# Ground-state correlation energy of beryllium dimer by the Bethe-Salpeter equation

## TL;DR

This paper uses advanced many-body perturbation theory methods, specifically GW and Bethe-Salpeter equations, to accurately compute the ground-state correlation energy of the challenging beryllium dimer, aligning well with experimental data.

## Contribution

It presents the first ab initio calculations of Be₂'s potential energy using GW and BSE, demonstrating improved accuracy over previous methods.

## Key findings

- GW corrections improve energy estimates at RPA level
- BSE calculations match experimental and high-level theoretical results
- Reproduces experimentally observed flattening of the potential

## Abstract

Since the '30s the interatomic potential of the beryllium dimer Be$_2$ has been both an experimental and a theoretical challenge. Calculating the ground-state correlation energy of Be$_2$ along its dissociation path is a difficult problem for theory. We present ab initio many-body perturbation theory calculations of the Be$_2$ interatomic potential using the GW approximation and the Bethe-Salpeter equation (BSE). The ground-state correlation energy is calculated by the trace formula with checks against the adiabatic-connection fluctuation-dissipation theorem formula. We show that inclusion of GW corrections already improves the energy even at the level of the random-phase approximation. At the level of the BSE on top of the GW approximation, our calculation is in surprising agreement with the most accurate theories and with experiment. It even reproduces an experimentally observed flattening of the interatomic potential due to a delicate correlations balance from a competition between covalent and van der Waals bonding.