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The distortive tendencies of π electrons in π-delocalized systems
P.C. Hiberty, LCP, Groupe de Chimie Théorique, 91405 Orsay Cedex, France S. Shaik, Department of Organic Chemistry, Hebrew University of Jerusalem, 91904 Jerusalem, Israel
1
What is the driving force for the regular geometry of benzene, allyl, etc… π bonds or (and?) σ bonds?
ÆE < 0
ÆE < 0
, ¥, +
, ¥, +
Are π bonds stabilized by delocalization?
2
The traditional view (Hückel): pure π effect ÆE < 0
ÆE < 0
E = 6ß
, ¥, +
E = 8ß
E = 2ß
, ¥, +
E= 2.8ß
• paradoxes ¹bonding energy
• unexplained experimental facts
« π bonds are stabilized by delocalization »
3
First paradox:results of Hückel with variable β β
β ¥
ÆE < 0
β−δ
β+δ ¥
β
β β+δ
β−δ
ÆE < 0
4
Some (many) paradoxes: ÆE < 0
H
H H
ÆE < 0 , ¥, +
H
ÆE < 0
H
H
H
H
H H
H3•, H3– distort to H2 + H•, H2 + H–
, ¥, +
3orbital, 3electron
3orbital, 3electron
≡ H- transfert transition state 3orbital, 4electron
C
H
C
3orbital, 4electron
≡ SN2 transition state
H
H
X
Y
M.J.S. Dewar, Organometallics 1, 1705 (1982) 5
The valence bond model of electronic delocalization: Any delocalized system can be considered as a transition state in an exchange reaction: H
H +
H H
¥ H
H H
H
¥ H +
H H
H
H
H
H
H H
H
H
H
H
H H
H
H
H H
Etc… 6
Example: the exchange reaction X• + X-X → [X--X--X]• → X–X + X•
X1–X2 X3•
X1• X2–X3
X1 –X2 X3• X1 X2 .............X3
X1 • X2–X3 X1 .......X2 ......X3
X1.............X2 X3
7
Example: the exchange reaction X• + X-X → [X--X--X]• → X–X + X• X1 ––––––X2 X3 •
X1 –X2 X3• X1 X2 .............X3
X1 • X2–X3 X1 .......X2 ......X3
X1.............X2 X3
8
Example: the exchange reaction X• + X-X → [X--X--X]• → X–X + X• X1 • X2––––––X3
X1 ––––––X2 X3 •
X1 –X2 X3• X1 X2 .............X3
X1 • X2–X3 X1 .......X2 ......X3
X1.............X2 X3
9
Example: the exchange reaction X• + X-X → [X--X--X]• → X–X + X• X1 • X2––––––X3
X1 ––––––X2 X3 •
G∝De(X–X)
X1 –X2 X3• X1 X2 .............X3
X1 • X2–X3 X1 .......X2 ......X3
X1.............X2 X3
10
Stability or unstability of X3• clusters: X• + X-X → [X--X--X]• → X–X + X• G = ∝ De(X-X)
G
G
G
Strong bonds (H3): Large barrier
Weaker bonds (Cl3): Smaller barrier
Weak bonds (Li3): Stable cluster
De(H2) = 110 kcal/mol H 3 and H6 very unstable
De(Cl2) = 58 kcal/mol Cl3 and Cl6 unstable
De(Li2) = 21 kcal/mol Li3 and Li6 stable11
Stability or unstability of X3• clusters: X• + X-X → [X--X--X]• → X–X + X• G = ∝ De(X-X)
G
G
Strong bonds (H3): Large barrier
G
Weaker bonds (Cl3): Smaller barrier
π bonds: De (πC-C) = 60 kcal/mol. Unstable delocalized systems ?
Weak bonds (Li3): Stable cluster
12
Benzene’s resistance to a Kekulé distortion
Total energy
∆E(tot) = ∆E(σ) + ∆E(π) >0 >0 ? How to probe ∆E(σ) alone? How to « turn off » π-bonding?
