Improved algorithm for the calculation of one-electron two-center integrals with STOs

In a previous article (J. Fernández Rico, R. López and G. Ramírez, J. Comp. Chem., 9 , 790 (1988)) we have proposed the calculation of molecular integrals involving STOs by means of some recurrence relations which use two sets ( h and H ) of overlap integrals (basic matrices). In the present paper, we derive explicit expressions of these integrals employing the two-range expansion of the 0s-function. This approach yields equations for the elements of the two basic matrices in terms of two further matrices, k (x,y) and i (x,y), and some auxiliary functions. Relations between the elements of these matrices and the functions are thoroughly explored and numerical tests are included for illustrating the behavior of the method.