Recent progress in the accurate and rapid evaluation of all Coulomb integrals over Slater-type orbitals

One of the main objectives in ab initio Slater research is rapid and accurate evaluation of the two-, three-, and four-center Coulomb integrals. General expressions for these integrals were obtained and evaluated for the first time using the single center strategy and requisite orbital translations. The alternative strategy using the Fourier transform of the B functions basis has been thoroughly explored by the Steinborn group. The analytical expressions of these integrals have been shown to be adapted to the use of nonlinear transformations to accelerate their convergence. A complete study of D-(due to Levin and Sidi) and (D) over bar -transformations (due to Sidi) for all these integrals has led to the improved HD and H (D) over bar methods, which greatly simplified the application of the above nonlinear transformations. The results presented show that the H (D) over bar method gives unprecedented accuracy with speedup by a factor of 5 over the (D) over bar approach and over 70 over the initial STOP method for four center terms. (C) 2001 John Wiley & Sons, Inc.