13
First try: distort the bare σ frame
+
+ +
+ +
+
+
+ + 1.4627
1.40
1.34
D6h
D3h
∆E(tot) = 7.2 kcal/mol
+
+ +
∆E(σ) + ∆E(π)
14
First try: distort the bare σ frame
+
+ +
+ +
+
+
+ + 1.4627
1.40
1.34
D6h
D3h
∆E(tot) = 7.2 kcal/mol
+
+ +
∆E(σ) + ∆E(π) 14.1 -6.9
15
Second try: distort the high spin state
↑
↑ ↑
↑ ↑ ↑
↑ ↑ ↑
D6h
∆E(tot) = 7.2 kcal/mol
↑ ↑
↑
D3h
∆E(σ) + ∆E(π) 14.5 -7.3
16
Third try: distort the « quasi-classical » state ↑
↓
↑
↓
↑
↓
↓
D6h
↑
↑ ↓
↑
↓
D3h
17
E
Dissociation curve of H2
(kcal/mole)
Quasiclassical state (nonbonding)
RHH 20 40
+
60
Covalent bond
Physical origin of the bond: spin exchange between AOs
80 100
Ψexact
18
Third try: distort the « quasi-classical » state ↑
↓
↑
↓
↑
↓
↓
D6h
∆E(tot) = 7.2 kcal/mol
↑
↑ ↓
↑
↓
D3h
∆E(σ) + ∆E(π) 12.5 -5.3
19
Schaefer et al.: orbital energy derivative study
Nuclear repulsion
Electron-nuclei attraction
Orbital energies
Q= Kekulean distortion
20
Schaefer et al.: orbital energy derivative study
Nuclear repulsion
Electron-nuclei attraction
Orbital energies
Q= Kekulean distortion
21
Schaefer et al.: orbital energy derivative study
Nuclear repulsion
Electron-nuclei attraction
Orbital energies
Q= Kekulean distortion
22
Results (hartree/Å2)
Allyl cation
1.442
-0.576
Allyl anion
0.501
-0.995
Benzene
1.727
-1.649 επ
εσ
- DQ
+∆Q
- DQ
+∆Q
23
Experimental consequence: shape of the excited potential surface π energies
π energies
total energies K2*
K1* 1B
K2*
K1*
2u(¹) 1B
K1
1A (¹) 1g
K2
2u
K1
RC
K2 1A 1g
RC
Traditional view
Challenging view
24
Frequency of the Kekulean (b2u) mode in the 1B2u state of benzene π energies
π energies
total energies K2*
K1* 1B
K2*
K1*
2u(¹) 1B
K1
1A (¹) 1g
RC
K2
2u
K1
K2 1A 1g
RC
Symmetrizing π system 1A1g 1B2u Reduced b2u frequency
Distortive π system 1A1g 1B2u
Exalted b2u frequency
25
Experimental results: benzene (1A1g –> 1B2u) the Kekulé (b2u) mode: 1B2u
All vibrational frequencies are decreased, but one ...
ω(b2u) = 1310 cm-1
1A1g Symmetrizing π system 1A1g 1B2u Reduced b2u frequency
ω(b2u) = 1571 cm-1
Distortive π system 1A1g 1B2u
Exalted b2u frequency
26
Experimental results: benzene (1A1g –> 1B2u)
1B2u
All vibrational frequencies are decreased, but the Kekulé mode
1A1g
Naphthalene (1A1g –> 1B2u) ∆ω(b2u): + 189 cm-1
Weakening the π bonds increases benzene’s resistance to distortion
Anthracene, etc…
27
Naphthalene (1A1g –> 1B2u)
K1
K2
Kc
Ψ∗ K1 K2 (B2u)
K1 + K2 (Ag)
Ψ0
28
Naphthalene (1A1g –> 1B2u)
K1
∗
K2
Kc Ψ∗
Ψ
K1 K2 (B2u)
K1 K2 (B2u)
K1 + K2 (Ag)
Ψ0
K1 + K2 (Ag)
Kekulean distortion Ψ0
29
Naphthalene (1A1g –> 1B2u) ∆ω(b2u): + 189 cm-1 : frequency exaltation
∗
Ψ∗
Ψ
K1 K2 (B2u)
K1 K2 (B2u)
K1 + K2 (Ag)
Ψ0
K1 + K2 (Ag)
Kekulean distortion Ψ0
30
Naphthalene (1A1g –> 1B2u)
Anthracene, etc….
