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Slater orbital molecular integrals with numerical fourier transform methods. I. (coplanar) multicenter exchange integrals over 1 s orbitals
Author(s) -
Graovac Ante,
Monkhorst Hendrik J.,
Zivkovic Tomislav
Publication year - 1973
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.560070209
Subject(s) - atomic orbital , fourier transform , slater type orbital , numerical integration , slater integrals , charge density , molecular orbital , charge (physics) , feynman integral , physics , distribution (mathematics) , order of integration (calculus) , feynman diagram , quantum mechanics , mathematics , mathematical analysis , linear combination of atomic orbitals , electron , molecule
Slater orbital r 12 −1 integrals are calculated with a numerical Fourier‐transform method based on a formulation first given by Bonham, Peacher and Cox. Spherical wave expansions are introduced that decouple the Feynman integrations for the charge distribution Fourier transforms. The Feynman integrals are evaluated semianalytically, and their properties are analyzed in detail. The final computational step involves a numerical integration over charge distribution quantities. Results for (coplanar) multicenter exchange integrals over 1 s orbitals are given. As long as the charge distributions are overlapping considerably, the method gives good results, even when these distributions are highly asymmetric. The method as presently implemented fails when highly disconnected charge distributions are involved.