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Aucun titre de diapositive

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one bond = an interaction between two singly occupied atomic orbitals ... Molecules displaying electron conjugation. The VB wave function Y(1 2) for the ground state ... – PowerPoint PPT presentation

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Title: Aucun titre de diapositive


1
Valence Bond Theory
Why doing VB? Basic principles Ab initio
methods Qualitative VB theory
2
The Valence Bond model
electron pairs are in local bonds
one bond an interaction between two singly
occupied atomic orbitals
Each bond is mainly covalent, but has some minor
ionic character
The Valence bond wave function is the Quantum
Mechanical translation of theLewis structure
3
Systems that cannot be described by a single
Lewis structure
  • Molecules displaying electron conjugation

The VB wave function Y(1?2) for the ground
state is a combination of two VB structures Y1
and Y2
Y(1?2) C1(Y1) C2(Y2)
Estimation of C1, C2, resonance energy
4
Why Doing Valence Bond and not only MO?
  • Some vital concepts
  • - hybridization
  • - resonance
  • - VSEPR
  • - Lewis structures
  • - Arrow-pushing language
  • - IR frequencies of C-H bonds
  • sp3-H, sp2-H, sp-H
  • Application to reactivity (the VBSCD model)
  • Standard teaching
  • VB has failed
  • The only correct theory is MO

5
Exemple the covalent H2 bond
Writing VB functions
Working hypothesis the electrons remain in
atomic orbitals
At equilibrium distance, 2 possible
déterminants
?ja jb ?
?jb ja ?
?ja jb ?
?jb ja ?
Correct wave function (for the covalent bond)

YHL
6
Writing VB functions beyond the two-electron/two
center case
Exemple the p-system of butadiene
Ycov
Ycov
7
Dissociation curve of H2
?ja jb ?
-20
-40
-60
-80
-100
8
Dissociation curve of H2
?ja jb ?
?jb ja ?

YHL ?
-20
YHL
-40
-60
-80
-100
9
Dissociation curve of H2
?ja jb ?
?jb ja ?

YHL ?
-20
Physical origin of the bond spin exchange
between AOs
YHL
-40
-60
-80
-100
10
Comparaison with MO description (Hartree-Fock)
YHF ??g ?g ?
??a ?b ??? ??b ?a ??????? ??????a ?a ??? ??b
?b ??
HH
HH HH
  • Simple MO description

??g ?g ?? 50 covalent 50 ionic
YHL 100 covalent
  • Simple VB description

11
Comparaison with MO description (Hartree-Fock)
YHF ??g ?g ?
??a ?b ??? ??b ?a ??????? ??????a ?a ??? ??b
?b ??
HH
HH HH
  • Simple MO description

??g ?g ?? 50 covalent 50 ionic
YHL 100 covalent
  • Simple VB description

72-79 covalent 21-28 ionic
  • Exact description

12
Exact description
  • In the VB framework

Yexact ????a ?b ??? ??b ?a ???? ?????a ?a ???
??b ?b ???
HH
HH HH
l, ? and the orbitals are optimized
simultaneously VBSCF method (Balint-Kurti, van
Lenthe)
13
Exact description
  • In the VB framework

Yexact ????a ?b ??? ??b ?a ???? ?????a ?a ???
??b ?b ???
HH
HH HH
  • In the MO framework

??g ?g ?? ??a ?b ??? ??b ?a ??????? ??????a ?a
??? ??b ?b ??
??u ?u ?? ??a ?b ??? ??b ?a ??????- ??????a ?a
??? ??b ?b ??
C1 ??g ?g ???? C2 ??u ?u ?? Yexact
14
The Generalized Valence Bond Method (GVB)
   


15
The Generalized Valence Bond Method (GVB)
   


YGVB ?????????a ?b ??? ??b ?a ???? ??????a ?a
??? ??b ?b ???
HH
HH HH
YGVB is formally covalent, but physically
covalent-ionic optimized
16
The Generalized Valence Bond Method (GVB)
 GVB pair  Overlapping distorted AOs


17
The Generalized Valence Bond Method (GVB)
 GVB pair  Overlapping distorted AOs


Generalization

 Four GVB pairs 
18
Hartree-Fock, GVB, CASSCF and correlation energy
SCF
Non-dynamical correlation energy
80
GVB
CASSCF (1764 conf)
19
Ab initio methods
Test case the bonding energy of FF
Nature of the wave function for F2
  • Hartree-Fock too much ionic
  • VBSCF

