Solutions of Atomic and Molecular Schrödinger Equations with One-dimensional Function Approach

一維函數方法求解原子和分子薛定諤方程

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)2286-2298
Journal / PublicationGaodeng Xuexiao Huaxue Xuebao/Chemical Journal of Chinese Universities
Volume42
Issue number7
Online published19 May 2021
Publication statusPublished - Jul 2021

Abstract

Rigorous numerical techniques to solve the Schrödinger equation are both interesting and desirable, particularly with one that can include new features beyond the standard methods. In this article, we review one-dimensional function (1D function) approach developed recently by us to obtain the solutions of the Schrödinger equations of atomic and molecular systems where one-dimensional basis functions have been applied to separate components. A uniform real-space grid representation of the electronic wavefunctions is employed; hence, a refinement technique of residual vector correction can be implemented. The 1D function approach facilitates such convenient numerical integrations that many problems related with the many-electron multi-center potential molecular integrals are circumvented. The converged energy is obtained from a strictly upper bound one, while the obtained two-electron Schrödinger wavefunction exhibits the electron correlation effect on one-electron distribution. Different from density functional theory or Hartree-Fock with the assumed particle-separability, the obtained solution treats more accurately many-body effect of electron correlation found in the electron-electron repulsion energy.
對薛定諤方程的嚴格數值求解, 尤其是發展標準方法之外的、包含新功能的解法, 一直是物理學研究的基本關注點. 本文介紹一種近些年發展的一維函數近似解方法, 該方法通過對波函數的不同坐標分量進行處理來求解原子和分子體系的薛定諤方程. 電子的試探波函數被離散化到實空間均勻格點上, 因此可以通過殘差矢量校正的方法對其進行改進. 一維函數方法本身的特征決定其非常利于數值積分, 避免了很多由常規的多電子、多中心勢分子積分所帶來的問題. 計算中, 最終能量是從嚴格的能量上限逐漸收斂所獲得, 計算出的兩電子薛定諤波函數呈現出常規單電子近似方法所含有的電子關聯效應. 不同于密度泛函理論及HartreeFock的單電子解法, 本方法對電子-電子排斥能的多體效應的處理更加精確.

Research Area(s)

  • 薛定谔方程的数值解, 一维函数法, 氢原子, 氦原子及其等电子离子, 氢分子及氢离子, Solutions of Schrödinger equations, One-dimensional function approach, Hydrogen atom, Helium and its isoelectronic ion, Hydrogen molecule and ion

Citation Format(s)

Solutions of Atomic and Molecular Schrödinger Equations with One-dimensional Function Approach. / SARWONO, Yanoar Pribadi; UR RAHMAN, Faiz; ZHAO, Rundong; ZHANG, Ruiqin.

In: Gaodeng Xuexiao Huaxue Xuebao/Chemical Journal of Chinese Universities, Vol. 42, No. 7, 07.2021, p. 2286-2298.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review