  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.
