Evaluation of two-electron integrals for explicit r12 theories

We present a practical scheme for the evaluation of nonstandard two-electron molecular integrals that appear in ab initio theories employing explicitly correlated wave functions with linear r12 terms (“linear r12” methods). In contrast with previous efforts, the target integrals are evaluated recursively via intermediates formulated solely in terms of Cartesian Gaussian functions. All working equations fit conveniently the framework of highly efficient Head-Gordon and Pople method of evaluation of electron repulsion integrals. Thus, only straightforward modifications of existing codes that employ HGP or HGP–PRISM scheme are necessary to implement our approach. High potential of the pathway is realized in a robust practical implementation.