Forces participating in the estabilization of theterciary structure
Cisteine, with sulphur containing lateral chains (S), may oxidateand form S-S BRIDGES
4ry Structure
Only present in proteins with more thanone polipeptidic chain
May participatecovalent and non covalent bonds
CONFORMATION OF PROTEINS
hierarchic structure
Sequence of aminoacids of thepeptidic skeletonand S-S
Array / distribution / ordering of the skeletonand lateral chains of the
protein in space
Describes the tridimensional order of the
protein
Stereochemistry
• The properties of many drugs depends on their stereochemistry:
CH3
HN
CH3
O
Cl
NH
O
Cl
NH
(S)-ketamine
CH3
HN
CH3
O
Cl
NH
O
Cl
NH
(R)-ketamine
anesthetic hallucinogen
La Coupe du Roi
Types of Stereoisomers
• Two types of stereoisomers:
– enantiomers
• two compounds that are nonsuperimposable mirror images of each other
– diastereomers
• Two stereoisomers that are not mirror images of each other
• Geometric isomers (cis-trans isomers) are one type of diastereomer.
(R) And (S) Nomenclature
• Stereoisomers are different compounds and often have different properties.
• Each stereoisomer must have a unique name.
• The Cahn-Ingold-Prelog convention is used to identify the configuration of each asymmetric carbon atom present in a stereoisomer.
– (R) and (S) configuration
(R) and (S) Nomenclature
• The two enantiomers of alanine are:
Natural alanine Unnatural alanine(S)-alanine (R)-alanine
CO2H
C
H2NH CH3
CO2H
C
H3C NH2
H
C
H
H3C
OCH2CH
3
Cl
(R) and (S) Nomenclature
1
23
4
Example priorities:
I > Br > Cl > S > F > O > N > 13C > 12C > 3H > 2H > 1H
C
CH3
NH2
FH
12
3
4
R,S Rules
A) Absolute Configuration
1) +/- tell us the interaction of light, not the exact structure of enantiomers
2) X-Ray Crystallography gives us Absolute Configuration
a) Crystals are regularly arranged solid forms
b) They Diffract X-rays regularly, so we can tell what atom is where
c) X-Ray and Polarimetry lets us match +/- with a specific structure
d) Similar molecules usually have same +/- correlation
B) R/S Labels
1) Cahn-Ingold-Prelog System assigns name to each enantiomer
2) Arrange substituents with lowest priority in back
a) Clockwise arrangement high-to-low = R (rectus = right)
b) Counterclockwise = S (sinister = left)
A
B
D
C
A
B
D
C
R enantiomer S enantiomer
Louis Pasteur 1822-1895
The scientific contributions of Pasteur were among the most valuable in the history of science,and he is claimed equally by chemistry and microbiology. Best known to chemists for his work on the tartaric acids, he recognized the structural relationships (now called chirality)responsible for optical isomerism, and that microorganisms can distinguish between enantiomers. Pasteur also showed that micro-organisms cause fermentation andvarious diseases, and he developed methods for "pasteurization" and for vaccination against anthrax and rabies. His work saved the wine,beer, and silkworm industriesfor France.
C
COO
H
HOCH3
CCH3
HHO
COO
C
H3N
H
H3C
C
H3N
H
H3C
C
COO H3NCH3
H
HOCH3
CCH3
HHO
COO H3NCH3
C
COOH
H
HOCH3
CCH3
COOH
HHO
+
(R) salt
(S) salt
CH3NH2
(R)
(S)
MirrorEnan-tiomer
C
COOH
H
HOCH3
CCH3
COOH
HHO
+
(R)
(S)
C
NH2
HH3C
(R)-1-PhenylamineAn R,R-salt
An S,R-salt
Resolution of racemic lactic acid
Dia-stereomer
X-ray crystallography can be used to determine the absolute
configuration of Chiral molecules when they crystallize in non
centrosymetric space groups. To understand how it is possible,
we must consider the effect of the "anomalous Dispersion" in
structure factors.
The "normal" elastic scattering.
The "Anómalous" dispersion refers to elastic effects
that are delayed due to absorption by atoms.
While this effect is not observable
in centrosymmetric crystals (where
Fhkl is real), it is observable in the
acentric crystals.
Annomalous Dispersion & Absolute Configuration
While this effect is not observable in a Centro-symmetric Crystal (where
Fhkl is real), it has an effect, however in the acentric crystals: Friedel law
is not valid in this second case. Given that the anomalous diffusion is a
delay, we can consider that the phase difference associated with this
delay (shown with red vectors) will be in the same "direction" (the angle
between the vector of dissemination and the vector of anomalous
diffusion is the same).
Modern detectors can
measure differences in
intensities between
reflections that would be
equivalent in accordance
with the law of Friedel. It
should be noted that in the
past, the anomalous
dispersion required the
presence of heavy atoms.
This requirement is not
necessary for the majority of
molecules using current
technology.
If there is no appreciable
Anomalous Dispersion resulting
structure factors are equivalent.
The values of the resulting
structure factors are altered when
there is Anomalous Dispersion.
Since the law of Friedel does not verify strictly structures in
non-centrosymmetric, there will be differences in intensities
of the reflections which should be equal. These reflections
are known as Bijvoet pairs.
For space groups not centrosimetricos we can then compare F (hkl) and F(-h-
k-l) to determine the absolute configuration.
This can be carried out by calculating F(hkl) and F(-h-k-l) to the structural
model and the same inverted model and comparing the figures calculated
from the experimental data.
F(obs) xyz model-F(calc) -x-y-z-model-
F(calc)
F(hkl) 200 160 190
F(-h-k-l) 180 150 170
The calculation is repeated for several hundred reflections confirm the
absolute configuration of the molecule.
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Bonds and interactions in crystals: Conformations and Chirality
Master of Crystallography and Crystallization – 2013
T01 – Mathematical, Physical and Chemical basis of Crystallography
END