The Valence Bond Way in Chemistry Sason Shaik, The Hebrew University VB for understanding reactivity June 27th, 2018 _Marseiiles 1 X In 2012 the 1 st VB workshop took place in Paris. This event made me very excited. X 0A> K>:LHG ?HK FR >Q<BM>F>GM P:L MA> ?:<M MA:M BG PA>G % started using VB theory to understand chemical reactivity , the VB landscape was barren, and there were very few groups which were still practicing this “ancient” art in Chemistry. X At those times, it was inconceivable to think about a sizable meeting dedicated to VB theory. In many ways, the Paris workshop was a historical event, which marked the rise of the phoenix from its ashes. Indeed, here we are again in the 4 th workshop in Marseilles!
Transcript
The Valence Bond Way in Chemistry Sason Shaik, The Hebrew University
VB for understanding reactivity June 27th, 2018 _Marseiiles
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In 2012 the 1st VB workshop took place in Paris. This event made me very excited.
started using VB theory to understand chemical reactivity, the VB landscape was barren, and there were very few groups which were still practicing this “ancient” art in Chemistry.
At those times, it was inconceivable to think about a sizable meeting dedicated to VB theory. In many ways, the Paris workshop was a historical event, which marked the rise of the phoenix from its ashes. Indeed, here we are again in the 4th workshop in Marseilles!
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It gives me therefore great pleasure to come to Marseilles to talk to this audience on “How to Understand Chemical Reactivity Using
Computational chemistry has at its disposal wonderful tools:
Powerful methods that can compute medium size molecules with accuracy of sub-kcal/mol. And DFT methods that describe enzymes with sometimes amazing accuracy.
Mead Bradock, 1747
•••The sky is the limit; with machine learning, one day a large enough computer will compute anything with chemical accuracy or more. Chemistry will enter paradise! [which was mapped already at the 18th Century by Bradock…]
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The computer doesn’t replace insight, as put beautifully by Eugene Wigner : “I am glad the computer understands this. But I would like to understand it too”.
“nightmare speech”: “Give us insight not numbers” or “Give us insight and good numbers”.
alongside good numbers.
Should this residence in Paradise be the end of Chemistry? Certainly not!
In the 1st main story, I shall attempt to demonstrate how the VB model creates unity for one of the most fundamental oxidative reactions in nature, the hydrogen atom transfer reaction; going from H + H2 all the way to P450 hydroxylation…
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It creates order, predicts mechanisms, and enables to estimate barriers from raw data
The 2nd main story will focus on the enzyme cytochrome P450, and its key oxidative reactions.
In telling this story, I shall try to show that VB modeling is a perfect interface between experiment & computations:
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In the short stories, I will show you a quick way to use the VB model, and how to gain quick insight into not so obvious results…
I will provide insight into stepwise mechanisms, incursion of intermediates, [EF effects on chemical reactivity – you already heard], may be some photochemistry, structure of radicals, etc.
But please be advised, the idea is NOT to make you VB experts in 1 hour & 15 minutes, but to show you part of the huge insight that VB provides to its user, with the hope that this will serve as an appetizer for more…
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Let me proceed with a short personal story; of how from an avid MO-afficionado, that it was necessary to return to the “ancient art” and develop a VB model. I shall then discuss how to construct this model and how to use it …
How Has the Long VB Odyssey Begun for Me?
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Here you can see an early cartoon, which my daughter drew for me.
‘child’ who studied a myriad of rules of the schools of physical organic and theoretical chemistry.
quite baffled, not knowing which one to obey and how should he create bridges and close the chasm between the schools.
But, as a devout fan of MO theory I was concerned because with the exception of “forbidden reactions” MO theory gave no clue as to the mechanisms by which barriers are formed...
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To Understand Chemical Reactivity one Must First formulate a general Mechanism of Barrier Formation, because this would Generate the Factors Governing Reactivity and will thereby enable a unified understanding of reactivity. But…
At some point it dawned upon me that:
At the beginning this was just an act of despair, sort of, “let’s see what will happen if…”.
But as time went by, I realized that what I was doing was simply mapping the MO-based wave functions into a collection of VB-structures (VBS), with different weights (wi): ΨΨMO-CI àà ΣΣi[wiΨΨVBS,i] You can do this decomposition yourselves for simple cases (VB book,
Philippe’s talk.
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After some head-scratching, I started to decompose MO and MO-CI wave functions into wave functions based on fragment orbitals.
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while doing the decomposition, more than just getting structures and weights, I found something very beautiful and general about the mechanism of barrier formation and electron reorganization in chemistry.
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My excitement can be sensed from the title I have chosen for this 1st paper:
Even the refereeing process which took well over a year did not diminish my excitement: I felt that I was on a verge of “understanding” chemical reactivity.
