Two‐electron repulsion integrals over Gaussian s functions

We present an efficient scheme to evaluate the [ 0 ] ( m ) integrals that arise in many ab initio quantum chemical two‐electron integral algorithms. The total number of floating‐point operations ( FLOPS ) required by the scheme has been carefully minimized, both for cases where multipole expansions of the integrals are admissable and for cases where this is not so. The algorithm is based on the use of a modified Chebyshev interpolation formula to compute the function exp(− T ) and the integral F m ( T ) = ∫ 0 1 u 2 m exp(− Tu 2 ) du very cheaply.