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

TL;DR

This paper introduces a recursive method for efficiently computing Gaussian integrals relevant to modeling two-dimensional quantum systems, improving computational efficiency for complex matrix elements.

Contribution

It presents a novel recursion formula for Coulomb integrals and related operators between 2D Gaussian orbitals, extending existing methods to more complex integral evaluations.

Findings

Developed a McMurchie-Davidson-like recursion for 2D Gaussian integrals

Enabled efficient calculation of Coulomb attraction and interaction matrix elements

Provided recurrence schemes for combined position, differential, and three-center integrals

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.