The MO-VB mapping gave two archetypal diagrams that describe the major reactivity patterns in ANY reaction. In a nutshell:
BΨr ΨpΨr Ψp
Ψint
PR R P
G
∆E≠
Reaction Coordinate
(a) (b)
∆Ec
R* P*
A ..//..B-C A--B--C A-B ..//..C
P*R*
Reaction Coordinate
Ψ*
VBSCD VBCMD
Barrier formation in a single step. R* is a promoted (exited) state
in which the reactants are prepared for bonding to become P, and so is P* on the other side
Intermediate formation in a stepwise mechanism, is derived from a low-energy VB structure that cuts through the main state curves, and leads to Internal catalysis
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Let me show you how we construct the VBSCD in steps for the simple case of Hydrogen atom abstraction (HAT) reactions:
covalent structures, which describe the bonds in the reactants and products. These are 1R and 1P.
2R,P and 3R,P are ionic structures for the HY and XH bonds, which are of secondary importance.
4 and 5 belong to excited states of reactants and products
– they involve 1e or 3e, and hence describe CT states of 1R and 1P
Let’s begin with the covalent structures of the reactants (R = 1R) and consider how it varies along the RC.
not spin-paired involves approximately a repulsive triplet wave function.
Here are the two covalent curves along the RC of HAT:
R P
structure of the products (P = 1P), in the reverse direction of the RC.
curves which interchange along the RC.
This interchange simply mirrors the interchanging bonds during the reaction.
The interchange of the covalent structures is a topological property of any chemical reaction
We can now bring the ionic structures of each bond, and simply mix them into the covalent structures at each point of the RC. In this manner, we dress each one of the covalent curves (in A) with ionic structures, and convert the curves to Lewis curves (B), thus obtaining intersecting Lewis curves with full-bond wave functions.
RP
AB
The intersecting Lewis state-curves is also a topological property of any chemical reaction, which involves breaking and making of covalent bonds
Add ionics Lewis State Curves
Gr and Gp are the promotion energies of reactants and products, which are singlet-to-triplet excitation energies of the bonds undergoing activation. B is the resonance energy of
the TS due to the avoided crossing, i.e., the VB mixing.
quantities that will serve us to quantify barriers.
In the subsequent step, we let the two Lewis-state curves mix with each other. As a result they avoid the crossing and generate the energy profile for the ground state reaction.
This profile is shown by the bold-brown energy curve.
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I could have repeated the same detailed process to construct VBSCDs for other reactions. The end result would have been similar to what you just saw. So we can generalize the diagram:
BΨrΨp
P
R
Gr
∆E≠
Reaction Coordinate
R* P*
∆Erp
Gp
It is a diagram with two intersecting state curves that are anchored in the ground states of reactants and products and their two promoted electronic states.
The mixing of the two state-curves leads to avoided crossing and a barrier formation on the ground state energy profile.
For self tutoring see: 38, 586
A Chemist’s Guide to Valence Bond Theory Ch. 6 Chem. Soc. Rev. 2014, 43, 4698
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We can also derive barrier expressions from the VBSCD, by
•A more explicit expression takes into account the thermodynamic driving force of the reaction, the average promotion gap, G0, and the average of the ƒ factors, ƒ0:
BΨrΨp
P
R
Gr
∆E≠
Reaction Coordinate
R* P*
∆Erp
Gp
using the promotion energies, G, and the resonance energy of the TS, B:
ƒGr = the height of the crossing point at the reactant side. It gauges the total deformation and repulsive interactions the reactants must experience in order to achieve resonance with the product.
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ƒGr
•The simplest expression is: ΔΔE‡= ƒGr - B
ΔΔE‡≈ƒ0G0 - B + 0.5ΔΔERP+0.5ΔΔERP2/G0
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process of VBSCD construction by using simple rules: To apply the rules, we draw the covalent structures of reactants and products, count the number of electrons on each fragment/atom, and see whether this number changes or not while passing from reactants to products.
Easy Construction of VBSCDs:
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Here are the covalent structures for a H-abstraction reaction. It is apparent that there is no change in the oxidation numbers of X, H, and Y:
And here are the covalent structures for a proton-abstraction reaction. It is apparent that here X and Y change their oxidation numbers. In the forward reaction X:− is oxidized while −, and vice versa in the reverse reaction:
Consider the two following archetypical reactions:
Once the oxidation numbers are assigned, this determines the nature of R* (P*) and of the corresponding promotion energies:
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The Promoted States in the VBSCD Involve two Elementary Excitation-Types, depending on whether there are or aren’t changes in the oxidations numbers of the fragments:
st Elementary Excitation: No change in the oxidation numbers- For reactions, which do not involve changes in the oxidation numbers of the reacting fragments, the bond pairs that will break during the reaction are decoupled in the promoted state R*, to their triplet states, and the electrons are paired anew as in P. For example, in the H-abstraction reaction the R* state would be the
doubet:
The corresponding promotion energy would then be given by the singlet-to-triplet decoupling energy of the bonds that are broken in the forward and reverse reactions: Gr ~ ΔΔEST(H-Y) and Gp ~ ΔΔEST(H-X)
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The 2nd Elementary Excitations: The fragments change their oxidation numbers during the reaction: For such reactions the promoted state R* involves a charge transfer from the fragment that gets oxidized (losing 1e) to the fragment that gets reduced (gaining 1e). For example, in the proton-abstraction reaction R* is the following charge-transfer (CT) state:
The corresponding promotion energy would then be the difference between the vertical ionization potential (I*) of the anion and the vertical electron affinity (A*) of the molecule: Gr = I*X: - A*(H-Y) and Gp = I*Y: - A*(H-X)
It involves electron transfer from X:− to the H-Y bond, which decouples the H-X bond, with the excess electron in (HY) − .
