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arXiv · 2010.07780

Hydrogen molecule spectrum by many-body GW and Bethe-Salpeter equation

Jing Li·Valerio Olevano
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Abstract

We check the ab initio GW approximation and Bethe-Salpeter equation (BSE) many-body methodology against the exact solution benchmark of the hydrogen molecule H$_2$ ground state and excitation spectrum, and in comparison with the configuration interaction (CI) and time-dependent Hartree-Fock methods. The comparison is made on all the states we could unambiguously identify from the excitonic wave functions' symmetry. At the equilibrium distance $R = 1.4 \, a_0$, the GW+BSE energy levels are in good agreement with the exact results, with an accuracy of 0.1~0.2 eV. GW+BSE potential-energy curves are also in good agreement with the CI and the exact result up to $2.3 \, a_0$. The solution no longer exists beyond $3.0 \, a_0$ for triplets ($4.3 \, a_0$ for singlets) due to instability of the ground state. We tried to improve the GW reference ground state by a renormalized random-phase approximation (r-RPA), but this did not solve the problem.

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Jing Li, Valerio Olevano. 2021-01-15. Hydrogen molecule spectrum by many-body GW and Bethe-Salpeter equation. https://doi.org/10.1103/physreva.103.012809

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