Towards GW Calculations on Thousands of Atoms

TL;DR

This paper introduces a new GW calculation algorithm that significantly reduces computational costs from $O(N^4)$ to $N^2$-$N^3$, enabling large-scale simulations of nanostructures and molecules.

Contribution

The authors develop a full-frequency GW algorithm with optimized parallel implementation, allowing accurate calculations on systems with thousands of atoms.

Findings

Validated accuracy on GW100 test set with low deviations

Achieved scalable computations on large graphene nanoribbons

Successfully computed local density of states across heterojunctions

Abstract

The GW approximation of many-body perturbation theory is an accurate method for computing electron addition and removal energies of molecules and solids. In a canonical implementation, however, its computational cost is $O(N^4)$ in the system size N, which prohibits its application to many systems of interest. We present a full-frequency GW algorithm in a Gaussian type basis, whose computational cost scales with $N^2$ to $N^3$. The implementation is optimized for massively parallel execution on state-of-the-art supercomputers and is suitable for nanostructures and molecules in the gas, liquid or condensed phase, using either pseudopotentials or all electrons. We validate the accuracy of the algorithm on the GW100 molecular test set, finding mean absolute deviations of 35 meV for ionization potentials and 27 meV for electron affinities. Furthermore, we study the length-dependence of quasiparticle energies in armchair graphene nanoribbons of up to 1734 atoms in size, and compute the local density of states across a nanoscale heterojunction.