Factorized structure of the long-range two-electron integrals tensor and its application in quantum chemistry

TL;DR

This paper presents two innovative approximation techniques for efficiently evaluating long-range Coulomb potentials and high-dimensional two-electron integrals in quantum chemistry, enhancing computational efficiency for molecular simulations.

Contribution

The paper introduces tensorized Chebyshev interpolation and the Fast Multipole Method for improved approximation of long-range interactions in quantum chemistry.

Findings

Both methods are efficient for medium-sized molecules.

Numerical experiments demonstrate the effectiveness of the approaches.

The paper provides detailed algorithms and comparisons.

Abstract

We introduce two new approximation methods for the numerical evaluation of the long-range Coulomb potential and the approximation of the resulting high dimensional Two-Electron Integrals tensor (TEI) with long-range interactions arising in molecular simulations. The first method exploits the tensorized structure of the compressed two-electron integrals obtained through two-dimensional Chebyshev interpolation combined with Gaussian quadrature. The second method is based on the Fast Multipole Method (FMM). Numerical experiments for different medium size molecules on high quality basis sets outline the efficiency of the two methods. Detailed algorithmic is provided in this paper as well as numerical comparison of the introduced approaches.