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

TL;DR

This study evaluates the accuracy of the many-body GW and Bethe-Salpeter equation methods in predicting the hydrogen molecule's spectrum, comparing results with exact solutions and other quantum chemistry approaches.

Contribution

It provides a benchmark assessment of GW+BSE against exact and traditional methods for the hydrogen molecule's ground and excited states.

Findings

GW+BSE accurately predicts energy levels within 0.2 eV at equilibrium.

Potential-energy curves from GW+BSE agree with exact results up to 2.3 a0.

Ground state instability limits the solution beyond certain internuclear distances.

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.