New expansion of the Boys function

摘要

We propose a new expansion for the Boys function integral(0)(1)t(2j)exp(-r(2)t(2)) dt appearing in the calculation of molecular two-electron matrix elements if Gaussian basis sets are employed. This expansion involves a power series involving the terms C-i,C-j(tau) (r(2)-R-2)(i) multiplied by exp(-tau r(2)), where tau is an optimized parameter tau epsilon [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 tau = 0. This is of some importance, particularly for higher j values. Further, the proposed expansion 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. (C) 1998 John Wiley & Sons, Inc. [References: 19]