Two-Electron Integrals over Gaussian Geminals

The evaluation of contracted two-electron integrals over a Gaussian geminal operator is pivotal to diverse quantum chemistry methods. In this article, using the unique factorization properties and the sparsity of these integrals, a novel, near-optimal computation algorithm is presented. Our method employs a combination of recently developed upper bounds, recurrence relations in the spirit of the Head-Gordon-Pople approach, and late- and early-contraction paths in the PRISM style. A detailed study of the FLOP (floating-point operations) cost reveals that the new algorithm is computationally much cheaper than any other previous scheme.