FF FF
FF
Optimized covalent vs ionic coefficients
  • GVB equivalent to VBSCF

20
Accuracy of the various methods
?E
Test case the dissociation of F2
FF F F

Calculation of ?E for F-F1.43Ã…, 6-31G(d) basis
  • Hartree-Fock - 37 kcal/mol (repulsive!)
  • Reason too much ionic
  • Full configuration interaction (6-31G(d) basis)
    30-33 kcal/mol
  • GVB, VBSCF

Only 15.7 kcal/mol
Reason we miss dynamic correlation.
What does this physically mean?
21
What is wrong with GVB and VBSCF?
GVB/VBSCF a closer examination
FF FF
FF
  • The coefficients and orbitals are optimized, but
  • The same set of AOs is used for all VB
    structures
  • optimized for a mean neutral situation

22
What is wrong with GVB and VBSCF?
GVB/VBSCF a closer examination
FF FF
FF
  • The coefficients and orbitals are optimized, but
  • The same set of AOs is used for all VB
    structures
  • optimized for a mean neutral situation

A better wave function
23
The  Breathing-Orbital  VB method (BOVB)
  • Provides optimized covalent-ionic coefficients
    (like GVB)

FF
FF FF
  • Different orbitals for different VB structures
  • Orbitals for FF will be the same as VBSCF
  • Orbitals for ionic structures will be much
    improved
  • One expects
  • A better description of ionic structures
  • A better bonding energy

24
Test case the dissociation of F2
?E
FF F F

Calculation of ?E for F-F1.43Ã…, 6-31G(d) basis
Iteration De(kcal) FF FF ?
FF Classical VB -4.6 0.813 0.187 GVB,VBSCF 15.
7 0.768 0.232 BOVB 1 24.6 0.731 0.269 2 27.9
0.712 0.288 3 28.4 0.709 0.291 4 28.5 0.710
0.290 5 28.6 0.707 0.293 Full CI 30-33

25
Improvements of the BOVB method
  • Improvement of the ionic VB structures
  • - basic level

- improved level ( split-level  or S)
The  active  orbital is split. This brings
radial electron correlation
26
  • Improvement of the interactions between
    spectator orbitals
  • Spectator orbitals can be

- local atomic orbitals
- bonding and antibonding combinations
Slightly better ( Delocalized  level or D)
27
The three levels of the BOVB method
  • Basic L-BOVB

All orbitals are localized, ionics are
closed-shell
  • SL-BOVB

All orbitals are localized, but active orbitals
in ionics are split
  • SD-BOVB
  • Active orbitals are split in ionics
  • Spectator orbitals are delocalized in all
    structures

28
Performances of the various BOVB levels
?E
Test case the dissociation of F2
FF F F

Method Req (Ã…) De(kcal/mol) 6-31G
basis set GVB 1.506 14.0
CASSCF 1.495 16.4 L-BOVB 1.485 27.9
SL-BOVB 1.473 31.4 SD-BOVB 1.449 33.9 Dunni
ng-Huzinaga DZP basis set SD-BOVB 1.443 31.6 E
stimated full CI 1.440.005
28-31 Experimental 1.412 38.3
29
Electron correlation in BOVB
  • Non-dynamic correlation (GVB, CASSCF)
  • Non dynamic correlation gives the correct
    ionic/covalent ratio

30
Electron correlation in BOVB
  • Non-dynamic correlation (GVB, CASSCF)
  • Non dynamic correlation gives the correct
    ionic/covalent ratio
  • Dynamic correlation
  • All the rest. This is what is missing in GVB.
  • BOVB brings that part of dynamic correlation
    that varies in the reaction

31
What is an accurate description of two-electron
bonding?
  • Spin exchange between two atomic orbitals
  • Electrons are on different atoms and they
    exchange their positions

32
What is an accurate description of two-electron
bonding?
  • Spin exchange between two atomic orbitals
  • Electrons are on different atoms and they
    exchange their positions
  • Charge fluctuation
  • Sometimes both electrons are on the same atom.
  • There is some charge fluctuation. All orbitals
    instantaneously rearrange in size and shape to
    follow the charge fluctuation (orbitals
     breathe ).
  • This is differential dynamic correlation

33
A Qualitative valence bond theory
Effective hamiltonian Heff (h(1) h(2) h(3)
.)
Parameters b, S, e
Similar model in the MO framework
34
A Qualitative valence bond theory
Overlap between determinants
Generate permutations - between identical
spins - only one side
35
A Qualitative valence bond theory
Hamiltonian matrix elements
Choice of an origin of energies
36
A Qualitative valence bond theory
The two-electron bond
?a b ?
?b a ?

