# The GW miracle: Many-body perturbation theory for the ionization potential of molecule

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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.
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https://hal-cea.archives-ouvertes.fr/cea-03516536
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Submitted on : Friday, January 7, 2022 - 11:30:10 AM
Last modification on : Wednesday, January 12, 2022 - 3:39:39 AM

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### Citation

Fabien Bruneval, Nike Dattani, Michiel van Setten. The GW miracle: Many-body perturbation theory for the ionization potential of molecule. Frontiers in Chemistry, 2021, 9, pp.749779. ⟨10.3389/fchem.2021.749779⟩. ⟨cea-03516536⟩

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