https://hal-cea.archives-ouvertes.fr/cea-03516536Bruneval, FabienFabienBrunevalSRMP - Service de recherches de métallurgie physique - DMN - Département des Matériaux pour le Nucléaire - CEA-DES (ex-DEN) - CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) - CEA - Commissariat à l'énergie atomique et aux énergies alternatives - Université Paris-SaclayDattani, NikeNikeDattaniHPQC Labsvan Setten, MichielMichielvan SettenIMEC - IMEC - KU Leuven - Catholic University of Leuven - Katholieke Universiteit LeuvenThe GW miracle: Many-body perturbation theory for the ionization potential of moleculeHAL CCSD2021[PHYS.QPHY] Physics [physics]/Quantum Physics [quant-ph][CHIM.THEO] Chemical Sciences/Theoretical and/or physical chemistryCEA, Contributeur MAP2022-01-07 11:30:102022-07-06 18:26:182022-01-10 15:37:20enJournal articleshttps://hal-cea.archives-ouvertes.fr/cea-03516536/document10.3389/fchem.2021.749779application/pdf1We 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 ($W_\mathrm{TDHF}$), 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: The neglected diagrams compensate almost perfectly, which makes $GW$ both accurate and fast.