Modification of Rys quadratures for two- and three-center electron repulsion integrals calculation

Integrals for Gaussian-type orbitals are the basis of every quantum chemical calculation. In this work, we present the efficient implementation of nuclear attraction and of two- and three-center electron repulsion integral calculations based on the Rys quadratures. It was found that some types of electron repulsion integrals can be calculated using modified Rys quadratures with fewer roots. Despite the overall effect of this modification being shown to be small, a 1.6-fold speed-up of some types of integral calculations was achieved. Overall, nuclear attraction integral calculations were shown to be 8-10 times faster compared to LIBINT in electrostatic potential calculation tasks. The speed of three-center electron repulsion integrals calculation was enhanced by a factor of 2-4 compared to LIBINT.