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

Jing Li (1) , Valerio Olevano (2)

1 CEA-LETI - Commissariat à l'énergie atomique et aux énergies alternatives - Laboratoire d'Electronique et de Technologie de l'Information
2 NEEL - TMC - Théorie de la Matière Condensée

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.

Domaines: Chimie-Physique [physics.chem-ph]

Jing Li, Valerio Olevano. Hydrogen molecule spectrum by many-body GW and Bethe-Salpeter equation. Physical Review A, 2021, 103 (1), pp.012809. ⟨10.1103/PhysRevA.103.012809⟩. ⟨hal-02999467⟩