Recent Applications of Modern Valence Bond Methods Symposium of the Lise-Meitner-Minerva Center Charge-shift bonds: A Specific Class of two-electron bonds

Recent Applications of Modern Valence Bond Methods

Symposium of the Lise-Meitner-Minerva Center

Charge-shift bonds: A Specific Class of two-electron bonds

P.C. Hiberty, Laboratoire de Chimie Physique,

Université de Paris 11

The classical paradigm of the A—X bond:

A-X = c1(A•–•X) + c2(A+ :X–) + c3(A:– X+)

10

A•–•X A+ :X– A:– X+

covalent ionic ionic

A X A X A X

Quantifying the classical paradigm of the A—X bond:

A-X = c1(A•–•X) + c2(A+ :X–) + c3(A:– X+)

10

A•–•X A+ :X– A:– X+

A X A X A X

Classical VB method : • Orbitals are those of the free atoms• c1-c3 are optimized

Very poor results (in terms of De)


A-X = c1(A•–•X) + c2(A+ :X–) + c3(A:– X+)

10

A•–•X A+ :X– A:– X+

A X A X A X

Modern VB methods :

• VBSCF :c1-c3 and orbitals are optimized simultaneously


A-X = c1(A•–•X) + c2(A+ :X–) + c3(A:– X+)

10

A•–•X A+ :X– A:– X+

A X A X A X

Modern VB methods :

• VBSCF :c1-c3 and orbitals are optimized simultaneously

• BOVB (Breathing Orbital Valence Bond) = VBSCF + “Different orbitals for different VB structures”

VBSCF(8-orbital optimization)

E = 14 kcal/mol

Test case: the dissociation of F2 F–F F• + F• E

6-31+G(d) basis:

E = 34 kcal/mol

Experiment ∆E = 38 kcal/mol

Hartree-Fock: E = -35 kcal/mol (repulsive)

Classical VB: E = -4 kcal/mol (repulsive)

BOVB(22-orbital optimization)

Software: XMVB program

Computer time:

Written by W. WU (Xiamen) and collaborators

Can do:

VBSCF, BOVB, VBCI, GVB, SCVB, etc.

Before 2008: BOVB much slower than VBSCF(more orbitals to optimize)

Software: XMVB program

Computer time:

Written by W. WU (Xiamen) and collaborators

Can do:

VBSCF, BOVB, VBCI, GVB, SCVB, etc.

Before 2008:

Since 2008:

BOVB much slower than VBSCF(more orbitals to optimize)

BOVB as fast as VBSCF

much faster

The classical paradigm of Covalent-Ionic Superposition (L. Pauling)3

•The homopolar or weakly polar bond

A+ :X-

A:- X+

REA• •X

• The covalent form is stabilized bysinglet spin-coupling

•RE is weak. Pauling takes RE= 0for A = X

•The polar bond

A+ :X-

A• •X

A:- X+

A Xδ+ δ−

RE

• The larger the electronegativity difference, the larger the RE

•The ionic bond• Small or no RE (NaCl, LiF…)

The classical paradigm of Covalent-Ionic Superposition (L. Pauling)3

•The homopolar or weakly polar bond

A+ :X-

A:- X+

REA• •X

• The covalent form is stabilized bysinglet spin-coupling

•RE is weak. Pauling takes RE= 0for A = X

H–H, H3C–CH3, H2N–NH2, HO–OH, F–F, Cl–Cl, etc…

Should all be of similar nature

Comparing F-Fvs H-H bonds, by means of ab initio VB:12

A-X = c1(A•--•X) + c2(A+ :X-) + c3(A:- X+) = c1cov + c2ion + c3ion’

F-F = 73% covalent, 27% ionicH-H = 76 % covalent, 24%ionic

•Two homonuclear bonds•Weights of covalent vs ionic components:

About the same

-1.200

-1.150

-1.100

-1.050

-1.000

-0.950

0.5 1.0 1.5 2.0 2.5 3.0

Exact

Covalent

E(au)

R(Å)

H2 → H• + H•

Dissociation energy curves

Covalent-ionic resonance energy (ReC-I )

Covalent VB structuresss covalent+ionic ground state

-1.200

-1.150

-1.100

-1.050

-1.000

-0.950

0.5 1.0 1.5 2.0 2.5 3.0

Exact

Covalent

E(au)

R(Å)-0.780

-0.760

-0.740

-0.720

-0.700

-0.680

-0.660

-0.640

1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6

E(au)

R(Å)Exact

Covalent

F2 → • + •H2 → H• + H•

ReC-I

Covalent-ionic resonance energy (ReC-I )


-1.200

-1.150

-1.100

-1.050

-1.000

-0.950

0.5 1.0 1.5 2.0 2.5 3.0

Exact

Covalent

E(au)

R(Å)-0.780

-0.760

-0.740

-0.720

-0.700

-0.680

-0.660

-0.640

1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6

E(au)

R(Å)Exact

Covalent

F2 → • + •H2 → H• + H•

It follows that the F-F bond owes its existence to the covalent-ionic fluctuation of the electron-pair even though its static charge is zero.

