FAST AND STABLE ALGORITHM FOR THE ANALYTICAL COMPUTATION OF 2-CENTER COULOMB AND OVERLAP INTEGRALS OVER SLATER-TYPE ORBITALS

Proceeding from analytical expressions for two-center kernel functions that we derived recently, we present new analytical formulas for the two-center Coulomb and overlap integrals over Slater-type orbitals. Th ese formulas are of an exceptionally simple analytical structure and h igh numerical efficiency. An especially important point is that for th e most frequently needed ranges of discrete quantum numbers, the formu las are completely stable in the cases of nearly equal scaling paramet ers or vanishing interatomic distances, except for one particular case of the Coulomb integral. No special asymptotic formulas are needed an y more to compute the two-center integrals over Slater-type orbitals i n these cases. Furthermore, a largely recursive formulation makes the integral evaluation very economical and fast: In particular, we assess the numerical performance of a new kind of angular momentum recurrenc es that we have proposed in a previous article [W. Hierse and P. M. Op peneer, J. Chem. Phys. 99, 1278 (1993)]. (C) 1994 John Wiley and Sons, Inc.