Evaluation of Gaussian integrals for the modeling of two-dimensional quantum systems

Abstract

We have developed a McMurchie-Davidson-like recursion formula for efficient evaluation of the Coulomb attraction and interaction matrix elements between two-dimensional primitive Cartesian Gaussian type orbitals. We also present recurrence schemes for combined position and differential operator integrals, and three-center Gaussian integrals. The Cartesian Gaussian orbitals are isotropic in the exponent, but with arbitrary centers and angular momentum.