F-F is a “covalent bond” of a special type: a “charge-shift bond”

RECS


-150,84

-150,82

-150,8

-150,78

-150,76

-150,74

-150,72

-150,7

1 1,5 2 2,5 3 3,5

-79,26

-79,24

-79,22

-79,2

-79,18

-79,16

-79,14

-79,12

-79,1

1 1,5 2 2,5 3 3,5

H3C-CH3

-111,2

-111,18

-111,16

-111,14

-111,12

-111,1

-111,08

1 1,5 2 2,5 3 3,5

H2N-NH2

HO-OH

-198,8

-198,75

-198,7

-198,65-198,6

1 1,5 2 2,5 3 3,5

F-F

Moving from left to right of the periodic table

Typical classical covalent bonds: H-H, C-C bonds, …

Typical charge-shift bonds: F-F, Cl-Cl, H-F, R3Si-Cl, …

Digging into the literature…

20

X X

Separate atoms

F–F, Cl–Cl, …Deficit of densityin the bonding region

H–H, H3C–CH3 …Density build-upin the bonding region

• Bonding density: positive for H2, negative for F2

Real phenomenon or VB artefact?Other signs (not VB) that charge-shift bonds are special

DFT/ELFStudies

DFT/ELFStudies

20

€

∇2

H-H

H3C-CH3

Na-Cl

-1.39

-0.62

+0.18

at BCP

€

∇2 at BCP

and at the bond critical point in AIM theory (Bader)

0.27

0.25

0.03

Covalent

Bonds

(large , > 0

(small , < 0)

Ionic bond

€

∇2

€

∇2

20

€

∇2

H-H

H3C-CH3

F-F

Cl-Cl

Na-Cl

-1.39

-0.62

+0.58

+0.01

+0.18

at BCP

€

∇2 at BCP

and at the bond critical point in AIM theory (Bader)

0.27

0.25

0.25

0.14

0.03

Covalent

Bonds

(large , > 0

?

(small , < 0)

Ionic bond

F2 and Cl2 are regarded as unexplained exceptions…

€

∇2

€

∇2

20

H-H

H3C-CH3

H2N-NH2

HO-OH

F-F

Cl-Cl

Na-Cl

-1.39

-0.62

-0.54

-0.02

+0.58

+0.01

+0.18

at BCP

€

∇2 at BCP

0.27

0.25

0.29

0.26

0.25

0.14

0.03

Covalent

bonds

Charge-shift

bonds

Ionic bond

9.2

27.7

43.8

56.9

62.2

48.7

8.1

Covalent-ionicRE (kcal/mol)

€

∇2 and at the bond critical point in AIM theory (Bader)

20

€

∇2

H-H

H3C-CH3

H2N-NH2

HO-OH

F-F

Cl-Cl

Na-Cl

-1.39

-0.62

-0.54

-0.02

+0.58

+0.01

+0.18

at BCP

€

∇2

L. Zhang, F. Ying, W. Wu, P.C. Hiberty and S. Shaik, Chem. Eur. J. 2008, in press.

at BCP

Complementing AIM theory

0.27

0.25

0.29

0.26

0.25

0.14

0.03

Covalent

bonds

Charge-shift

bonds

Ionic bond

9.2

27.7

43.8

56.9

62.2

48.7

8.1


correlates with RE =>

€

∇2 and at the bond critical point in AIM theory (Bader)

20

Real phenomenon or VB artefact?

and in the framework of AIM theory (Bader)

€

∇2

H-H

H3C-CH3

H2N-NH2

HO-OH

F-F

Cl-Cl

9.2

27.7

43.8

56.9

62.2

48.7

-1.39

-0.62

-0.54

-0.02

+0.58

+0.01


at thebond critical point

€

∇2

Two signatures ofcharge-shift bonding

• Depleted electron density at mid-bond• Positive Laplacian of the density at bcp

Free R3Si+ cations areextremely rare

P. Su, L. Song, W. Wu, S. Shaik and P.C. Hiberty, J. Phys. Chem. A 2008, 112, 2988

R3Si+

Free R3C+ cations exist in water…

C

H3C

H3CCH3

C

H3C

H3CCH3

ClCl SN1

Easy heterolysis of (CH3)3C-Cl in water (SN1)…

(CH3)3C+ is a free cationIn solution

Easy because the C-Cl bond is polar…

∆G≠ = 19.5 kcal/mol

Very easy heterolysis of Na-Cl in water…

Na+ is a free cation

The NaCl bond is very polar…

Solvolysis is very fast…

ClClNa Na

(CH3)3Si-Cl does not heterolyse in solution

Whatever R, the free R3Si+ ion does not exist in solution

Bond polarities :

Si

H3C

H3CCH3

Si

H3C

H3CCH3

ClCl

(CH3)3C–Cl < (CH3)3Si–Cl < Na–Cl

1 2 3 4 5 6 7

0

20

40

60

80

100

120

140

160

180

200

E (k

cal/m

ol)

Bond length

1 2 3 4 5 6 7

0

20

40

60

80

100

120

140

160

180

200

Bond length

E (k

cal/m

ol)

R• + X•R•–•X

R+X–

42 kcal/mol62 kcal/mol

Comparaison of (CH3)3C-Cl and (CH3)3Si-ClIn the gas phase

(CH3)3C-Cl (CH3)3Si-Cl

R+ X–

R• + •X

QuickTime™ and aTIFF (non compressé) decompressor

are needed to see this picture.

