Chapter9多原子的半经验方法 1.n-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
Chapter 9 多原子的半经验方法 1. π- 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
1.n-electron approximation (1) i=i>i ri core (2) V(①：第i个π电子在核与电子场中的势能， 由变分原理，极小化变分积 imfp,H.p.dr)={E:p》
1. π-electron approximation 1 1 1 core ^ ^ i i j i ij n n H H ( i ) r = = = + 1 2 2 core ^ H i V( i ) = − + (1) (2) 由变分原理, 极小化变分积 V(i):第i个π电子在核与电子场中的势能. ^ * Min( d ) , H E
2 The free-electron MO method 1 如果：忽略， 且 V=0, in a certain region outside this region 有：H.p.=E.0 (3) o.-i9 (4) core H.(=e (5)
2 .The free-electron MO method V= , outside this region 如果: 忽略, 且 V=0, in a certain region 1 rij 有: ^ H E = i i n = (3) (4) ^ i i i H ( ) e core i = (5)
E.- e (6) 维情况，有 e- h' m. n,=1,2…(7) 由Paui原理，有： 2 HOMO-LUMO Excitation
i i 1 n E e = = (6) 一维情况,有 2 2 i i 2 i , 1,2,...... 8 h n m l e n e = = (7) 由Pauli 原理,有: ... 1 2 3 4 ... 1 2 3 4 HOMO-LUMO Excitation
AE=m=es-en⅓=hn% 2egcyn7n.+ (8) 对于Polyenes: 设单键长，1，双键长，2，考虑MOs离域，两端分别增加 1+ 则电子运动的区域： 息++g++=0-+60 2 =2k+30+4)=22k+2+10+4 =2(n.+100+4)
n 1 2 2 E hc hv e e n + = = − = (8) 1 n 2 2 2 e 1 1 ( ) ( 1) 8 e e n n h hc m l C + = − = + 对于Polyenes: 设单键长, l1 , 双键长, l2 , 考虑MOs离域, 两端分别增加 1 2 . 则电子运动的区域: 3 1 4 4 l l + 1 2 1 2 1 2 1 2 1 2 1 2 3 1 3 ( 1) ( )( ) 2 2 2 1 1 (2 3)( ) (2 2 1)( ) 2 2 1 ( 1)( ) 2 c kl k l l l l l l k l l k l l n l l + + + + = + + = + + = + + + = + +