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平面共轭分子的π轨道假3D投影图绘制

徐菁涵, 石小飞, 张文静, 魏东辉   

  1. 郑州大学化学学院, 河南 郑州 450001
  • 收稿日期:2026-03-13 录用日期:2026-05-07
  • 通讯作者: 魏东辉, 张文静 E-mail:donghuiwei@zzu.edu.cn ; zhangwj@zzu.edu.cn Donghui Wei, Wenjing Zhang
  • 基金资助:
    河南省自然科学基金杰出青年科学基金项目(252300421039)

Plotting pseudo-3D projection of π orbitals for planar conjugated molecules

Jinghan Xu, Xiaofei Shi, Wenjing Zhang, Donghui Wei   

  1. College of Chemistry, Zhengzhou University, Zhengzhou 450001, Henan Province, China
  • Received:2026-03-13 Accepted:2026-05-07
  • Contact: Donghui Wei, Wenjing Zhang E-mail:donghuiwei@zzu.edu.cn ; zhangwj@zzu.edu.cn

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摘要： 本文基于前期工作基础，开发了使用Excel程序绘制平面共轭分子π轨道的假3D投影图方法。相较于之前报道的切面等值线图的减维制图思路，本文介绍的轨道二维投影图可实现离域π轨道图的假3D效果展示，使轨道形状、节面等微观信息得以更形象地展示。该方法操作简单，无需安装专业软件，易于推广。涉及的公式推导及图形绘制过程有助于学生加深对原子轨道线性组合为分子轨道(LCAO-MO)法等概念的数学理解，提升其数形转换能力。

关键词: 平面共轭分子, π分子轨道, Excel, 降维投影法, 假3D投影图

Abstract: Building upon our previous work, we present an Excel-based method for generating pseudo-3D projections of π orbitals for planar conjugated molecules. Unlike previously reported dimension-reduction approaches using contour maps, our two-dimensional projection method achieves a pseudo-3D visualization of delocalized π orbitals, enabling more intuitive representation of microscopic features including orbital shapes and nodal planes. This user-friendly technique requires no specialized software installation and demonstrates high potential for broad implementation. The incorporated formula derivation and graphical plotting processes facilitate students’ mathematical comprehension of fundamental concepts such as the Linear Combination of Atomic Orbitals to Molecular Orbitals (LCAO-MO) method while enhancing their data-visualization skills.

Key words: Planar conjugated molecules, π Molecular orbital, Excel, Dimensionality reduction projection, Pseudo-3D projections