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 123