YVB
a,b pure AO gt purely covalent bond
a,b GVB pair gt fully correlated bond
2ßS
Reminder In MO theory De 2b/(1S)
De(2-e)
E(YVB )
1 S2
37
A Qualitative valence bond theory
The triplet Pauli repulsion
?a b ?
?b a ?

YT
Reminder MO theory
-2ßS
E(YT )
1- S2
The same!
38
Triplet Pauli repulsionwhy YMO ?YVB ?
  • The MO picture
  • The VB picture

? a b ?
YMO ??g ?u ?? ?(ab)(a-b) ? ?aa ?- ?ab ?
?ba ? - ?bb ? ? YVB ?
Whenever the MO and VB wave functions of an
electronic state are equivalent, the VB energy
can be estimated using qualitative MO theory
39
Other cases where YMO ?YVB ?
The three-electron bond
Example the helium cation dimer He2
  • The MO picture
  • The VB picture

??a ?a ?b ?
??a ?b ?b ?
YMO ??g ?g ?u ??? ??a ?a ?b ??? ??a ?b ?b
????YVB
ß(1-3S)
Interaction energy De E(He\He) - E(He) -
E(He)
1- S2
40
Elementary interaction energies in qualitative VB
vs MO theories
VB
MO
ß
ß
One-electron bond (A? B)
1 S
1 S
2ßS
2ß
Two-electron bond (A-B)
1 S2
1 S
ß(1-3S)
ß(1-3S)
Three-electron bond (A\B)
1- S2
1- S2
-4ßS
-4ßS
4-e repulsion (A?? ??????B)
1- S2
1- S2
-2ßS
-2ßS
Triplet repulsion (A? ?B)
1- S2
1- S2
41
Thumb rule VB energy of a single determinant
-2nßS
Energy of a determinant with n (neighboring? ?????
1- S2
-2ßS/(1-S2)
triplet repulsion
(VB and MO)
(VB and MO)
-4ßS/(1-S2)
4-e repulsion
0
(VB only)
spin-alternated determinant
-2ßS/(1-S2)
(VB only)
3-e repulsion
bond single electron
-ßS/(1-S2)
(VB only)
bond bond
-ßS/(1-S2)
(VB only)
42
The  failures  of valence bond theory
1) Dioxygen molecule OO or ?OO? ?
OO, singlet state
?OO? , diradical displaying two 3-e
bonds, triplet state
43
The  failures  of valence bond theory
1) Dioxygen molecule OO or ?OO? ?
E(S)
E(T)
E(S) - E(T)
Qualitative VB predicts O2 to be a triplet
diradical Pauling, 1931 (!)
44
The  failures  of valence bond theory
2) The two ionization potentials of CH4
  • The MO model

Two valence MO energies gt two IPs
  • The VB model

Four equivalent local bonds gt only one IP ?
45
The  failures  of valence bond theory
2) The two ionization potentials of CH4
-E -b -b -b -b -E -b -b -b -b -E -b -b -b -b -E
0
Qualitative VB predicts CH4 to have two IPs
46
Conclusions
  • VB and MO two complementary theories.
  • lower level MO too much ionic, VB not enough
  • elaborate level MO ??VB
  • There are nothing such as VB failures
  • VB specific concepts
  • Lewis structures, arrow pushing language,
  • transferable local bonds, hybridization,
    resonance energy
  • Applications to chemical reactivity
  • Valence bond state crossing diagrams (next
    lecture)

47
Some reading
Valence Bond Theory. Its History, Fundamentals,
and Applications. A Primer. S. Shaik and P.C.
Hiberty, Reviews in Computational Chemistry 20,
1-100 (2004) A
conversation on VB vs MO Theory A Never-Ending
Rivalry? R. Hoffmann, S. Shaik and P.C. Hiberty,
Acc. Chem. Res. 36, 750-756 (2003)
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