On the Cholesky Decomposition for electron propagator methods: General aspects and application on C60

TL;DR

This paper presents a parallel program P-RICDΣ that uses Cholesky decomposition to efficiently and accurately treat large molecules in electron propagator methods, demonstrated on C60.

Contribution

It introduces a new parallel software leveraging Cholesky decomposition for electron propagator calculations, with controlled error and application to large molecules.

Findings

Cholesky decomposition errors are minimal at moderate thresholds.

The program accurately computes electron affinities and ionization potentials.

Demonstrated effectiveness on the C60 molecule.

Abstract

To treat the electronic structure of large molecules by electron propagator methods we developed a parallel computer program called P-RICD$\Sigma$. The program exploits the sparsity of the two-electron integral matrix by using Cholesky decomposition techniques. The advantage of these techniques is that the error introduced is controlled only by one parameter which can be chosen as small as needed. We verify the tolerance of electron propagator methods to the Cholesky decomposition threshold and demonstrate the power of the P-RICD$\Sigma$ program for a representative example (C60). All decomposition schemes addressed in the literature are investigated. Even with moderate thresholds the maximal error encountered in the calculated electron affinities and ionization potentials amount to a few meV only, and the error becomes negligible for small thresholds.