On the combination of two methods for the calculation of multicenter integrals using exponential-type orbitals

The possible combination of two methods for the calculation of multicenter two‐electron integrals using STO and B function basis sets is discussed. The first method (Method I), which is of approximate nature, is based on a simplified version of the so‐called Σ‐factorization method [A. W. Niukkanen and L. A. Gribov, Theor. Chim. Acta 62, 443 (1983)], where the radial part of the two‐center one‐electron density ρab(r) is represented as a sum of two radial functions fa(r) and fb(r), placed on two different centers a and b. After such a transformation, the calculation of the two‐electron integrals boils down to the calculation of some type of Coulomb integrals. The second method (Method II), which calculates each integral separately to a given accuracy, is based on Mobius‐type quadrature used for a three‐dimensional integral representation for the two‐electron integral of B functions [E. O. Steinborn and H. H. H. Homeier, Int. J. Quantum Chem. Symp. 24, 349 (1990)]. In Method I, the choice of the radial functions placed on the different centers has an essential influence on the final value of the multicenter integrals. In the present study of Method I, a rather simple approximation of the radial part was made that reproduced the qualitative behavior of the molecular integral curves as function of the geometry rather well. At the present state of development, Method I produces fast order‐of‐magnitude estimates that are useful for screening purposes, i.e., to decide which integrals have to be evaluated more accurately by other methods like Method II. Method II reproduces data given in the literature [R. M. Pitzer and D. P. Merrifield, J. Chem. Phys. 52, 4782 (1970)] correctly. © 1992 John Wiley & Sons, Inc.