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

### Submission summary

 As Contributors: Valerio Olevano Arxiv Link: https://arxiv.org/abs/1812.00932v2 Date submitted: 2019-11-13 Submitted by: Olevano, Valerio Submitted to: SciPost Physics Discipline: Physics Subject area: Condensed Matter Physics - Computational Approaches: Theoretical, Computational

### 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.

###### Current status:
Editor-in-charge assigned

### Submission & Refereeing History

Submission 1812.00932v2 on 13 November 2019

## Reports on this Submission

### Strengths

1-formalism development
2-comparisons with state of the art techniques
3-explanations of the discrepancies

### Weaknesses

1-Basis set dependency is missing
2-missing BSSE estimates

### Report

The present article proposes to apply many-body derived schemes to estimate correlation energies in the difficult test-case of Be2 dimer dissociation. By comparing with experimental and very accurate results their different approximations, the authors propose that BSE+GW scheme is very accurate too. The formalism presentation is clear and the results convincing. I strongly recommend the present article suitable for publication. However I would be pleased if the authors could comment on the basis set dependency of their proposed scheme, as well as on their BSSE estimates. Even if they exclude it by following the recommendation of Baerends et al, it remains an important source of errors especially in the case of Be2, see Chem. Phys. Lett. 416, 370 (2005) for instance.

• validity: top
• significance: high
• originality: high
• clarity: top
• formatting: good
• grammar: excellent