直链和单环共轭多烯本征行列式递推公式及本征能级的推导  

Derivations of the Recurrence Formula for Eigendeterminants and Eigenenergy Levels of Linear and Monocyclic Conjugated Polyenes

作　　者：张冬菊[1] 蔡欣懿 宋其圣[1] Dongju Zhang;Xinyi Cai;Qisheng Song(School of Chemistry and Chemical Engineering,Shandong University,Jinan 250100,China)

机构地区：[1]山东大学化学与化工学院,济南250100

出　　处：《大学化学》2022年第7期287-293,共7页University Chemistry

基　　金：国家自然科学基金(21773139)。

摘　　要：休克尔(Hückel)分子轨道法是描述共轭体系π电子运动的近似模型,《结构化学》教科书中通常直接给出其本征行列式和其本征能级的递推公式,缺乏推导过程。本文用数学归纳法推导了直链和单环共轭多烯本征多项的递推公式,给出了对应本征能级的通式、特点和规律,适于未掌握群论和图论等数学工具的学生学习使用。The Hückel molecular orbital method is an approximate model to describe the interactions of π-electrons in a conjugate system. In structural chemistry textbooks, the recursive formulas for the eigendeterminants and eigenenergy levels of conjugated π-electrons systems have been directly provided, without derivation. Based on mathematical induction, this work shows how these recursive formulas are derived for linear and monocyclic conjugated polyenes, and clarifies the characteristics and regularity of the eigenenergy levels. This information is suitable for students who lack mathematical knowledge with regard to topics such as the group theory and graph theory.

关 键 词：共轭多烯 本征行列式 递推公式 本征能级 

分 类 号：G64[文化科学—高等教育学] O6[文化科学—教育学]