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=Volume 9 - 2021

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=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 ($W_\mathrm{TDHF}$),
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.