The dissection algorithm for the second-Born self-energy

TL;DR

This paper introduces an efficient dissection algorithm for calculating the second-Born self-energy in many-body perturbation theory, significantly reducing computational effort by focusing on relevant Coulomb integrals.

Contribution

The paper presents a novel dissection algorithm that improves the efficiency of second-Born self-energy calculations by selectively processing significant Coulomb integrals.

Findings

Algorithm reduces computational scaling for large basis sets

Demonstrated efficiency gain in organic molecule calculations

Applicable to one-particle Kohn-Sham basis sets

Abstract

We describe an algorithm to efficiently compute the second-Born self-energy of many-body perurbation theory. The core idea consists in dissecting the set of all four-index Coulomb integrals into properly chosen subsets, thus avoiding to loop over those indices for which the Coulomb integrals are zero or negligible. The scaling properties of the algorithm with the number of basis functions is discussed. The computational gain is demonstrated in the case of one-particle Kohn-Sham basis for organic molecules.