New expansion of the Boys function

Abstract

ABSTRACT:We propose a new expansion for the Boys function H t exp yr t dt 0 appearing in the calculation of molecular two-electron matrix elements if Gaussian basis Ž . sets are employed. This expansion involves a power series involving the termsmultiplied by exp y r , where is an optimized parameter g 0, 1 . The performances of the introduced expansion are discussed and illustrated by some numerical experiments. It appears that the proposed expansion is considerably shorter than the customary Taylor series, which in turn is the special case for s 0. This is of some importance, particularly for higher j values. Further, the proposed expansion Ž . enables a single expression for calculating erf x for the whole range of variable x. The recursive relations for the expansion coefficients are derived and the truncation errors are estimated. A new method for calculating the Boys function by means of asymptotic series is represented too.

A rigorous and optimized strategy for the evaluation of the Boys function kernel in molecular electronic structure theory

“…For large values of x , both recursions have the same reported accuracy. Primorac introduced a new expansion of the Boys function that is, however, not part of this study as it was reported by Primorac himself to be inaccurate at higher orders. Other analytical recurrence relations have been derived by Guseinov and Mamedov: with k being any integer denoting a recursive offset to n .…”

Boys function evaluation on graphical processing units

“…(1) cannot be expressed in closed analytical form. There exists a solid amount of numerical methods for its evaluation in the literature [4,5,7,[9][10][11]. The most efficient in practical applications are those which rely on pretabulating function values on a dense grid of points and applying relatively short Taylor-type expansions [4,7,12].…”