Beyond quasi-particle self-consistent $GW$ for molecules with vertex corrections

Abstract

We introduce the ${\Sigma }^{\text{BSE}}@L^{\text{BSE}}$ self-energy in the quasi-particle self-consistent $GW$ (qs$GW$) framework (qs${\Sigma }^{\text{BSE}}@L^{\text{BSE}}$). Here, $L$ is the two-particle response function which we calculate by solving the Bethe-Salpeter equation with the static, first-order $GW$ kernel. The same kernel is added to $\Sigma$ directly. For a set of medium organic molecules, we show that including the vertex both in $L$ and $\Sigma$ is crucial. This approach retains the good performance of qs$GW$ for predicting first ionization potentials and fundamental gaps, while it greatly improves the description of electron affinities. Its good performance places qs${\Sigma }^{\text{BSE}}@L^{\text{BSE}}$ among the best-performing electron propagator methods for charged excitations. Adding the vertex in $L$ only, as commonly done in the solid state community, leads to devastating results for electron affinities and fundamental gaps. We also test the performance of BSE@qs$GW$ and qs${\Sigma }^{\text{BSE}}@L^{\text{BSE}}$ for neutral charge-transfer excitation and find both methods to perform similar. We conclude that ${\Sigma }^{\text{BSE}}@L^{\text{BSE}}$ is a promising approximation to the electronic self-energy beyond $GW$. We hope that future research on dynamical vertex effects, second-order vertex corrections, and full self-consistency will improve the accuracy of this method, both for charged and neutral excitation energies.

5 figures

References in corpus (14)

• Quasiparticle self-consistent $GW$ method; a basis for the independent-particle approximation
• First-principles GW calculations for fullerenes, porphyrins, phtalocyanine, and other molecules of interest for organic photovoltaic applications
• The GW compendium: A practical guide to theoretical photoemission spectroscopy
• Quasi-Particle Self-Consistent $GW$ for Molecules
• QUESTDB: a database of highly-accurate excitation energies for the electronic structure community
• Fully self-consistent $GW$ and quasi-particle self-consistent $GW$ for molecules
• Beyond the GW approximation: combining correlation channels
• On the dangers of partial diagrammatic summations: Benchmarks for the two-dimensional Hubbard model in the weak-coupling regime
• Electronic Structure of Chromium Trihalides beyond Density Functional Theory
• Optical response and band structure of LiCoO2 including electron-hole interaction effects
• GWΓ + Bethe-Salpeter equation approach for photoabsorption spectra: Importance of self-consistent GWΓ calculations in small atomic systems
• Improved quasiparticle self-consistent electronic band structure and excitons in $\beta$-LiGaO${}_2$
• Many body theory beyond GW : towards a complete description of 2-body correlated propagation
• Tensor hypercontraction for self-consistent vertex corrected GW with static and dynamic screening; applications to molecules and solids with superexchange