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

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 $R=1.4a_0$, 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 $2.3a_0$. The solution no longer exists beyond $3.0a_0$ for triplets ($4.3a_0$ 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.

6 pages 4 figures, 2 table

References in corpus (4)

• First-principles GW calculations for fullerenes, porphyrins, phtalocyanine, and other molecules of interest for organic photovoltaic applications
• Bond Breaking and Bond Formation: How Electron Correlation is Captured in Many-Body Perturbation Theory and Density-Functional Theory
• Benchmarking theory with an improved measurement of the ionization and dissociation energies of H${}_2$
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• Scrutinizing $GW$-based methods using the Hubbard dimer
• Encoding electronic ground-state information with variational even-tempered basis sets