化学学报 ›› 1980, Vol. 38 ›› Issue (4): 305-310.    下一篇

论文

分子轨道的差分方程法

李向平   

  1. 北京工业学院
  • 投稿日期:1978-06-20 发布日期:2013-06-03

MOLECULAR ORBIT DETERMINATION BY SOLVING THE DIFFERENCE EQUATION

LI XIANG-PING   

  1. Beijing Institute of Technology
  • Received:1978-06-20 Published:2013-06-03

对于分子轨道的计算,提出了差分方程法,即将轨道系数α看成为原子编号q(或坐标)的函数,并称此函数α=f(q)为轨道载波。由此,可将轨道系数的联立方程组转变成以载波α=f(q)为未知函数的差分力程,解差分方程的边值问题可求得轨道载波和轨道能级。对直链和单环形共轭分子,其差分方程为(α-E)f(q)+β[f(q+1)+f(q-1)]=0 α,β和E分别为原子的库仑积分,成键两原子间的交换积分和分子轨道能量。根据不同的边界条件,对于由n个碳原子为骨架组成的直链共轭烯烃和正n边形共轭烯烃用此法进行计算,求得的轨道系数公式和能级公式与已知结果相符。

The determination of the energy level formula of molecular orbit and the determination of orbit coefficient formula by the method of solving the difference equation is presented.Concreta calculations have been made, taking straight chain conjugated olefins and monocyclic ring conjugated olefins as examples.The orbit coeflicienta is taken as a function of the code number q of an atom and this function is called the carrier wave of the molecular orbit,α=f(q) is used to represent the carrier wave.A difference eqnation is used to replace the simultaneous equations of the orbit.