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Computer‐generated formulas for exchange integrals over slater‐type orbitals
Author(s) -
Jones Herbert W.
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.560280815
Subject(s) - atomic orbital , slater type orbital , series (stratigraphy) , slater integrals , spherical harmonics , type (biology) , mathematics , slater determinant , integer (computer science) , function (biology) , physics , mathematical physics , quantum mechanics , mathematical analysis , molecular orbital theory , computer science , electron , paleontology , ecology , biology , evolutionary biology , programming language
Formulas for two‐center exchange integrals using Slater‐type orbitals with equal screening constants are produced by employing computer algebra in the implementation of the Löwdin alpha function method which expands displaced orbitals in an infinite series of spherical harmonics. Our use of a C ‐matrix with integer elements in connection with the alpha function gives exact results for each term of an infinite series in the generated formulas. It is possible to terminate the series for the value of the exchange integral by “extrapolating to infinity” using judiciously chosen rearrangements and expansions of the formulas: as an example the Sugiura formula for 1 s orbitals is produced to illustrate the technique.