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Let’s now make a few quick applications of the rules, and use them to predict and organize
reactivity data:
Consider first the recombination reaction X: + R+ àà +X–R
Since there are changes in the oxidation numbers of the nucleophile and the carbocation, the promoted state R* in the VBSCD is a vertical charge-transfer state having: G = IX:* – AR+*
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ΔΔEVB‡= ƒG - B
G
ƒGB
ΔΔEVB‡
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X: + R+ àà +X–R; G = IX:*- AR+*
Let’s not bother at the moment about ƒ and B and focus on the correlation of reactivity with G. For a reaction series where the carbocation R+ is common (e.g., the cation Y-pyronin), the only variable of G is the vertical ionization potential of the nucleophile X: (X:−), IX:*.
experimental free energy barriers in aqueous solution vs. the vertical ionization potential of the nucleophile X: in the same solvent.
Note the extent of order brought by the VBSCD to the concept of nucleophilicity, using a single fundamental property.
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Consider now the following two reactions which are both WH-allowed:
C
C
C C
C
C
C
CC
C
CC
ΔΔH≠ = 49 kcal/mol
ΔH = -67 kcal/mol ΔH = -44 kcal/mol
ΔΔH≠ = 22 kcal/mol
Fomally Allowed
It is seen that the 2+2+2 reaction with the higher thermodynamic driving force has strangely a much larger reaction barrier. Why?
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Since there are no redox changes of the atoms, the promotion energies in the VBSCDs of the two reactions are singlet-triplet decoupling of the bonds that break during the reaction:
C
C
C
CC
C
CCC C
C C
C
C
C
C
C
C
C
CC
C
CC
G = 3ΔΔESTG = ΔΔEST
(diene) + ΔΔEST(ethene)
= 303 kcal/mol = 179 kcal/mol
G value for the 2+2+2 reaction. The small G in the DA reaction is due to ΔΔEST
(diene) which is only 78 kcal/mol compared with 202 kcal/mol for two ethene molecules in 2+2+2.
ΔΔE≠ = ƒG - B & e.g., ƒ = 0.3 and B-const, then the difference of 124 kcal/mol in G values will predict correctly that the Diels Alder reaction should have a lower barrier than the 2+2+2 reactions, by 36 kcal/mol (vs. 37, ab initio)
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And finally, here are two Forbidden 2+2 Reactions. Again, there is no redox during the reaction and hence, the promotion energies involve singlet-triplet decoupling of the two ππ-bonds:
CH2
CH2 H2C
H2C CH2
CH22
42.2 k/mol
SiH2
SiH2 H2Si
H2Si SiH2
SiH22
4-10 k/mol
GC=2ΔΔEST(ππππ*)=202kcal/mol
GSi=2ΔΔEST(ππππ*)=80kcal/mol
•With a difference GC - GSi = 120 kcal/mol, usage of ƒ =0.3 leads to a barrier difference of 36 kcal/mol, thus highlighting the fact that the formally forbidden reaction of Si is in fact extremely fast!
kcal/mol !
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The VBSCD enables to articulate the effects of the major barrier factors:
BEP Rate-equilibrium
Symmetry & Trajectory Promotion-state Effects
Plenty of examples are given in Chapter 6 in the VB book and in the recommended reviews, and in the many papers by my group.
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Having shown the utility of the VBSCD for making quick assessments, let us talk about
the second diagram type the VBCMD.
states, which do not correlate to the ground states & change horizontally along the reaction coordinate as in (a). These states will mix into the TS of the elementary reaction, as in (a).
stable, relative to the crossing point of the two main curves (Lewis curves) as in (b)
This latter case corresponds to the second diagram, which is called: the VB Configuration Mixing Diagram (VBCMD).
Here, an intermediate state curve crosses the two principal curves, and the three-state mixing leads to a stepwise mechanism with an intermediate. The intermediate state has
electronic structure different than those of the R and P states.
Taken together the two diagrams can model a wide range of reactivity patterns, for all reaction types.
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VBCMD
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Some Examples of VBCMD
VBCMD
(a) Ionic Structures that are usually high in energy, cross well below the covalent curves, leading to a stepwise mechanism, e.g., SN1 or SN2Int
(b) One of the many excited states, other than R* and P*, may get low enough and cross the main curves that describe the reaction R →→ P. We shall show an example for P450 H-abstraction reactivity.
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The Impact of a Single Electron
(FHF)
ΦHL(r) ΦHL(p)~~
E
(b)
E
ΦHL(p)ΦHL(r)
(a)
(F – H+ F)
(F – H+ F– )
F__H // F– F– // H__F(F__H__F)– F__H // F F // H__F(F__H__F)
(F H+ F– )
With one electron less, the ionic structure loses at least 50% of its stabilization and rises in energy. The result is that species is a high energy TS (20 kcal/mol higher than F + HF), compared with the highly stable (FHF) − where the triple ionic structure, F:− H+ −F: is of very low energy.