∆ω(b2u): + 189 cm-1 : frequency exaltation
∗
Ψ∗
Ψ
K1 K2 (B2u)
K1 K2 (B2u)
K1 + K2 (Ag)
Ψ0
K1 + K2 (Ag)
Kekulean distortion Ψ0
31
Mills-Nixon effect
∆
∆
( )
1 ( B2u )
32
Mills-Nixon effect
∆
∆
( )
1 ( B2u )
33
Mills-Nixon effect
∆
∆
( )
1 ( B2u )
Alterned geometry in the ground state, Restored symmetry in the π → π* excited state
34
An apparent contradiction: π distortivity vs allyl ’s barrier to rotation
1)
π bonds are forced by the σ frame to delocalize
2)
or
35
An apparent contradiction: π distortivity vs allyl ’s barrier to rotation K2*
K1*
× K1
π
×
ground state
= K1 ↔ K2
K2
36
An apparent contradiction: π distortivity vs allyl ’s barrier to rotation K2*
K1*
• K1
π
×
×
ground state
•
symmetrical rotated
= K1 ↔ K2
K2
37
An apparent contradiction: π distortivity vs allyl ’s barrier to rotation K2*
K1*
• K1
π
×
×
ground state
•
symmetrical rotated
= K1 ↔ K2
K2
relaxed rotated
38
An apparent contradiction: π distortivity vs allyl ’s barrier to rotation K1*
K2*
K1*
• K1
π
×
K1
K2
•
K2
× σ+π
σ
×
•
K2*
ground state symmetrical rotated relaxed rotated
39
What is the role of resonance energy? K1 *
K2 *
¹
K1
σ+π
K2 σ
Weak resonance energy (CBD, linear polyenes): alternated geometry
40
What is the role of resonance energy? K1 *
K2 *
¹
K1
¹
σ+π
K2 σ
Weak resonance energy (CBD, linear polyenes): alternated geometry
K2 *
K1 *
K1
σ+π
K2
σ
Large resonance energy (benzene, aromatics): regular geometry
RE diminishes π distortivity but does not change its sign
41
Summary and Conclusion ,
, aromatic systems...
, ¥, +
Duality of the π component Distortive towards a localizing distortion
Stabilized by resonance
Experimental consequences: Thermodynamic stability, aromaticity
S0 → S1 increases resistance to distortion, or restores symmetry 42
A unique law for π and σ delocalized systems: • Strong or medium binders are distortive (Hn, π bonds, organic TSs…) • Weak binders are stable aggregates (Lin, Nan…) H
π
H
H
H H
H
3orbital, 3electron
3orbital, 3electron
H
H
H
C
H
C
H-transfer transition state 3orbital, 4electron
3orbital, 4electron
H
H
H
X
Y
SN2 transition state
43
Sason Shaik Hebrew University, Jerusalem
David Danovitch Hebrew University, Jerusalem Avital Shurki Hebrew University, Jerusalem
44
45
Israël
Hebrew University, Jerusalem • Sason Shaik • David Danovitch • Avital Shurki Beer Sheva University • Rony Bar
France
Université de Paris-Sud • Jean-Michel Lefour • Philippe Maître • Avital Shurki
46
Strong or medium bonds:unstable delocalized systems - De(H2) = 110 kcal/mol H3 and H6 very unstable - De(Cl2) = 58 kcal/mol Cl3 and Cl6 unstable
Weak bonds: stable delocalized systems - De(Li2) = 21 kcal/mol Li3 and Li6 stable
π bonds: De (πC-C) = 60 kcal/mol. Unstable delocalized systems ?
