Symbolic calculation of auxiliary functions for molecular integrals over slater orbitals

Abstract

Symbolic calculation is applied to the evaluation of molecular integrals over Slater orbitals (STOs). A recurrence scheme is developed for some new auxiliary functions that facilitate this work. Closed expressions are developed independently for use in spot checks. A table of formulas for the individual functions has been constructed and made available on-line. Applications are discussed. The derivations and tabulations were performed mechanically in runs that produced both the original typeset account of this study and more detailed documentation without manual transcription.

Reexamination of the calculation of two-center, two-electron integrals over Slater-type orbitals. I. Coulomb and hybrid integrals

“…The second problem of the single-center expansions is the catastrophic digital erosion during calculations of the auxiliary quantities [16,17], which seems to be extremely difficult to overcome. A promising work-around is the use of the symbolic computational environments such as Mathematica [18][19][20], but at present the symbolic methods are typically orders of magnitude slower than the numerical ones. Since the time the single-center methods were first proposed, several new (or more general) expansion techniques have been developed.…”

Symbolic computation of integrals by recurrence

“…This notation provided the key to the development and documentation of the numerous 3-term recurrence formulas in [6].…”

“…Computer algebra is being used increasingly, however, to generate recurrence schemes interactively that are too tedious to construct by hand. Recent examples include [6,7].…”

Combining Slater-type orbitals and effective core potentials

“…Interestingly enough, there has been a significant progress on this issue in recent years. In fact, looking at only the past 15 years, there are many notable works of Bouferguene et al [10][11][12][13], Rico et al [14][15][16][17][18][19][20][21][22][23][24], Hoggan et al [25][26][27][28][29][30], Pachucki [31][32][33][34][35], and others [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52]. In particular, for the diatomic systems STOs can be now used routinely [51].…”