Use of STOs in Hartree-Fock calculations: Error analysis and variance-minimized pseudospectral method

Abstract

In this study it is demonstrated that STO (Slater-type orbital) basis sets are particularly well suited to pseudospectral Hartree–Fock calculations. The reduction of two-electron integrals, to ones that are (at worst) equivalent to a one-electron integral over three centers, eliminates the need for slowly convergent one-center expansions. This allows all integrals to be calculated quickly and accurately in either spherical or ellipsoidal coordinates. A new variance-minimized variant of the pseudospectral method is derived and applied to a number of small closed-shell molecules. The performance of the algorithm is assessed relative to purely spectral calculations employing STO and GTO (Gaussian-type orbital) basis sets. The pseudospectral operator is used to assess the errors contained in solutions found by the purely spectral method. The suitability of a number of different de-aliasing set types is also examined. Orthogonal sets of hydrogen-like eigenfunctions were found to be optimal. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1537–1548, 1999