2-CENTER OVERLAP INTEGRALS OVER SLATER-TYPE ORBITALS CONSTRAINED TO A SPHERICAL INTEGRATION VOLUME - ANALYTICAL EXPRESSIONS

A special type of two-center overlap integral is considered in which the integration does not extend over the whole space, but is constrained to the interior or exterior of a sphere about one of the centers of the orbitals. It is shown that exact, closed analytical expressions can be derived for this kind of two-center integral over Slater-type orbitals. These analytical expressions are of a very simple analytical structure and allow for a rapid integral evaluation. By applying the angular momentum recurrences which we proposed recently [W. Hierse and P. M. Oppeneer, J. Chem. Phys. 99, 1278 (1993)], the evaluation performance can be further accelerated. In the frequently occurring case of nearly equal scaling parameters the analytical integral expressions are totally stable, but in the (pathological) case of one vanishing scaling parameter the integral over the interior volume is not stable. Exact integration formulas for the latter limiting case are also given.