The GW Miracle in Many-Body Perturbation Theory for the Ionization Potential of Molecules - Bruneval, Fabien; Dattani, Nike; van Setten, Michiel J. (Frontiers in Chemistry, 2021)
We use the GW100 benchmark set to systematically judge the quality of several perturbation theories against high-level quantum chemistry methods. First of all, we revisit the reference CCSD(T) ionization potentials for this popular benchmark set and establish a revised set of CCSD(T) results. Then, for all of these 100 molecules, we calculate the HOMO energy within second- and third-order perturbation theory (PT2 and PT3), and GW as post Hartree-Fock methods. GW is by far the most accurate approximation for the ionization potential. Going beyond GW by adding more diagrams is a tedious and dangerous activity: We tried to complement GW with second-order exchange (SOX), with second-order screened exchange (SOSEX), with interacting electron-hole pairs (W_TDHF), and with a GW density-matrix (γ^GW). Only the γ^GW result has a positive impact. Finally using an improved hybrid functional for the non-interacting Green's function, considering it as a cheap way to approximate self-consistency, the accuracy of the simplest GW approximation improves even more. We conclude that GW is a miracle: The neglected diagrams compensate almost perfectly, which makes GW both accurate and fast.