Calculation of two center Coulomb integral by the use of fourier transform method

In this work; by the use of Fourier transform method, a general and analytical expression have been presented for two-center Coulomb integral over STO?s. The analytical expression obtained for two-center Coulomb integral includes binomial coefficients, Gaunt coefficients and some auxiliary molecular integrals. The accurate calculation of two-center Coulomb integrals depends especially on the accurate calculation of these auxiliary molecular integrals. Therefore, the main part of the work has been devoted to the accurate calculation of these auxiliary molecular integrals. In this manner, analytical and reccurrence relations have been presented for the appearing auxiliary molecular integrals. The best working ranges of the presented alternative formulae for the auxiliary molecular integrals have been obtained and used in the calculation of two-center Coulomb integrals.Computer programs for the obtained general and analytical expression of two-center Coulomb integral, Gaunt coefficients and appearing auxiliary molecular integrals have been constructed in Maple 13 symbolic programming language. Using this computer program, two-center Coulomb integrals have been calculated in the case of arbitrary quantum parameters, and listed as tables with comparison of the literature values.As a result, it is observed that the calculated two-center Coulomb integrals by the use of the algorithm presented in this work, agree well with the available literature values.