Chemistry 4420
Dr. Y. Zhao
Topic 1 Chemical Bonding & Molecular Orbital
•
•
•
•
•
•
Bonding Generalization (VB vs MO Theories)
Resonance Theory
Hybridization and Electronegativity
Hardness and Softness
Valence Shell Electron Pair Repulsion (VSEPR)
Qualitative MO Theory
When applying VB theory to more complex molecules, the
true molecular state can be described by a linear combination
of a number of hypothetical states or structures; in other
word, the actual molecule is a resonance hybrid of these
structures.
Rules for the selection of hypothetical structures:
(a) having similar energies
(b) having the same relative positions of the nuclei
(c) having the same number of unpaired electrons
1. Bonding Generalization
• Valence Bond (VB) Theory (Heitler and London, 1927)
ΨI = c·a(1)b(2) ΨII = c·a(2)b(1)
Ha
Hb
ΨVB = c·ΨI + c·ΨII
= c·a(1)b(2) + c·a(2)b(1)
• Molecular Orbital (MO) Theory
ΨI = c1·a(1) + c2·b(1)
e.g. CH3NO2
E
O
H3 C N
Ψ 1, Ψ 2
O
H3 C N
O
Structure 1
Ψ1
Eresonance
O
Ψ
structure 2
Ψ2
Benzene
ΨII = c1·a(2) + c2·b(2)
ΨMO = ΨI·ΨII = c12·a(1)a(2) + c22·b(1)b(2)
+ c1·c2[a(1)b(2) + a(2)b(1)]
a(1)a(2) Ha:- Hb+
b(1)b(2) Ha+ Hb:-
ƒ Neither VB nor MO predicts dissociation energy accurately
ƒ Both VB and MO can be modified
ƒ They are both approaches not answers
Kekule
Dewar
Common error alert: Each resonance structure doesn’
doesn’t
really exist. Don’
Don’t mix resonance with tautomerization.
tautomerization.
3. Hybridization and Electronegativity
2. Resonance Theory
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Chemistry 4420
Dr. Y. Zhao
• Molecular structure of methane
MOs of methane based on hybridization theory
C-H 1.091 Å
H-C-H 109.5º
1s
sp3
AOs of carbon
2p
E
H
C
2s
• Are there sp3-hybridized orbitals in methane?
Photonelectron Spectroscopy (PES)
1s
sp3 hybridization
E
The three different binding
energies observed do not agree
with the sp3 hybridization model.
sp3
Rationalization using MO theory
1s
+
3
4
2p
1t2
1s
2s
H
C
2a1
2
Chemistry 4420
Dr. Y. Zhao
Case study: Structures and reactivities of propellanes
• MOs of Methane
The change in hybridization is associated with a change of
electronegativity; the more “s” characteristic, the more
electronegative, and vice versa.
+
1S (H)
2s (C)
2a1
[3,3,3]
ring strain
(kcal/mol)
[3,2,2]
65
34
[3,2,1]
[2,2,2]
[2,2,1]
67
93
104
[1,1,1]
102
stable
stabilities decreas as ring strains increase
[3,2,1] undergoes bromination instaneously at -50 °C, [2,21] can only
be observed at solid argon at 45 K; however, [1,1,1], which has a
comparable ring strain to [2,2,1], is surprisingly stable.
+
1S (H)
2Px (C)
1t2
Rationalization: [1,1,1] has an “inverted” center bond, the rupture of
which does not lead to significant relief of ring strain.
+
sp2
"inverted"
more p character
2Py (C)
1S (H)
1t2
There is a considerable charge density on the external sides of the
bridge atoms of [1,1,1]; therefore, radical and electrophilic addition
reactions may occur.
I
+
I
I2
(PhS)2
1S (H)
2Pz (C)
1t2
sp3
PhS
SPh
NO2
O2N
NO2
Bu3SnH
H
SnBu3
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Chemistry 4420
Dr. Y. Zhao
5. Valence Shell Electron Pair Repulsion (VSEPR)
• Electronegativity and Bond Polarity
Electronegativity is the power of an atom in a molecule to
attract electrons to itself (Pauling)
χp: 9,65(χp,A – χp,B)2 = DAB – (DAA × DBB)1/2
Mulliken: χM ~ (I + EA)/2
• Feynman’s electrostatic theorem: the force on a nucleus
can be calculated from classical electrostatics if the charge
distribution is known.
• Mutually repulsive points are arranged on the sphere as
far away from each other as possible.
