1. p- electron approximation

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Chapter 9 ?????????

• 1. p- electron approximation
• 2. The free-electron MO method
• 3. The Huckel MO method
• 4. Conjugated Chain Molecules
• 5. Monocyclic Conjugated Polyenes
• 6. Polycyclic Conjugated Polyenes
• 7. Charges, Bond Orders and Free Valences
• 8. General Semi-empirical MO Methods

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1. p-electron approximation
(1)
(2)
V(i)?i?p?????s???????.
?????, ??????
3
2 .The free-electron MO method
?? ??, ? V0, in a certain
region
V , outside this region
?
(3)
(4)
(5)
4
(6)
????,?
(7)
?Pauli ??,?
5
(8)
??Polyenes
????, l1, ???, l2, ??MOs??, ??????
. ????????
6
??(8)??
3 . The Huckel MO method
(11)
(12)
(13)
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r1,2,3,.nc
(14)
????
(15)
??
(16)
for Cr Cs bonded
(17)
for Cr Cs not bonded together
(18)
8
(19)
?????(normalization condition )
(20)
4. Conjugated Chain Molecules
(21)
9
????
(22)
(23)
10
???????
(24)
k1, 2, 3, , N
k1, 2, 3, , N
(25)
u1, 2, 3, , N
?????
(26)
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ci 1.618 , 0.618, -0.618 , -1.618
???
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????????? (Nodal Planes and Energy Levels)

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The ground state of Butadine in C2h symmetry
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HOMO LUMO
???? HOMO
LUMO
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5. Monocyclic Conjugated Polyenes.
HMO results
k 0, 1, , nc-1
MO levels
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4n 2 rule (??????)
C4H4 a triplet ground state
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???? C6H6
k0
k1
k5
k2
k4
k3
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????????? ? MO
Similarly
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The symmetry species of MOs
 
MO
Symmetry species
The ground state
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6. Polycyclic Conjugated Polyenes
Naphthealene
????
r 1, 2, , 10
?????
?? , ????????
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???????
C1 C2 C3 C4
C5 C6 C7 C8
C9 C10
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??Huckel??
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?
, ,
x -1 ,
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x 1 ,
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7. p- Electron Charges, Bond Orders, Free Valence
???
Electron charges
Where the sum is over the MOs
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For 1,3-butadiene ,
Theorem. For the ground states of a neutral
alternant hydrocarbon, all the Huckel electron
charges qr are 1 .
Bond Orders
For butadiene ,
P12 2(0.372)(0.602)2(0.602)(0.372)0.894 P23
2(0.602)(0.602)2(0.372)(0.372)0.447
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The total bond orders are
bond contribution included
Correlation of Bond lengths with Bond Orders
Rc-c vs Prs
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Free Valence Index
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8. General Semi-empirical MO Methods
The Extended Huckel Method.
???Hamilton ?????Hamiltonian ???
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??????
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??????
?Koopmans????VSIP??? VSIP Valence-state
ionization Potential
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?
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The CNDO , INDO , and NDDO Methods
CNDO The complete neglect of differential
overlap method.
INDO The Intemediate neglect of differential
overlap method.