2013-7-25 Chemistry Department of Fudan University 23
Physical Chemistry I
Chapter V Polyatomic Molecular Structure
caa cbb ccc
a 0 b ' 0 1 2 0 ' c
For isolated double bond system, the total energy of the four π electrons will be:
E L 4( )
The energy difference is called delocalization energy (DE)
Physical Chemistry I
Chapter V Polyatomic Molecular Structure
§5-2-1.Hückel Molecular Orbital Theory (HMO) The main idea of HMO 1.Take σ-πorbitals Apart
Chemistry Department of Fudan University
Physical Chemistry I
Chapter V Polyatomic Molecular Structure
x 3x 1 0
4 2
x1 1.618
x2 0.618 x3 0.618
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Physical Chemistry I
Chapter V Polyatomic Molecular Structure
2. Conjugate Carbocyclic Alkene
Dn ' ( x ) Dn ( x ) Dn 2 ( x ) 2
The general solution of in Dn ( )
1. Conjugate straight chain alkene
Number of C atom: n
n order secular determinant:
Dn ( x ) xDn 1 ( x ) Dn 2 ( x )
D0 (x) 1
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D1 ( x) x
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Chapter V Polyatomic Molecular Structure
§5-2-2.Illustrative Examples of HMO Straight chain alkene---butadiene
2013-7-25
Chemistry Department of Fudan University

2m 2 cos n
(m=1, 2, ……, n)
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Chemistry Department of Fudan University
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Physical Chemistry I
Chapter V Polyatomic Molecular Structure
2013-7-25
Chemistry Department of Fudan University
Physical Chemistry I
Chapter V Polyatomic Molecular Structure
The general solution of in Dn ( )

m 2 cos n 1
E1 C 1 3 C


E2 C 2C
E3 C 1 3 C
2013-7-25 Chemistry Department of Fudan University 18


Physical Chemistry I
Chapter V Polyatomic Molecular Structure
i H ij 0
(i j ) ( i j 1) (i j and i j 1)
S ij
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1 0
(i j ) (i j )
2
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Physical Chemistry I
For CO2:
O 2
O 1
Therefore:
x2 1 1 0
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0 1 x2
17
x 1
0
Chemistry Department of Fudan University
Physical Chemistry I
Chapter V Polyatomic Molecular Structure
x4 1.618
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E1 1.618 E2 0.618 E3 0.618 E4 1.618
5
Chemistry Department of Fudan University
Physical Chemistry I
Chapter V Polyatomic Molecular Structure
2 n p
orbitals
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Chemistry Department of Fudan University
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Physical Chemistry I
Chapter V Polyatomic Molecular Structure

m n
1. Normal m=n
2. Electron sufficient m>n
0
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0
1
Chemistry Department of Fudan University
Physical Chemistry I
Chapter V Polyatomic Molecular Structure
2.To the π orbitals, HMO assumes:
Chemistry Department of Fudan University
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Physical Chemistry I
Chapter V Polyatomic Molecular Structure
§5-2-4. Conjugate Inorganic Molecule
H ii x
2
3 2
2013-7-25 Chemistry Department of Fudan University 24
3
Physical Chemistry I
Chapter V Polyatomic Molecular Structure
E 0 0 E 0 0 0 E 0 0 E
E x
x 1 0 0
1 x 1 0
0 1 x 1
0 0 1 x
4
0
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E D 2 E1 2 E2 2( 1.618 ) 2( 0.618 ) 4 4.472
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Chemistry Department of Fudan University
8
Physical Chemistry I
Chapter V Polyatomic Molecular Structure
DE E L E D 0.472
2013-7-25 Chemistry Department of Fudan University 9
Physical Chemistry I
Chapter V Polyatomic Molecular Structure
§5-2-3. Graphic Theory
x ( C ) /
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x O O
0
O
0
x
O
O 0 x O
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Chemistry Department of Fudan University
Physical Chemistry I
Chapter V Polyatomic Molecular Structure
H ij x
2013-7-25 Chemistry Department of Fudan University 15
Physical Chemistry I
Chapter V Polyatomic Molecular Structure
CO2 molecule
O
C
O
O E C O 0 C O C E C O 0 0 C O O E
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Physical Chemistry I
Chapter V Polyatomic Molecular Structure
Delocalization Energy The four πelectrons fill two lowest orbitals, the total energy of the system is:
2013-7-25
Chemistry Department of Fudan University
22
Physical Chemistry I
Chapter V Polyatomic Molecular Structure
1. Open three-center bonding
3c-2e bonding in B2H6
2013-7-25 Chemistry Department of Fudan University 6