Beyond quasi-particle self-consistent $GW$ for molecules with vertex corrections
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916608675414016 |
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| author | Förster, Arno |
| author_facet | Förster, Arno |
| contents | We introduce the $Σ^{\text{BSE}}@L^{\text{BSE}}$ self-energy in the quasi-particle self-consistent $GW$ (qs$GW$) framework (qs$Σ^{\text{BSE}}@L^{\text{BSE}}$). 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 $Σ$ directly. For a set of medium organic molecules, we show that including the vertex both in $L$ and $Σ$ 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$Σ^{\text{BSE}}@L^{\text{BSE}}$ 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$Σ^{\text{BSE}}@L^{\text{BSE}}$ for neutral charge-transfer excitation and find both methods to perform similar. We conclude that $Σ^{\text{BSE}}@L^{\text{BSE}}$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_01581 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Beyond quasi-particle self-consistent $GW$ for molecules with vertex corrections Förster, Arno Chemical Physics We introduce the $Σ^{\text{BSE}}@L^{\text{BSE}}$ self-energy in the quasi-particle self-consistent $GW$ (qs$GW$) framework (qs$Σ^{\text{BSE}}@L^{\text{BSE}}$). 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 $Σ$ directly. For a set of medium organic molecules, we show that including the vertex both in $L$ and $Σ$ 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$Σ^{\text{BSE}}@L^{\text{BSE}}$ 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$Σ^{\text{BSE}}@L^{\text{BSE}}$ for neutral charge-transfer excitation and find both methods to perform similar. We conclude that $Σ^{\text{BSE}}@L^{\text{BSE}}$ 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. |
| title | Beyond quasi-particle self-consistent $GW$ for molecules with vertex corrections |
| topic | Chemical Physics |
| url | https://arxiv.org/abs/2412.01581 |