Benchmarking GW against exact diagonalization for semi-empirical models

TL;DR

This paper benchmarks the GW approximation against exact diagonalization for semi-empirical pi conjugated molecules, analyzing its accuracy in calculating energies and excitations, and discusses its limitations and the role of derivative discontinuity.

Contribution

It provides a comparative analysis of GW and exact diagonalization for semi-empirical models, highlighting GW's strengths and limitations in molecular energy calculations.

Findings

GW captures about 65% of the groundstate correlation energy.

GW underestimates electron affinities and ionization potentials by ~2.5%.

One-shot G0W0 improves excitation energy predictions.

Abstract

We calculate groundstate total energies and single-particle excitation energies of seven pi conjugated molecules described with the semi-empirical Pariser-Parr-Pople (PPP) model using self-consistent many-body perturbation theory at the GW level and exact diagonalization. For the total energies GW captures around 65% of the groundstate correlation energy. The lowest lying excitations are overscreened by GW leading to an underestimation of electron affinities and ionization potentials by approximately 0.15 eV corresponding to 2.5%. One-shot G_0W_0 calculations starting from Hartree-Fock reduce the screening and improve the low-lying excitation energies. The effect of the GW self-energy on the molecular excitation energies is shown to be similar to the inclusion of final state relaxations in Hartree-Fock theory. We discuss the break down of the GW approximation in systems with short range interactions (Hubbard models) where correlation effects dominate over screening/relaxation effects. Finally we illustrate the important role of the derivative discontinuity of the true exchange-correlation functional by computing the exact Kohn-Sham levels of benzene.