F− + H-F F + H-F
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nucleophilic displacements on carbon proceed via a TS, which is pentacoordinated. By contrast, in the case of silicon the pentacoordinate species is a stable intermediate. Why?
Let’’s have a close first look at ionic structures of C-Cl and Si-Cl bonds:
:Cl
Rion = 2.22 Å
SiHH
HC :Cl
Rion = 2.48 Å !!!
Rcov = 1.97 Å Rcov = 1.81 Å
R(CH3+)= 0.67 ÅR(SiH3
+)= 0.31 Å
HH
H
-1.0+1.111
-0.037
-1.0+0.155
+0.282
R3Si+ is a small ion in the direction of the C3 rotation axis, small like a proton. Thereby it will allow close approach of anions and significant electrostatic stabilization. This is due to the positive charge localization on Si vs. the delocalization over all the atoms in the carbocation Q(Si) = +1.11; Q(C) = +0.155.
SN2(C) vs. SN2(Si)
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Here are the VBCMDs for SN2(C) vs. SN2(Si):
L
Si
L L
XX
C
L
X
L
L
X
R P R P
X: / L3Si__X X__SiL3 / :X
Reaction Coordinate
X__CL3 / :XX: / L3C__X
Reaction Coordinate
X – Si+ X–
EE ΦHL(p)ΦHL(r)
ΦHL(r) ΦHL(p)
X – C+ X–
The triple ionic structure for Si is very stable, since all the positive charge is localized on Si. This makes Si+ effectively small like a proton, which therefore has a tendency to make stable hyper coordinated intermediates in the SN2(Si) process by cov-ion resonance.
C+ ionic structure is not so stable, so the hyper-coordinated species is a TS
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An Interesting Manifestation of the Small Size of Si+ :
The carbon analog has an asymmetric C-F…..C+ Structure! It has an intact C-F bond and a C+ center on the other side.
Thus, we have a symmetric (Si---F---Si)+ cation due to low energy Si+ :F− +Si structure that crosses below the covalent structures:
Let me turn now to the main story that focuses on hydrogen atom transfer (HAT) and try to apply the VB model to pattern and predict reactivity:
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processes occurring in nature and in oxidative chemistry: Most chemical oxidations begin with HAT. P450 and nonheme enzymes oxidize organic substrates by initial HAT. Heme enzymes, e.g., HRP, build the cell walls in plants by initial HAT from phenols. Cell membranes are destroyed by HAT. Proteins form plaques by HAT. DNA damage occurs by HAT. HAT occurs during combustion and in atmospheric processes…
The list is endless, attesting to the immense importance of HAT.
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Here is the VBSCD for a standard HAT Reaction, which you have already seen
As you recall, the promotion gap in this VBSCD is the vertical singlet-triplet promotion (ΔΔEST) of the H-Y and X-H bonds that are broken and formed. Semi-empirical VB theory shows that ΔΔEST, for a general A-B bond, can be
approximated as: ΔΔEST(H-Y) = 2DA-B ; D is the vertical bond strength. This is why we are using in the diagram 2DH-Y & 2DH-X
RE RE is the Reorganization Energy of the radical to become prepared for bonding & it involves both geometric and electronic terms.
delocalized radicals, and zero for atomic radicals.
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Here is a graphic illustration of the difference between bond dissociation energy (BDE) and the vertical bond strength (D):
Let us go back now to the VBSCD
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How Do we evaluate the resonance energy of the TS, B?
An extensive VB study* of simple HAT reactions and a semi-empirical estimate** showed that B can be approximated as ½ BDE, where BDE is the bond dissociation energy of the bond undergoing breaking or making.
* Su et al, JACS, 2007, 127, 8204. ** Lai et al, ACIE, 2012, 51, 5556
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For this purpose we must use the explicit expression for the barrier: ΔΔE‡≈ƒ0G0 + 0.5ΔΔErp + ΔΔErp
2/2G0 - B Where, G0 = DHY + DXH (the average promotion gap) ƒ0= 0.3 B = ½ [BDE(av)] = ¼ [BDEHY + BDEHX] ΔΔErp = BDEHY - BDEHX
From this expression it follows that all one needs for the application are simply BDE and D data & nothing else!
Let me proceed with a general treatment of HAT reactions, and project the unity brought about by the VB model:
•To this end, we considered 45 reactions including simple H-Cl, Br, CH3, SiH3,
GeH3, OH, SH, HCC, NCCH2, etc.), of identity and nonidentity processes, as well as, all P450 HAT reactions I will discuss later. Here is the plot of the VB-barriers vs. CCSD(T)/CBS and DFT barriers:
•It seems that the VB model can indeed predict trends in barriers of many seemingly unrelated reactions, and can do so based on raw data.
This is a powerful conclusion from the VB model.
