Evaluation of Slater-type geminal integrals using tailored Gaussian quadrature

A simple, yet effective algorithm is developed for evaluating two-electron Slater-type geminal and Yukawa potential integrals over Gaussian-type orbitals (GTOs), which arise in the so-called explicitly correlated methods, on the basis of the recent work of Ten-no [S. Ten-no, Chem. Phys. Lett. 398 (2004) 56; S. Ten-no, J. Chem. Phys. 126 (2007) 014108]. Gaussian quadrature is used in analogy with the Rys quadrature method for electron repulsion integrals. The quadrature grids are obtained by the two-dimensional Chebyshev interpolation. This algorithm is especially efficient for integrals over GTOs with high angular momenta, which are present owing to the use of the resolution-of-the-identity approximation.