Stochastic GW calculations for molecules

TL;DR

This paper demonstrates that the stochastic GW (sGW) method provides highly accurate quasiparticle energies for molecules, with near-linear computational scaling, enabling calculations on much larger systems than traditional GW methods.

Contribution

The paper validates the accuracy of the sGW approach for molecules and details its theoretical foundation and implementation, expanding its applicability for large-scale systems.

Findings

sGW achieves close agreement with deterministic GW for ionization energies

Mean absolute deviation of 0.05-0.09 eV from benchmark GW results

sGW scales nearly linearly with system size, enabling large system calculations

Abstract

Quasiparticle (QP) excitations are extremely important for understanding and predicting charge transfer and transport in molecules, nanostructures and extended systems. Since density functional theory (DFT) within the Kohn-Sham (KS) formulation does not provide reliable QP energies, many-body perturbation techniques such as the GW approximation are essential. The main practical drawback of GW implementations is the high computational scaling with system size, prohibiting its use in extended, open boundary systems with many dozens of electrons or more. Recently, a stochastic formulation of GW (sGW) was presented [Phys. Rev. Lett. 113, 076402 (2014)] with a near-linear-scaling complexity, illustrated for a series of silicon nanocrystals reaching systems of more than 3000 electrons. This advance provides a route for many-body calculations on very larges systems that were impossible with previous approaches. While earlier we have shown the gentle scaling of sGW, its accuracy was not extensively demonstrated. Therefore, we show that this new sGW approach is very accurate by calculating the ionization energies of a group of sufficiently small molecules where a comparison to other GW codes is still possible. Using a set of 10 such molecules, we demonstrate that sGW provides reliable vertical ionization energies in close agreement with benchmark deterministic GW results [J. Chem. Theory Comput, 11, 5665 (2015)], with mean (absolute) deviation of 0.05 and 0.09eV. For completeness, we also provide a detailed review of the sGW theory and numerical implementation.