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Lai, Li, Chen, Shaik, ACIE, 2012, 51, 2-25
Let us try then to gain some insight into this successful application, by looking at the barrier expression:
To make life simpler, I will consider an èè
The corresponding barrier is: ΔΔE‡XX=fG–B=0.6DHX - ½BDEHX Since DHX = BDEHX + |RE | , we can plug it into the equation. Then the identity barrier becomes simply: ΔΔE‡XX=0.1[BDEHX] + 0.6|RE |
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This in turn means that a major factor of the identity barrier will, be the reorganization energy, RE , that is required “to prepare
”. Let us see how this works.
Here are Identity Reactions, BDE/RE values, VB- barriers (ΔΔE‡XX=
The VB model can reproduce the barriers for identity reactions… Compare H/H2 vs. CH3/CH4 and HCC/HCCH vs. CNCH2/CH3CN [CH3CN is a solvent for radical reactions]. The major factor of the barrier is RE, which is the “preparation energy” of the radical. The insight is lucid… 49
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Nonidentity Reactions: Here are the predicted VB barriers plotted against the experimental free energies of activation
It is seen that the closed-shell abstractors have higher barriers than the open-shell radical abstractors.
The reason is simple: closed-shell abstractors pay an energy price to prepare a radical at the abstractor center along the RC! 50
Closedshell
Openshell
ΔΔE‡(1)≈ƒ0G0 + 0.5ΔΔERP + ΔΔERP
2/2G0 - B
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Let me turn now to the story of hydrogen atom transfer (HAT) in Cytochrome P450.
predicts HAT barriers well, I restricted myself here to showing you that the VB model can be applied quite naturally even to this complex system, where it leads to insight about mechanism. Subsequently I shall treat other P450 reactions.
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Cytochrome P450 is a large family of enzymes, generated by more than 4,000 different genes in the various forms of “life”.
P450s activate O2, and form an active species that oxidizes organic molecules as means of neutralization of xenobiotics, and of biosynthesis for example, of steroids, brain chemicals, molecules with anti cancer activity, etc.
These enzymes which look like impossibly intricate cathedrals, are also ever so beautiful objects, so much so that I have been spellbound ever since I started investigating P450s…
P450camP450 2D6
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The active species of this enzyme is called Compound I (Cpd I).
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S
NN
NFeN
O
CO2-(CH2)2
H3C
H3C
CO2-(CH2)2
CHCH2
CHCH2CH3
CH3
Cys
The electronic structure of Cpd I reveals that its FeO moiety is an analog of the 3O2 molecule, with a triplet configuration in π* type d-orbitals and a third electron residing in a porphyrin orbital marked as a2u.
Therefore, Cpd I has two spin states depending on the direction of the spin in the a2u orbital. These states are almost degenerate in energy.
valent oxo-iron moiety embedded in a porphyrin cation radical ligand.
Cpd I
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The translation of this electronic structure from MO to VB is straightforward.
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π*FeO
πFeO
σFeO
(δ 2σ*xy0σ*z20)
Fe
O
S
Fe
O
S
MO VB
(δ 2σ*xy0σ*z20)
a2u
Both pictures, but especially so the VB representation, show that the ferryl moiety (FeO) is an oxyl radical
The σ-orbital is the Lewis bond between Fe and O. π2π*1 electrons correspond to two resonating 3-electron bonds in
two perpendicular planes. 2u electron is represented by the porphyrin radical
cation.
Here is the VB diagram for Alkane Hydroxylation by Cpd I CT state
This is a common feature for the two spin states with an exception of a small rebound barrier for the quartet state.
Considering the oxidation numbers, one can see that the direct transformation of the alkane, R-H, to the alcohol product, R-OH, involves crossing of the ground state curve with a high-lying charge transfer state curve.
However, the process is catalyzed by an intermediate state wherein Cpd I uses its oxyl radical center to make a bond to the triplet promoted H-R bond.
the high ridge for the direct oxo-transfer & splits the process into oxidative H-abstraction followed by radical-rebound to form the alcohol complex.
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The VBCMD for C-H hydroxylation by P450 provides a glimpse of the root cause why both experimentally and computationally, one finds a stepwise mechanism. These issues have been discussed in great detail in the original literature, e.g., ACR 2010, 43, 1154-1165
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As I already showed you, the VB model is quite general and not limited to HAT. Let me flush before your eyes a few applications of the model to other P450 reactions:
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LSHS
CT state
GLS/HS = IRR’S:- ACpd I + / ΔΔE(ππ* èè dz2)
Here are the VB diagrams for sulfoxidation by Cpd I in the two spin states. Look at the change of the oxidation numbers of S and O: this means that the promoted states involve charge transfer:
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And here are the results of the VB modeling for this reaction:
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ΔΔEVB‡= ƒG - B, Where: G = charge transfer energy /+ d to d promotion (in HS quartet state):
GLS/HS = IRR’S:- ACpd I + / ΔΔE(ππ* èè dz2)
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Arene Activation by P450:
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ΔΔEVB‡= ƒG - B, Where: G = ΔΔEST(ArX) ƒ = 0.3 B scales with the CT energy gap
charge transfer state
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Arene and Olefin Activation by P450, Using the Same Equation:
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ΔΔE‡= 0.3G - B, Where: G = ΔΔEST(ArX or olefin) and B scales with the CT energy gap
CT
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As a FINAL Story, I have chosen a random collection of examples from reactivity, electronic structure and photochemistry. Just to show the beauty of VB theory, and its panoramic applicability!
