On the evaluation of overlap integrals with exponential‐type basis functions

Abstract

AbstractThe numerical properties of a one‐dimensional integral representation [H.P. Trivedi and E. O. Steinborn, Phys. Rev. A 27, 670 (1983)] for the overlap integral 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. B functions possess a very simple Fourier transform that results in relatively simple general formulas for molecular integrals derivable using the Fourier transform method. In addition, molecular integrals for other ETOs, like the more common Slater‐type orbitals, can be written as finite linear combinations of integrals with B functions because these functions span the space of ETOs. The integrand of the integral representation mentioned above shows peculiarities requiring special quadrature methods, especially in the case of highly asymmetric charge distributions. It is shown that good results can be obtained using Möbiustransformation‐based quadrature rules well suited for the numerical integration 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)]. The method based on Möbius‐type quadrature is compared to several other methods — based on other quadrature rules, finite sums, and infinite series representations together with convergence acceleration — to evaluate overlap integrals with B functions. The numerical results indicate that the new quadrature schemes are more efficient than are the other methods.