AUTHOR=Bruneval Fabien , Dattani Nike , van Setten Michiel J. 

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

JOURNAL=Frontiers in Chemistry

VOLUME=9

YEAR=2021

URL=https://www.frontiersin.org/journals/chemistry/articles/10.3389/fchem.2021.749779

DOI=10.3389/fchem.2021.749779

ISSN=2296-2646

ABSTRACT=<p>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, <italic>GW</italic> as post-Hartree-Fock methods. We found <italic>GW</italic> to be the most accurate of these three approximations for the ionization potential, by far. Going beyond <italic>GW</italic> by adding more diagrams is a tedious and dangerous activity: We tried to complement <italic>GW</italic> with second-order exchange (SOX), with second-order screened exchange (SOSEX), with interacting electron-hole pairs (<italic>W</italic><sub>TDHF</sub>), and with a <italic>GW</italic> density-matrix (<italic>γ</italic><sup><italic>GW</italic></sup>). Only the <italic>γ</italic><sup><italic>GW</italic></sup> 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 <italic>GW</italic> approximation improves even more. We conclude that <italic>GW</italic> is a miracle: Its subtle balance makes <italic>GW</italic> both accurate and fast.</p>