Cubic-scaling all-electron GW calculations with a separable density-fitting space-time approach

TL;DR

This paper introduces a cubic-scaling all-electron GW computational method using a separable density-fitting space-time approach, enabling efficient calculations on large molecular systems without localization assumptions.

Contribution

The authors develop a novel GW implementation that achieves cubic scaling with standard Gaussian basis sets using a separable RI framework, avoiding localization or sparsity assumptions.

Findings

Cubic-scaling GW calculations demonstrated on large molecular sets.

Accurate results comparable to Coulomb-fitting calculations with meV precision.

Scalability shown on defected hexagonal boron-nitride flakes with up to 6000 electrons.

Abstract

We present an implementation of the $GW$ space-time approach that allows cubic-scaling all-electron calculations with standard Gaussian basis sets without exploiting any localization nor sparsity considerations. The independent-electron susceptibility is constructed in a time representation over a non-uniform distribution of real-space locations $\lbrace {\bf r}_k \rbrace$ optimized within a separable resolution-of-the-identity framework to reproduce standard Coulomb-fitting calculations with meV accuracy. The compactness of the obtained $\lbrace {\bf r}_k \rbrace$ distribution leads to a crossover with the standard Coulomb-fitting scheme for system sizes below a few hundred electrons. The needed analytic continuation follows a recent approach that requires the continuation of the screened Coulomb potential rather than the much more structured self-energy. The present scheme is benchmarked over large molecular sets and scaling properties are demonstrated on a family of defected hexagonal boron-nitride flakes containing up to 6000 electrons.