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Numerical methods for multicenter integrals for numerically defined basis functions applied in molecular calculations
Author(s) -
Talman James D.
Publication year - 2003
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.10538
Subject(s) - slater integrals , order of integration (calculus) , basis (linear algebra) , basis function , convergence (economics) , coordinate space , physics , space (punctuation) , statistical physics , mathematics , quantum mechanics , mathematical analysis , computer science , geometry , economics , economic growth , operating system
An alternative approach to using functions defined analytically as basis functions for molecular orbital calculations is to use functions defined numerically on some mesh. It is then necessary to evaluate various integrals involving products of such functions that are centered at different points in space, usually the nuclei. This article discusses in detail the problem of evaluating overlap and kinetic energy integrals, nuclear attraction three‐center integrals, and electron–electron repulsion four‐center integrals for such functions. The problem of evaluating these functions in translated coordinate systems, which arises in density functional theory applications, and the associated convergence problems are also discussed. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003