Gas phase



Gas phase

The covalent-ionic resonance energy of (CH3)3SiCl is larger than that of (CH3)3CCl by 20 kcal/mol

Does the charge-shift character of Si-Cl persist in solution?

1 2 3 4 5 6

0

20

40

60

80

100

120

140

160

180

200

E (k

cal/m

ol)

Bond length1 2 3 4 5 6 7

0

20

40

60

80

100

120

140

160

180

200

E (k

cal/m

ol)

Bond length

Dissociation of (CH3)3Si-Cl

62 k/m 51 k/m

13 k/m

R+ X–

R•–•XR•–•X

R+ X–



Gas phase



Aqueous phase

• The ionic curve becomes flat

• Resonance energy is large at Req (57 kcal/mol)

=> Heterolytic dissociation is difficult

• Free energy of heterolytic dissociation (calculated) = 41 kcal/mol

57

1 2 3 4 5 6

0

20

40

60

80

100

120

140

160

180

200

E (k

cal/m

ol)

Bond length1 2 3 4 5 6 7

0

20

40

60

80

100

120

140

160

180

200

E (k

cal/m

ol)

Bond length

Dissociation of (CH3)3Si-Cl

62 k/m 51 k/m

13 k/m

R+ X–

R•–•XR•–•X

R+ X–



Gas phase



Aqueous phase

• The ionic curve becomes flat

• Resonance energy is large at Req (57 kcal/mol)

=> Heterolytic dissociation is difficult

• Free energy of heterolytic dissociation (calculated) = 41 kcal/mol

57

If the REC-I were20 kcal/mol smaller inthe Si-Cl bond R3Si-Cl would dissociate in water

The problem of “inverted bonds” in propellanes

H2C CH2

H2C

H

H

H2C CH2

H2C

-2 H•

[1.1.1] propellane


H2C CH2

H2C

H

H

H2C CH2

H2C

-2 H•

∆E(S-T) = 109 kcal/mol

=> not a diradical


H2C CH2

H2C

H

H

H2C CH2

H2C

-2 H•

∆E= 143 kcal/molwhereas cutting two C-H bonds

should cost 2 104 kcal/mol

Low heat of formation

Extra stability of 65 kcal/mol


H2C CH2

H2C

H

H

-2 H•

H2C CH2

H2C

∆E= 143 kcal/molwhereas cutting two C-H bonds

should cost 2 104 kcal/mol

Low heat of formation

Extra stability of 65 kcal/mol

Short distance (1.60 Å)What kind of bond

is this ?

What kind of bond is it?Controversies in the literature

H2C CH2

H2C

• There is no bond !- Hybrid AOs (sp1.5) are outward directed


H2C CH2

H2C

• There is no bond !- Hybrid AOs (sp1.5) are outward directed- Very weak electron density between the carbons

H2C CH2

H2C

H

H

(similar to this)


H2C CH2

H2C

€

∇2 = +10.3

€

∇2 = -13.0


- Positive at bond critical point

€

∇2


• There is a bond !- low heat of formation

all of the arguments put forward for the existence of a central bond in [1.1.1] propellane can be matched with a counterargument, except for the heat of formation

E.R. Davidson:

H2C CH2

H2C

€

∇2 = +10.3

€

∇2 = -13.0



€

∇2

What kind of bond is it?

H2C CH2

H2C

€

∇2 = +10.3

€

∇2 = -13.0

€

∇2

- Very weak electron density between the carbons


- extra stability of 65 kcal/mol

The three features characterize charge-shift bonding

577211

1.60Å 1.8Å

E(kcal/mol)

RC-C(Å)ground state

covalent

Valence bond calculations (BOVB)

C

CH2

C

H2C

CH2

C

H2C

C

H2C

CH2

The covalent curve is repulsive

577211

1.60Å 1.8Å

E(kcal/mol)

RC-C(Å)ground state

covalent

Valence bond calculations (BOVB)

C

CH2

C

H2C

CH2

C

H2C

C

H2C

CH2

The covalent curve is repulsiveThe resonance energy is huge

C

C

C

C

C

A typical charge-shiftbond

• A category of its own

- Revealed by VB

- Confirmed by electron densities

• Some experimental manifestations• A wide domain

- bonding in cage molecules (some short, some long…)

- Some M-M bond in organometallics

- many bonds involving silicon

- many hypervalent compounds

Perspectives of charge-shift bonding

Catalytic cycles…

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Pr. S. Shaik

Pr. B. Silvi,Dr. B. Braida,

Dr. D. Lauvergnat

Pr. W. Wu &collaborators

A three-center interaction…

Documents

Recent Applications of Modern Valence Bond Methods Symposium of the Lise-Meitner-Minerva Center Charge-shift bonds: A Specific Class of two-electron bonds