高等学校化学学报 ›› 1993, Vol. 14 ›› Issue (2): 228.

• 研究论文 • 上一篇    下一篇

超球坐标下原子、分子体系的变分计算——氦原子和氢负离子基态

邓从豪, 张瑞勤, 冯大诚   

  1. 山东大学理论化学研究窒, 济南 250100
  • 收稿日期:1992-01-29 修回日期:1992-11-19 出版日期:1993-02-24 发布日期:1993-02-24
  • 通讯作者: 邓从豪
  • 基金资助:

    国家自然科学基金

Variational Calculations of Atoms and Molecules in Hyperspherical Coordinates ——Ground States of Helium Atom and Hydrogen Negative Ion

DENG Cong-Hao, ZHANG Rui-Qin, FENG Da-Cheng   

  1. Theoretical Chemistry Laboratory, Shandong University, Jinan, 250100
  • Received:1992-01-29 Revised:1992-11-19 Online:1993-02-24 Published:1993-02-24

摘要: 应用超球坐标表示氦原子和氢负离子的薛定谔方程。将二电子原子在三维空间中的运动转化为单电子原子在六维空间中受广义库仑力作用的运动。我们给出了六维空间广义角动量算符的本征值与本征函数,并以此本征函数做基构造超球波函数,得到超球径微分方程。以广义Laguerre多项式表示超球径波函数,运用密度矩阵和线性变分法得到非正交基下超球径波函数满足的久期方程,最后求得能量和波函数。计算结果与精确的计算符合良好。

关键词: 超球坐标, 线性变分, 非正交基

Abstract: In this paper, the hyperspherical coordinates are used to describe the Schrodinger equation of He and H-.The equation of motion of two-electron atom in 3-Dspace is transformed into that of one-electron atom in 6-Dspace, subjected to generalized Coulombic potential.The cigenfunctions of the generalized angular momentum operator are used as a basis set for the hyperspherical wavefunc-tion, with which a coupled differential equation of hyperradial wave-function is obtained, By describing the hyperradial wave-function with generalized Laguerre polynomials, a secular equation is gotten for the non-orthogonal basis set of hyperradial wavefunction by means of linear variational method.The calculated ground state energies of He and H- agree well with precise values.

Key words: Hyperspherical coordinates, Linear variation, Non-orthogonal basis set

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