Chapter9多原子的半经验方法教学课件.pptVIP

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. π-electron approximation (1) (2) 由变分原理, 极小化变分积 V(i):第i个π电子在核与σ电子场中的势能. 2 .The free-electron MO method V= , outside this region 如果: 忽略, 且 V=0, in a certain region 有: (3) (4) (5) (6) 一维情况,有 (7) 由Pauli 原理,有: (8) 对于Polyenes: 设单键长, l1, 双键长, l2, 考虑MOs离域, 两端分别增加 . 则电子运动的区域: 代入(8)式有: 3 . The Huckel MO method (11) (12) (13) 由线性变分法有: r=1,2,3,….nc (14) 久期方程: (15) 积分 for Cr Cs bonded (16) for Cr Cs not bonded together (17) (18) 归一化条件(normalization condition ) (19) (20) 4. Conjugated Chain Molecules (21) 本征方程: (22) (23) 由行列式理论有: k=1, 2, 3, …, N (24) k=1, 2, 3, …, N u=1, 2, 3, …, N (25) 例子:丁二烯 (26) ci =1.618 , 0.618, -0.618 , -1.618 波函数: ? 分子轨道节面与能级 (Nodal Planes and Energy Levels) : The ground state of Butadine in C2h symmetry HOMO LUMO 一般情况: HOMO: LUMO: 5. Monocyclic Conjugated Polyenes. HMO results : k= 0, 1, …, nc-1 MO levels: 4n + 2 rule (占满成键轨道) C4H4 a triplet ground state 分子轨道 C6H6 k=0 k=1 k=5 k=2 k=4 k=3 简并轨道的线性组合 实 MO Similarly ? Symmetry species MO The symmetry species of MOs The ground state: 6. Polycyclic Conjugated Polyenes Naphthealene 久期方程: r = 1, 2, …, 10 久期行列式: 利用 , 对波函数进行分类: 原子轨道等价组: C1 = C2 = C3 = C4 C5 = C6 = C7 = C8 C9 = C10 根据Huckel近似: 令: x = -1 , , , *