J Math Chem (2009) 45:1153–1165
DOI 10.1007/s10910-008-9398-z
ORIGINAL PAPER
Analytical evaluation for two-center nuclear attraction
integrals over slater type orbitals by using Fourier
transform method
Selda Özcan · Emin Öztekin
Received: 1 April 2008 / Accepted: 10 June 2008 / Published online: 15 July 2008
© Springer Science+Business Media, LLC 2008
Abstract In this study, we shall suggest analytical expressions for two-center
nuclear attraction integrals over STO’s with a one-center charge distribution by using
Fourier transform method. The derivation is based on partial-fraction decompositions
and Taylor expansions of rational functions. Analytical expressions obtained by this
method are expressed in terms of Gegenbauer, and binomial coefficients and linear
combinations of STO’s. Finally, it is relatively easy to express the Fourier integral
representations of two-center nuclear attraction integrals with a one-center charge dis-
tribution mentioned above as finite and infinite of series of STO’s and irregular solid
harmonics which may be considered to be limiting cases of STO’s.
Keywords Slater type orbitals · Gegenbauer polynomials · Irregular solid
harmonics · Two-center nuclear attraction integrals
1 Introduction
As is well known, in molecular electronic structure calculations based on the linear
combination of atomic orbitals (LCAO)-molecular orbitals (MO) approximation, the
estimation of energies and other properties of molecular systems require the calcula-
tion of a large number of molecular integrals over atomic orbitals (AOs). The choice
of reliable basis functions is of prime importance in accurate quantum chemistry
S. Özcan (B )
Department of Physics, Faculty of Science and Arts, Amasya University, Amasya, Turkey
e-mail: sozcan@omu.edu.tr
E. Öztekin
Department of Physics, Faculty of Science and Arts, Ondokuz Mayis University, Samsun, Turkey
e-mail: eminoz@omu.edu.tr
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