47
P.C. Hiberty, LCP, Groupe de Chimie Théorique, 91405 Orsay Cedex, France S. Shaik, Department of Organic Chemistry, Hebrew University of Jerusalem, 91904 Jerusalem, Israel
1
What is the driving force for the regular geometry of benzene, allyl, etc… π bonds or (and?) σ bonds?
ÆE < 0
ÆE < 0
, ¥, +
, ¥, +
Are π bonds stabilized by delocalization?
2
The traditional view (Hückel): pure π effect ÆE < 0
ÆE < 0
E = 6ß
, ¥, +
E = 8ß
E = 2ß
, ¥, +
E= 2.8ß
• paradoxes ¹bonding energy
• unexplained experimental facts
« π bonds are stabilized by delocalization »
3
First paradox:results of Hückel with variable β β
β ¥
ÆE < 0
β−δ
β+δ ¥
β
β β+δ
β−δ
ÆE < 0
4
Some (many) paradoxes: ÆE < 0
H
H H
ÆE < 0 , ¥, +
H
ÆE < 0
H
H
H
H
H H
H3•, H3– distort to H2 + H•, H2 + H–
, ¥, +
3orbital, 3electron
3orbital, 3electron
≡ H- transfert transition state 3orbital, 4electron
C
H
C
3orbital, 4electron
≡ SN2 transition state
H
H
X
Y
M.J.S. Dewar, Organometallics 1, 1705 (1982) 5
The valence bond model of electronic delocalization: Any delocalized system can be considered as a transition state in an exchange reaction: H
H +
H H
¥ H
H H
H
¥ H +
H H
H
H
H
H
H H
H
H
H
H
H H
H
H
H H
Etc… 6
Example: the exchange reaction X• + X-X → [X--X--X]• → X–X + X•
X1–X2 X3•
X1• X2–X3
X1 –X2 X3• X1 X2 .............X3
X1 • X2–X3 X1 .......X2 ......X3
X1.............X2 X3
7
Example: the exchange reaction X• + X-X → [X--X--X]• → X–X + X• X1 ––––––X2 X3 •
X1 –X2 X3• X1 X2 .............X3
X1 • X2–X3 X1 .......X2 ......X3
X1.............X2 X3
8
Example: the exchange reaction X• + X-X → [X--X--X]• → X–X + X• X1 • X2––––––X3
X1 ––––––X2 X3 •
X1 –X2 X3• X1 X2 .............X3
X1 • X2–X3 X1 .......X2 ......X3
X1.............X2 X3
9
Example: the exchange reaction X• + X-X → [X--X--X]• → X–X + X• X1 • X2––––––X3
X1 ––––––X2 X3 •
G∝De(X–X)
X1 –X2 X3• X1 X2 .............X3
X1 • X2–X3 X1 .......X2 ......X3
X1.............X2 X3
10
Stability or unstability of X3• clusters: X• + X-X → [X--X--X]• → X–X + X• G = ∝ De(X-X)
G
G
G
Strong bonds (H3): Large barrier
Weaker bonds (Cl3): Smaller barrier
Weak bonds (Li3): Stable cluster
De(H2) = 110 kcal/mol H 3 and H6 very unstable
De(Cl2) = 58 kcal/mol Cl3 and Cl6 unstable
De(Li2) = 21 kcal/mol Li3 and Li6 stable11
Stability or unstability of X3• clusters: X• + X-X → [X--X--X]• → X–X + X• G = ∝ De(X-X)
G
G
Strong bonds (H3): Large barrier
G
Weaker bonds (Cl3): Smaller barrier
π bonds: De (πC-C) = 60 kcal/mol. Unstable delocalized systems ?
Weak bonds (Li3): Stable cluster
12
Benzene’s resistance to a Kekulé distortion
Total energy
∆E(tot) = ∆E(σ) + ∆E(π) >0 >0 ? How to probe ∆E(σ) alone? How to « turn off » π-bonding?
