An O(N^3) implementation of Hedin's GW approximation for molecules

TL;DR

This paper presents an efficient O(N^3) implementation of Hedin's GW approximation for molecules, leveraging locality and spectral function manipulation to enable large system calculations.

Contribution

The authors introduce a scalable GW method for molecules that reduces computational complexity by exploiting locality and spectral techniques, improving feasibility for large systems.

Findings

Achieved O(N^3) scaling for GW calculations on molecules

Implemented spectral function manipulation using FFT to avoid Green's function singularities

Reduced memory requirements through Coulomb interaction compression

Abstract

We describe an implementation of Hedin's GW approximation for molecules and clusters, the complexity of which scales as O(N^3) with the number of atoms. Our method is guided by two strategies: i) to respect the locality of the underlying electronic interactions and ii) to avoid the singularities of Green's functions by manipulating, instead, their spectral functions using FFT methods. To take into account the locality of the electronic interactions, we use a local basis of atomic orbitals and, also, a local basis in the space of their products. We further compress the screened Coulomb interaction into a space of lower dimensions for speed and to reduce memory requirements. The improved scaling of our method with respect to most of the published methodologies should facilitate GW calculations for large systems. Our implementation is intended as a step forward towards the goal of predicting, prior to their synthesis, the ionization energies and electron affinities of the large molecules that serve as constituents of organic semiconductors.