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Long‐Range multicenter integrals with slater functions: Gauss transform‐based methods
Author(s) -
Rico J. Fernández
Publication year - 1993
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.540141010
Subject(s) - range (aeronautics) , gauss , representation (politics) , simple (philosophy) , context (archaeology) , series (stratigraphy) , mathematics , series expansion , slater integrals , order of integration (calculus) , mathematical analysis , statistical physics , physics , quantum mechanics , paleontology , philosophy , materials science , epistemology , politics , political science , law , composite material , biology
The separation of the short‐ and long‐range terms in the potentials generated by pairs of Slater functions is reformulated in the context of the Gauss transform method. Analytic expressions of the long‐range potentials (in closed form) are derived for equal exponents and generalized (as expansion series) for different exponents. Additionally, the representation of these potentials from small sets of charges or lowest‐order multipoles is examined, paying special attention to their values and optimal positions. Finally, numerical tests of the formal developments are presented. It is concluded that the long‐range three‐ and four‐center integrals can be calculated with high accuracy in a simple and relatively inexpensive manner. © John Wiley & Sons, Inc.