13
First try: distort the bare σ frame
+
+ +
+ +
+
+
+ + 1.4627
1.40
1.34
D6h
D3h
∆E(tot) = 7.2 kcal/mol
+
+ +
∆E(σ) + ∆E(π)
14
First try: distort the bare σ frame
+
+ +
+ +
+
+
+ + 1.4627
1.40
1.34
D6h
D3h
∆E(tot) = 7.2 kcal/mol
+
+ +
∆E(σ) + ∆E(π) 14.1 -6.9
15
Second try: distort the high spin state
↑
↑ ↑
↑ ↑ ↑
↑ ↑ ↑
D6h
∆E(tot) = 7.2 kcal/mol
↑ ↑
↑
D3h
∆E(σ) + ∆E(π) 14.5 -7.3
16
Third try: distort the « quasi-classical » state ↑
↓
↑
↓
↑
↓
↓
D6h
↑
↑ ↓
↑
↓
D3h
17
E
Dissociation curve of H2
(kcal/mole)
Quasiclassical state (nonbonding)
RHH 20 40
+
60
Covalent bond
Physical origin of the bond: spin exchange between AOs
80 100
Ψexact
18
Third try: distort the « quasi-classical » state ↑
↓
↑
↓
↑
↓
↓
D6h
∆E(tot) = 7.2 kcal/mol
↑
↑ ↓
↑
↓
D3h
∆E(σ) + ∆E(π) 12.5 -5.3
19
Schaefer et al.: orbital energy derivative study
Nuclear repulsion
Electron-nuclei attraction
Orbital energies
Q= Kekulean distortion
20
Schaefer et al.: orbital energy derivative study
Nuclear repulsion
Electron-nuclei attraction
Orbital energies
Q= Kekulean distortion
21
Schaefer et al.: orbital energy derivative study
Nuclear repulsion
Electron-nuclei attraction
Orbital energies
Q= Kekulean distortion
22
Results (hartree/Å2)
Allyl cation
1.442
-0.576
Allyl anion
0.501
-0.995
Benzene
1.727
-1.649 επ
εσ
- DQ
+∆Q
- DQ
+∆Q
23
Experimental consequence: shape of the excited potential surface π energies
π energies
total energies K2*
K1* 1B
K2*
K1*
2u(¹) 1B
K1
1A (¹) 1g
K2
2u
K1
RC
K2 1A 1g
RC
Traditional view
Challenging view
24
Frequency of the Kekulean (b2u) mode in the 1B2u state of benzene π energies
π energies
total energies K2*
K1* 1B
K2*
K1*
2u(¹) 1B
K1
1A (¹) 1g
RC
K2
2u
K1
K2 1A 1g
RC
Symmetrizing π system 1A1g 1B2u Reduced b2u frequency
Distortive π system 1A1g 1B2u
Exalted b2u frequency
25
Experimental results: benzene (1A1g –> 1B2u) the Kekulé (b2u) mode: 1B2u
All vibrational frequencies are decreased, but one ...
ω(b2u) = 1310 cm-1
1A1g Symmetrizing π system 1A1g 1B2u Reduced b2u frequency
ω(b2u) = 1571 cm-1
Distortive π system 1A1g 1B2u
Exalted b2u frequency
26
Experimental results: benzene (1A1g –> 1B2u)
1B2u
All vibrational frequencies are decreased, but the Kekulé mode
1A1g
Naphthalene (1A1g –> 1B2u) ∆ω(b2u): + 189 cm-1
Weakening the π bonds increases benzene’s resistance to distortion
Anthracene, etc…
27
Naphthalene (1A1g –> 1B2u)
K1
K2
Kc
Ψ∗ K1 K2 (B2u)
K1 + K2 (Ag)
Ψ0
28
Naphthalene (1A1g –> 1B2u)
K1
∗
K2
Kc Ψ∗
Ψ
K1 K2 (B2u)
K1 K2 (B2u)
K1 + K2 (Ag)
Ψ0
K1 + K2 (Ag)
Kekulean distortion Ψ0
29
Naphthalene (1A1g –> 1B2u) ∆ω(b2u): + 189 cm-1 : frequency exaltation
∗
Ψ∗
Ψ
K1 K2 (B2u)
K1 K2 (B2u)
K1 + K2 (Ag)
Ψ0
K1 + K2 (Ag)
Kekulean distortion Ψ0
30
Naphthalene (1A1g –> 1B2u)
Anthracene, etc….