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There is a lot of talk about proton-coupled electron transfer (PCET) mechanisms and their relations to the HAT mechanism. Once you become proficient in the VB model you can immediately see that PCET blends proton- transfer and HAT curves, as seen below:
There is a VB mixing and avoided crossing of 4 state-curves along the same reaction coordinate. This blending brings
about new reactivity patterns, which can easily be recognized from plots of deformation energies vs. barriers.
Here are many “H” transfers. The black and reed data point correspond to HAT, where one can see ΔΔE≠ ~ ΔΔEdef , namely the barrier derives from the deformation energy of the reactants in the TS.
The blue data points are PCET mechanisms, where one can see that ΔΔE≠ << ΔΔEdef , namely the reactants in the TS maintain a very strong interaction energy, ΔΔEint due to the VB mixing of 4 state-curves.
Thus, in PCET the reactants deform more in order to enjoy greater stabilization via the interaction energy of the 4-state mixing
ΔΔEint
Slope = 1
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CASSCF:“2ππ bond +”: based on EBO = 2.2-2.3. Weak dative σσ-bonding A few kcal/mol as in Be2
MO: 2ππ bond based on BO of HF
VB: 4 bonds (three internal + one exo-bond).
HF
Quadruple Bond
The Bond Order (BO) Disparity in C2
Without going into the disparity, let me tell you how VB views C2 and explain the novelty in this new picture
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VB Calculations show the following key observables of the Quadruple Bond
Thus, the quadruple bond structure reproduces the key observables of C2! This has been just shown yesterday by Ruedenberg from CASSCF. Novelty: a double-σσ-bonding!
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A New Aufbau Principle for Diatomic Molecules?
Recently, Havenith et al* showed that B2 has a triple bond, in a bonding motif analogous to C2, with a double-σσ-bonding:
The double σσ-bond fails in Be2 because the promotion energy is much higher than the bonding energy, and Be2 remains as a dimple on the energy surface. However, this unusual bonding becomes apparent in B2 and it continues to C2. Many other diatomic species must have this bonding type!!!
bonding in diatomic molecules!!!
They found that the 1-electron ππ bonds are rather weak and the bonding is dominate by the double σσ-bond – Highly important finding!
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VB Structures provide immediate and lucid insight into electronic effects. Here is an example of the origins of spin polarization in allyl radical as emerging from EPR:
+0.6 +0.6-0.2
|abc| |abc| |abc|
Db = DQCDa
Dc
DQC
QC is spin-alternant, & hence having the lowest energy & it controls the wave function of allyl radical, and cause spin-polarization.
state…
The spin-alternant determinant of the pentadienyl radical shows that the negative spin density will now shift to the carbons flanking the central one. The next homolog will have it back on the central carbon, etc. So easy!
Erel = 0
EPR
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VBSCD and Photochemical Reactivity
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VBSCD and Photochemical Reactivity
The importance of potential energy funnels in photochemistry was pointed out by Oosterhoff and Michl.
Later, Horst Köppel has shown that these funnels are in fact conical intersections which can shuttle excited state complexes to ground state products in a very fast time scale.
Ruedenberg has derived the conditions for having a conical intersection for polyatomic molecules.
Mike Robb and the late Fernando Bernardi devised electronic structure methods to locate such conical intersections, and have shown how many photoreaction mechanisms utilize these intersection to shuttle products to the ground states.
In the next few slides I would like to show you how to think about conical intersections using VB diagrams, and how to predict products of photochemical reactions.
The relevant material can be found in the VB book in Chapter 6.
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Conical Intersections Play a Key Role
R P1
hυConical Intersection
with S0
Excited State
Sn
P1
CI
P2R
Ground State
S0
Product of the thermal Reaction
A conical intersection is a point on a seam that connects the excited and ground states. It is a spike that gets stabilized along two coordinates which lead to different photoproducts, P1 and P2. P1 is usually identical to the product of the thermal reaction, while P2 is a new product.
predict the nature of the P2 type products?
A new product (there may be a few)
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Let me show you again the VBSCD Up to now, we focused on the TS for the ground state, ΨΨ≠. But in fact, the avoided crossing of the VB state-curves generate also an excited state, ΨΨ*:
In photochemistry, what matters is the interplay between this pairs of states, ΨΨ≠ and ΨΨ*, which we call the “twin states”.
We are now going to use the twins to discuss photoreactivity.
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RR =
ab c − ab c ; PP =
ab c − a b c
≠ = RR PP ;
* = RR + PP =
ab c − a b c
X --- H --- X a b c
Let us predict the conical intersection in a HAT reaction:
→→
[2|abc| - (|abc|+|abc|)]
(X----H----X) X2 + H
This conclusion is general - e.g., photochemistry of allyl and higher radicals will lead to 1,3-cyclized products.
