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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 ( 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: Its subtle balance makes  GW  both accurate and fast.

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