Efficient and rapid numerical evaluation of the two-electron, four-center Coulomb integrals using nonlinear transformations and useful properties of sine and Bessel functions
Two-electron, four-center Coulomb integrals are undoubtedly the most difficult type involved in A initio and density functional theory molecular structure calculations. Millions of such integrals are required for molecules of interest; therefore rapidity is the primordial criterion when the precision has been reached. This work presents an extremely efficient approach for improving convergence of semi-infinite very oscillatory integrals, based on the nonlinear (D) over bar -transformation and some useful properties of spherical Bessel, reduced Bessel, and sine functions. The new method is now shown to be applicable to evaluating the two-electron, four-center Coulomb integrals over B functions. The section with numerical results illustrates the unprecedented efficiency of the new approach in evaluating the integrals of interest. (C) 2002 Elsevier Science (USA).
nonlinear transformations bessel functions oscillatory integrals semi-infinite integrals molecular multicenter integrals convergence accelerators