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

Evaluation of two‐center, three‐ and four‐electron integrals over Slater‐type orbitals in elliptical coordinates

“…The evaluation of the two‐center integrals in the frame of SCC method in the basis of Slater orbitals seems to be an important but not completely solved problem. There are many methods of calculation of the two‐electron integrals, i.e., the contemporary solutions 17–26 in the spherical coordinates and 27, 28 in the elliptical coordinates. Some three‐ and four‐electron integrals in elliptical coordinates where evaluated by Rothstein 29 but in his results the greatest power of the r ij functions is 1.…”