Stochastic GW Calculations for Molecules

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. 2014, 113, 076402) 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 large 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, 2015, 11, 5665), with mean (absolute) deviation of 0.05 and 0.09 eV. For completeness, we also provide a detailed review of the sGW theory and numerical implementation.