The GW Miracle in Many-Body Perturbation Theory for the Ionization Potential of Molecules

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. We found GW to be the most accurate of these three approximations for the ionization potential, by far. 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 (gamma(GW)). Only the gamma(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: Its subtle balance makes GW both accurate and fast.

Automated summary

This study systematically evaluates the quality of several perturbation theories against high-level quantum chemistry methods, finding GW to be the most accurate approximation for ionization potentials. Attempts to improve upon GW by adding more diagrams were mostly unsuccessful, with only the inclusion of a GW density-matrix showing positive impact. Additionally, using an improved hybrid functional for the non-interacting Green's function further enhanced the accuracy of the simplest GW approximation.