Calculation of STOs electron repulsion integrals by ellipsoidal expansion and large-order approximations

摘要

For general two-electron two-centre integrals over Slater-type orbitals(STOs), the use of the Neumann expansion for the Coulomb interaction potentialyields infinite series in terms of few basic functions. In many important casesthe number of terms necessary to achieve convergence by a straightforwardsummation is large and one is forced to calculate the basic integrals of highorder. We present a systematic approach to calculation of the higher-orderterms in the Neumann series by large-order expansions of the basic integrals.The final expressions are shown to be transparent and straightforward toimplement, and all auxiliary quantities can be calculated analytically.Moreover, numerical stability and computational efficiency are also discussed.Results of the present work can be used to speed up calculations of the STOsintegral files, but also to study convergence of the Neumann expansion anddevelop appropriate convergence accelerators.