∆ω(b2u): + 189 cm-1 : frequency exaltation
∗
Ψ∗
Ψ
K1 K2 (B2u)
K1 K2 (B2u)
K1 + K2 (Ag)
Ψ0
K1 + K2 (Ag)
Kekulean distortion Ψ0
31
Mills-Nixon effect
∆
∆
( )
1 ( B2u )
32
Mills-Nixon effect
∆
∆
( )
1 ( B2u )
33
Mills-Nixon effect
∆
∆
( )
1 ( B2u )
Alterned geometry in the ground state, Restored symmetry in the π → π* excited state
34
An apparent contradiction: π distortivity vs allyl ’s barrier to rotation
1)
π bonds are forced by the σ frame to delocalize
2)
or
35
An apparent contradiction: π distortivity vs allyl ’s barrier to rotation K2*
K1*
× K1
π
×
ground state
= K1 ↔ K2
K2
36
An apparent contradiction: π distortivity vs allyl ’s barrier to rotation K2*
K1*
• K1
π
×
×
ground state
•
symmetrical rotated
= K1 ↔ K2
K2
37
An apparent contradiction: π distortivity vs allyl ’s barrier to rotation K2*
K1*
• K1
π
×
×
ground state
•
symmetrical rotated
= K1 ↔ K2
K2
relaxed rotated
38
An apparent contradiction: π distortivity vs allyl ’s barrier to rotation K1*
K2*
K1*
• K1
π
×
K1
K2
•
K2
× σ+π
σ
×
•
K2*
ground state symmetrical rotated relaxed rotated
39
What is the role of resonance energy? K1 *
K2 *
¹
K1
σ+π
K2 σ
Weak resonance energy (CBD, linear polyenes): alternated geometry
40
What is the role of resonance energy? K1 *
K2 *
¹
K1
¹
σ+π
K2 σ
Weak resonance energy (CBD, linear polyenes): alternated geometry
K2 *
K1 *
K1
σ+π
K2
σ
Large resonance energy (benzene, aromatics): regular geometry
RE diminishes π distortivity but does not change its sign
41
Summary and Conclusion ,
, aromatic systems...
, ¥, +
Duality of the π component Distortive towards a localizing distortion
Stabilized by resonance
Experimental consequences: Thermodynamic stability, aromaticity
S0 → S1 increases resistance to distortion, or restores symmetry 42
A unique law for π and σ delocalized systems: • Strong or medium binders are distortive (Hn, π bonds, organic TSs…) • Weak binders are stable aggregates (Lin, Nan…) H
π
H
H
H H
H
3orbital, 3electron
3orbital, 3electron
H
H
H
C
H
C
H-transfer transition state 3orbital, 4electron
3orbital, 4electron
H
H
H
X
Y
SN2 transition state
43
Sason Shaik Hebrew University, Jerusalem
David Danovitch Hebrew University, Jerusalem Avital Shurki Hebrew University, Jerusalem
44
45
Israël
Hebrew University, Jerusalem • Sason Shaik • David Danovitch • Avital Shurki Beer Sheva University • Rony Bar
France
Université de Paris-Sud • Jean-Michel Lefour • Philippe Maître • Avital Shurki
46
Strong or medium bonds:unstable delocalized systems - De(H2) = 110 kcal/mol H3 and H6 very unstable - De(Cl2) = 58 kcal/mol Cl3 and Cl6 unstable
Weak bonds: stable delocalized systems - De(Li2) = 21 kcal/mol Li3 and Li6 stable
π bonds: De (πC-C) = 60 kcal/mol. Unstable delocalized systems ?
47
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