Decreasing order of repulsion:
Lp – Lp > Lp – Bp > Bp – Bp
Allred and Rochow: χAR ~ [(3590 Zeff/r2) + 0.744]
Allen: χM ~ (nsεs + npεp)/(ns + np)
H
H
C
N
H
H
H
4. Hardness and Softness
H
O
H
H
Cl
Polarizability is related to the size of atoms or ions and
the ease with which the electron cloud can be distorted.
LUMO
wide bandgap
“Hard” species
H
narrow bandgap
“soft” species
H
C
108º
H
H110º52’
Cl is more electronegative than C
C-H bond gets shorter and closer to C
6. Variable Hybridization and Molecular Geometry
Spn
λ2 = n
HOMO
Fractional “s” character = 1/(1 + λ2) and ∑ 1/(1 + λ2) = 1
Hardness: η = (I – EA)/2
Softness: σ = 1/ η
Fractional “p” character = λ2/(1 + λ2) and ∑ λ2/(1 + λ2) = 3
(Carey, p 20-23)
• soft species is more reactive
• hard acid prefers hard base; vice
versa
• Principle of maximum hardness
Interorbital angle (θab):
1 + λaλbcosθab = 0
Cl
a
b C b
H b H
H
λa2 = 2.86 C-H sp2.86
λb2 = 3.50 C-Cl sp3.50
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Chemistry 4420
Dr. Y. Zhao
• internuclear bond angle vs. interorbital bond angle
Interorbital bond angle is based on
hybridization model:
Interorbital angle (θ
(θab):
1 + λaλbcosθ
cosθab = 0
• Other indirect methods to measure hybridization
J13C-H(cps) = 500/(1 + λa2)
(Muller and Pritchard)
-4
rC-H = 1.1597 – 4.17 × 10 J13C-H
Log krel = 0.129 J13C-H -15.9
(Streitwieser et al)
• Methylene chloride
internuclear bond angles:
Cl
a
H
C
H
b
Cl
Cl-C-Cl = 111º47’ λa2 = 2.69, λb2 = 3.37
H-C-H = 112º0’
λb2 = 2.67
The discrepancy can be better explained by
a “curved bond”
bond” model
H
C
H
H
Coupling constant (Hz)
J (13C-1H)
161
134
• Fluoromethane
F
Species
Internuclear bond angles:
H-C-F = 108.9º (H-C-Cl = 108.0º in CH3Cl)
F is more electronegative than Cl
“Curved bond”
bond” model: θ = 106.7º
106.7º
• Cyclopropane (a bent bond model)
H-C-H = 115.1º (exp.)
C-H bond: sp2.36 C-C bond: sp2.69
Calcd C-C-C bond angle = 111.8º (> 60º)
128
124
123
122
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Chemistry 4420
Dr. Y. Zhao
The bent bond pulls the electron pair of the carbanion
closer to the center of the internuclear axis of the C-C
bond.
• Bent bond model vs. σ,π model
ethene
H
H
H
H
H
2
sp hybridization model
H
H
H
H
H
H
C
H
ElectronElectron-electron repulsion decreases as the
interorbital bond angles increase
H
• Rationalization of acidities of hydrocarbons
Decreasing acidity order:
• Conformation of propene
H
H
H
H
H
H
H
>
C
H
>
C
σ,π model description:
the more “s” character, the more electronegative
Then, how about bent bond model?
H
H
H
all staggered
H
H
H
B
CH2
H
H
H
H
A
C H
C
H
bent bond model: C-C = 1.32 Å
H
C
H
H
H
conformer A is more stable
than B (by ca. 2 kcal/mol),
why?
CH2
H
all eclipsed
• Which model is “correct”?
The answer is neither! Both models are useful and
must be used with case. Usually, both should reach the
same conclusion when great detail is considered.
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Chemistry 4420
• van’
van’t Hoff’
Hoff’s bonding modeling using tetrahedra
Dr. Y. Zhao
• cumulative double bonds
J. H. van’t Hoff proposed this bonding model at the age of 22. He received
harsh criticisms from several contemporary famous chemists immediately
after publishing it. History later on proved that van’t Hoff was right!
• single bonds
• double bonds
This was perhaps the most amazing prediction of stereochemistry,
which was experimentally confirmed 60 years later.
• triple bonds
A set of tetrahedron models made by van’t Hoff himself in 1875.
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Chemistry 4420
Dr. Y. Zhao
Take home message:
Our mistake is not that we take our theories too seriously, but that
we do not take them seriously enough…Even worse, there often
seems to be a general agreement that certain phenomena are just
not fit subjects for respectable theoretical and experimental effort.
By Stephen Weinberg, physics Nobel prize winner
Further reading
Please read the first chapter and practice the exercise
questions as many as possible.
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