Efficient evaluation of integrals for density functional theory: Nonlinear D transformations to evaluate three-center nuclear attraction integrals over B functions

Density functional theory requires precise numerical values for three-center nuclear attraction integrals, best obtained over slater-type orbitals (STOs). Efficient evaluation of three-center nuclear attraction integrals over STOs to predetermined accuracy is made possible by applying the nonlinear D and (D) over bar transformations. These methods are implemented in Fortran subroutines. This work shows how the conditions of applicability for these transformations are readily proven to be satisfied using the Axiom symbolic computation system. Axiom also provides exact values of the integrals for comparison. Their evaluation by standard numerical quadrature methods (Gauss-Laguerre), proves inadequate: Certain parameters lead to inaccurate values for the integrals, whereas the transformed integrals are highly accurate and rapidly evaluated. (C) 1998 John Wiley & Sons, Inc.