Low rank factorization of the Coulomb integrals for periodic coupled cluster theory

TL;DR

This paper introduces a low-rank tensor factorization of Coulomb integrals in periodic systems, significantly reducing computational costs in coupled cluster calculations.

Contribution

It presents a novel low-rank decomposition method for Coulomb integrals that enables more efficient periodic coupled cluster computations.

Findings

Coulomb integrals can be approximated with small matrices.

The matrix computation scales as O(N^4).

Application to water adsorption energy calculation.

Abstract

We study the decomposition of the Coulomb integrals of periodic systems into a tensor contraction of six matrices of which only two are distinct. We find that the Coulomb integrals can be well approximated in this form already with small matrices compared to the number of real space grid points. The cost of computing the matrices scales as O(N^4) using a regularized form of the alternating least squares algorithm. The studied factorization of the Coulomb integrals can be exploited to reduce the scaling of the computational cost of expensive tensor contractions appearing in the amplitude equations of coupled cluster methods with respect to system size. We apply the developed methodologies to calculate the adsorption energy of a single water molecule on a hexagonal boron nitride monolayer in a plane wave basis set and periodic boundary conditions.