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.