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Formulas for three‐center exchange integrals by computer implementation of the Löwdin α‐function method
Author(s) -
Jones Herbert W.
Publication year - 1984
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.560260810
Subject(s) - center (category theory) , spherical harmonics , atomic orbital , series (stratigraphy) , slater integrals , function (biology) , recurrence relation , representation (politics) , mathematics , mathematical analysis , physics , quantum mechanics , chemistry , electron , paleontology , evolutionary biology , politics , political science , law , biology , crystallography
By use of computer algebra and expansions of orbitals about a single center in spherical harmonics with a matrix representation for the α‐function coefficients it is possible to produce formulas for each term of an infinite series that represents the value of a three‐center exchange integral. Only seven terms are required to get six decimal digits for triatomic hydrogen. This method is readily generalized to solve all three‐center exchange integrals over Slater‐type orbitals.