Inspection of ΨΨ* reveals that the coupling is between the AOs a & c, namely between the two X groups. On the other hand, ΨΨ≠ has a triplet relationship between a & c . As such, the distortion that will create a CI is the following
2
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CI
CH3
X X
CH3
Q (CI Coordinate)CH3
X XHH
C
H
E
Ψ∗(A'')
Ψ≠(A')
+
[(X ∴∴ X)–]*
(X ∴∴ X)–
m
The CI and Products in the photo-stimulated SN2 reaction can be rationalized in a similar manner:
products
Experimental data by M.A. Johnson show these products in the photo-stimulation of I-/CH3I and Br-/CH3Br
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CH2
CHCH
H2C CH2
CHHC
H2C
R P1
Consider the photo-stimulated reaction of Butadiene:
thermal
a
bc
d
Ψabcd = |(ab - ab)(cd - cd)| =
= |abcd| - |abcd| - |acbd| + |abcd|
In a similar fashion the wave function of the thermal product P1 is given by ΨΨbc(ad) and can be obtained by taking the product of the b-c and a-d bonds wave functions:
R =
As shown in the Book in Chapter 6, the wave function for the butadiene reactant , R, is simply the product of the two bonds a-b and c-d:
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RR = ab cd − abcd − a bcd + a bc d
PP = abc d − a bcd − ab cd + abc d
≠ = RR - PP = 2 ab c d − ab cd − abcd + 2 ab cd − abc d − a bc d
* = RR + PP = − ab cd − ab cd + abc d + a bc d
The Wave functions of the Twin-States in the Reaction of Butadiene:
ΨΨ* has a-c & b-d coupling (you can verify by writing the wave function ΨΨac(bd) & comparing it with the expression for R + P).
At the geometry of butadiene the a-c and b-d couplings in ΨΨ* are weak, and a distortion will be required to lead to P2 ; because of this weakness one can get also the diradical P2’’.
Since ΨΨ* is R + P, appropriate distortions can localize it to either R (back to butadiene) or P (cyclobutene). P2 P2’’
C
CC
C
R+P R+P
C
CC
Ca
bc
d
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CH2
CHCH
H2C CH2
CHHC
H2C
H2C
CHHC
CH2
CH2CH
HC
H2C
R P1 P2 P2'
Summary of Expected Products of the photo-stimulated reaction of Butadiene:
P2, P2’’ are in accord with experiment and with calculations of conical intersection
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I have a feeling I have talked enough and it is time to conclude: I have tried to project the unique and wide-ranging insight that VB
theory offers a into so many areas of chemistry: It creates order, predicts mechanisms, estimates barriers for complex
reactions, enables one to think about excited states and photoreactivity, and it elucidates also complex MR/MC wave functions. And there are many, many more topics, like bonding, etc. …
classroom and into the research desk of chemists!
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Wenzhen Lai (47 reactions!), Chunsen Li (more than 30 reactions) Hui Chen (CH activation) Usha Dandamudireaction) Samuel de Visser (2008, Cpd I)Devesh Kumar (2008, Cpd I)
AA NNeeww BBooookk oonn TTeeaacchhiinngg CChheemmiissttrryy
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Before doing so, let me clarify the difference between bond dissociation energy (BDE) and the vertical bond strength D, and why the latter is used in the promotion energy gap expression: Gr = ΔΔEST(C-H) ~ 2DC-H
relaxation of the radical, while D does not.
the VBSCD is a vertical state we use for the promotion gap, the D and not the BDE.
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As a FINAL Story, I have chosen a topic which excites me now very much: The Catalysis of Reactions by Oriented External Electric Fields. Long ago I was playing with the idea of oriented external-electric fields (OEEFs) as a catalyst, and I reasoned why it should be so:
Thus, since the transition state is the locus where the bonds of the reactants are converted to those of the products, I reasoned that OEEFs should catalyze non-redox reactions, by increasing the contribution of ionic structure in the TS. I called the specific orientation of the OEEF that imparts catalysis, as the Reaction Axis Rule, because the requisite electronic reorganization from of reactants to products occurs along this Axis.*
Here are the two Diels Alder reactions, we studied:
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The reaction axis is Z, and this is where we expect catalysis by the OEEF. I will show you however, that OEEF can control also the Endo/Exo ratio.
A key reaction in chemical synthesis is the Diels-Alder reaction, which involves making two C-C bond in concert. We want to catalyze it.
Let’s start with predictions:
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Here is the VB diagram for a generic DA reaction. It has reactant’s and product’s Lewis curves, and an exited charge transfer (CT) state that can mix by symmetry and stabilize the TS for the reaction.
Further, as the field gets larger, we expect that the CT structure will cross below the principal states and will lead to a stepwise mechanism
a negative EF along Z will stabilize this CT state and catalyze thereby the reaction.
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The calculations verify these predictions: Here are barriers plotted against the the strength of the field:
It is seen that a negatively-oriented field along the reaction axis lowers the barrier by about 8 kcal/mol (~106 enhancement), while a positively oriented field will inhibit the reaction by the same amount.
catalysisinhibition
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Finally, the TS in the catalytic region becomes increasingly asynchronous, and eventually we have a zwitterionic TS, which collapses into a zwitterionic intermediate.
