Calculation of multi-center integrals for the region of moderate and weak overlap

In this study a general formula was established for multi-center integrals over Gaussian basis sets using the two-center expansion of nuclear attracti on and electron repulsion potentials. The terms of the formula are the anal ytical functions of interatomic distances. Three kinds of integrals contained in these formulae can be evaluated analy tically. In the presented method, unlike many other popular methods, the nu merical integrations procedure is unnecessary since it does not contain the incomplete gamma function. A computer program was written and tested for v arious orbitals. The calculations show that the series converge very rapidl y.