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Remarks on the overlapping‐sphere method for molecular orbitals
Author(s) -
Slater J. C.,
Connolly J. W. D.
Publication year - 2009
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.560100814
Subject(s) - radius , spheres , mathematical analysis , infinity , physics , scattering , space (punctuation) , atomic orbital , schrödinger equation , quantum mechanics , mathematics , linguistics , philosophy , computer security , astronomy , computer science , electron
In preference to the overlapping‐sphere multiple‐scattering method for solving the self‐consistent‐field problem for a molecule or atomic cluster, the authors recommend a cellular method. Each nucleus is surrounded by a cell, and the cells taken together fill all space and do not overlap. The cells in such a case as a diatomic molecule extend out to infinity. For an approximation one can assume a spherically symmetrical potential in each cell. The general solution of Schrödinger's equation within a cell is then set up as a linear combination of solutions of the spherical problem for a single energy, but for different l and m values. In order to have the functions regular at the nucleus and at infinity, one must join two independent solutions for each l value, one regular at the origin and the other at infinity, over the surface of a sphere of radius r 1, on which the functions are made continuous, but the normal derivatives are discontinuous. The coefficients of the functions are so chosen that the sum is continuous with continuous derivative over the spheres of radius r 1, and over the planes separating neighboring atoms. In practice, one uses a finite sum of functions, perhaps for i = 0, 1, ·, 10, and applies the conditions of continuity at enough points to determine the coefficients. By expressing the potential and the radial functions as power series in r , or in r ‐ r 0, one can get a convenient analytic solution of Schrödinger's equation. The various steps involved in this method have been studied, but they have not yet been combined into a computer program, so that this paper is regarded as a progress report.