IMPROVED QUADRATURE METHODS FOR THE FOURIER-TRANSFORM OF A 2-CENTER PRODUCT OF EXPONENTIAL-TYPE BASIS FUNCTIONS

The numerical properties of a one-dimensional integral representation [H.P. Trivedi and E.O. Steinborn, Phys. Rev. A 27, 670 (1983)] for the Fourier transform of a two-center product of certain exponential-type orbitals (ETOS), the B functions [E. Filter and E.O. Steinborn, Phys. Rev. A 18, 1 (1978)], are examined. These functions span the space of ETOS. Hence, molecular integrals for other ETOS, like the more common Slater-type orbitals, may be found as finite linear combinations of integrals with B functions. The main advantage of B functions is the simplicity of their Fourier transform that makes the derivation of relatively simple general formulas for molecular integrals with the Fourier transform method possible. The integrand of the integral representation mentioned above shows sharp peaks, making, in the cases of highly asymmetric charge distributions and/or large momentum vectors, usual quadrature methods rather slow. New quadrature schemes are presented that utilize Mobius-transformation-based quadrature rules. These rules are well suited for the numerical quadrature of functions possessing a sharp peak at or near one boundary of integration [H. H. H. Homeier and E.O. Steinborn, J. Comput. Phys. 87, 61 (1990)]. Numerical results are presented that illustrate the fact that the new quadrature schemes are much more efficient than are automatic quadrature routines.