螺旋对称(n1)构型高分子的LCAO/TO-LCTO/HO-LCHO/PO处理——Ⅰ.(21)螺旋对称高分子能带的计算

TREATMENT ON THE ELECTRONIC ENERGY BANDS OF THE HELIX-SYMMETRICAL HIGH POLYMER BY LCAO/TO-LCTO/HO-LCHO/PO

螺旋高分子不仅具有平移对称性,而且有转动对称性.我们用一种新的线性组合方法LCAO/TO-LCTO/HO-LCHO/PO(T——translation-periodic,H——periodic)推导了螺旋对称高分子的久期方程,使它的建立和求解都大为简化,并使其阶数从n×P(n为螺旋轴的重数,也表示平移单元中包含的螺旋单元数;P为每个螺旋单元中的原子轨道数)降为P阶.本文还制定了直接解复广义本征值问题的EHMO计算方案.以聚乙烯和聚乙炔为例做了电子能带结构的计算.

Helix-symmetrical polymer possesses not only translation symmetry,but also rotation symmetry.We apply a new linear combination method named as LCAO/TO-LCTO/HO-LCHO/PO to derive its secular matrix equation.In such a manner,setting-up and solving of the equation may be simplified to a great extant.The scheme of the helix-symmetrical polymer is shown in Fig.1 in the Chinese Text.Let x(r(?)),η(k|r)andφ(k,m|r)be AO,TO(Translation-Periodic Orbital)and HO(Helix-Periodic Orbital)respectively.Then,we can obtain the secular matrix equation(6)via steps LCAO/TO,LCTO/HO and LCHO/PO in terms of Eq.(1)to Eq.(4).As examples,the energy bands of polyacetylene and polyethylene have been calculated by EHMO using the present method.