An efficient algorithm for the generation of two-electron repulsion integrals over gaussian basis functions

A synthesis of certain of the features of the recently developed HGP method of Head-Gordon and Pople with some of the constructs of the well-established McMurchie-Davidson (MD) scheme has led to the development of a new algorithm for the computation of the two-electron repulsion integrals which arise in conventional ab initio quantum chemical calculations using Gaussian basis sets. As in the MD scheme, derivatives of the two-electron integrals with respect to the nuclear coordinates are obtained very efficiently by the new algorithm. Moreover, in the spirit of the HGP approach, as much of the computational effort as possible is performed outside the contraction loops. This is achieved through the intermediacy of scaled, partially contracted integral sets and through the use of a near-optimal solution to the central tree-search problem. Explicit FLOP (floating point operation) counts suggest that the new algorithm is typically a factor of 2 cheaper than the HGP method for contracted basis sets.