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A numerical solution of the pair equation of a model two‐electron diatomic system
Author(s) -
Bodoor Khaled,
Kobus Jacek,
Morrison John
Publication year - 2015
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.24921
Subject(s) - diatomic molecule , helium atom , schrödinger equation , partial differential equation , atom (system on chip) , chemistry , hydride , grid , differential equation , electron , atomic physics , physics , hydrogen , quantum mechanics , molecule , mathematics , computer science , geometry , embedded system
It has been well‐documented that about 90% of the total correlation energy of atomic systems can be obtained by solving so‐called pair equations. For atoms, this approach requires solving partial differential equations (PDE) in two variables. In case of a diatomic molecule, we face devising a method for treating PDEs in five variables. This article shows how a well‐established finite difference method used to solve Hartree–Fock equations for diatomic molecules can be extended to solve numerically a model two‐electron Schrödinger equation for such systems. We show that using less than 100 grid points in each variable, it is possible to obtain the total energy of the helium atom and hydrogen molecule with a chemical accuracy and the S energy of the helium atom and hydride ion as accurately as the best results available. © 2015 Wiley Periodicals, Inc.