The use of special coordinate axes in direct and semi-direct implementations of second-order perturbation theory, including the derivation of a horizontal recurrence relation

Abstract

A horizontal recurrence relation (HRR) is derived which may be used in the generation of two-electron repulsion integrals (ERIs). Also, special Cartesian coordinate axes may be used to reduce the number of intermediate terms. Heretofore, the use of local axis systems entailed rotations every time a shell quadruple of ERIs was computed. Recently, we pointed out the possibility of postponing the transformation using choices of Cartesian reference frames based on nuclear positions. In our pilot implementation of direct and semi-direct Møller–Plesset second-order perturbation theory (MP2) we construct the integrals in local coordinate systems and perform the back-transformation in the middle of the AO to MO integral transformation, rather than rotating the ERIs after the computation of each shell quadruple. The efficacy of this approach depends on whether the gains in ERI computation are greater than the losses incurred in transformation. Preliminary CPU profiles indicate that the increased time spent in rotating axes is quite small. Keywords: horizontal recurrence relation, second-order perturbation theory.