Clearly, there is a perfect match between the VB predictions and the computational results.
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And also the Exo/Endo ratio is controllable: Since maleic anhydride has a dipole in the y direction, we expected that it should be possible to control the endo/exo ratio by applying an OEEF along the y-axis.
at a negative Fy we find exo selectivity, whereas at a positive Fy we find endo selectivity.
interactions”. It is entirely the action of the electric field.
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In summary therefore: Usage of OEEF enables one to control catalysis or inhibition of the DA reaction as well as its endo/exo selectivity at will!
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The prediction of catalytic power of OEEF on the DA reaction was elegantly verified by Ciampi and Coote (Aus.) & Darwish and Diez -Perez (Barc.):
field, using an STM tip holding the diene and a gold electrode holding the dienophile, such that the field ran parallel to the Reaction Axis.
conducting junction & the team could observe a tunneling current, for the product formation events.
They verified that only one of the field orientations, the one stabilizing the CT structure I, leads to catalysis. [Nature, 2016]
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There are plenty of other applications, which will take more and more time. Those interested can look at the VB book and the various reviews mentioned along the talk. It is time for me to summarize my talk.
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I have tried to project the unique and wide-ranging insight that VB theory offers into so many areas of chemistry:
It creates order, predicts mechanisms, estimates barriers for complex reactions.
In addition, it enables one to think about excited states and photoreactivity, and it elucidates also complex MR/MC wave functions. And there are many, many more topics, like bonding, etc. which are discussed in reviews and the VB monograph.
I think it is time to bring back VB theory into the classroom and into the research desk of chemists! My visit to many, many meetings shows that this culture is coming back, BIG, even if in different forms.
Allow me to move on to nonidentity reactions, and try to address a recent issue:
Many in the community are of the opinion that H-abstraction requires a radical abstractor and is facilitated by it. Recently Schwarz and his collaborators demonstrated clearly the reactivity impact of spin density on the abstractor site.
that closed shell reagents like Cl2CrO2 and R4N+MnO4
- can abstract hydrogen atoms from alkanes. Recently, with similar findings primarily of Mayer, but also of Ruchardt, Schreiner, Limberg, Fukuzumi, and others, the above view was questioned: Do We Need at All a Radical to Abstract a Hydrogen Atom?
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I would like to bridge these seemingly opposing views by means of the VB modeling.
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Closedshell
Openshell
To apply the model, we examined nonidentity reactions of radical and closed-shell abstractors. And here are some of the cases:
It is seen that the closed-shell abstractor has a higher promotion energy due to the need to prepare a radical at the Cr=O bond by triplet de-coupling of the corresponding ππ-bond electron pair. This is the root cause of the higher barrier for Cl2CrO2 compared with the oxyl radical having the same reaction driving force.
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Closed-shell oxyl radical
In a glimpse, here are the VBSCDs for an oxyl radical abstractor compared with a closed-shell oxo abstractor, having the same ΔΔErp
Back to the question: Must we have a radical to abstract a hydrogen atom?
The answer of the VB modeling is: NO we don’t, at least not initially. But,… because the radical buildup on the abstractor site is required by electronic structure principles, we’ll have to pay the cost of creating this radical along the reaction coordinate. Thus, both views are complementary. They are not in contradiction. Radicals are efficient H-abstractors, but closed-shell molecules can also do the job, albeit generally at a higher price.
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Having understood the mechanistic scenario, let us focus now on reactivity patterns in the H-abstraction step, which is rate determining. Here are the reactions we looked at:
NFe
N
NN
L
O
+ R-HN
FeN
NN
L
OH/R
L = SH, OAc, Cl, CF3SO3
15 16 17 18
R-H = cyclohexane
Different alkanes
Different Cpd I’s
So, now we have a large enough data base to apply the VB model semi-quantitatively and see whether we can understand the trends
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If indeed so, we can proceed to estimate barriers from raw data! This is the beauty of VB theory
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Here is the VB model for the rate-determining H-abstraction step:
Let’s focus on the simple expression for the barrier: ΔΔE‡= ƒGr - B. The expression is useful if we have a reaction family wherein ƒ and B are constants. In such a case, the variation in the barriers will depend only on Gr.
Using semi-empirical VB theory, it is possible to derive the following expressions for our limited series: Gr = ΔΔEST(H-Y) ~ 2DH-Y ƒ=0.3 & B ≅≅ 0.5BDEweak~ 0.5BDEOH
As such, ƒ and B are in principle constants and the simple equation is usable.
The correlation of the so-estimated VB barriers (ΔΔE‡≈ 0.3[2DCH]- ½ BDEOH) with the DFT computed ones is shown here:
Shaik, Lai, Chen, Wang, ACR, 2010, 43, 1154
Considering the large variation of the alkanes and the different Cpd I species, I showed you before, the correlation is not too bad...
This means that the VB model is capable of predicting the trends in the barriers of a key reaction of cytochrome P450 and for a variety of substrates and Cpd I species & all this from raw data.
