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

### Submission summary

 As Contributors: Valerio Olevano Arxiv Link: https://arxiv.org/abs/1812.00932v3 Date accepted: 2020-01-24 Date submitted: 2020-01-17 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.

### Ontology / Topics

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Published as SciPost Phys. 8, 020 (2020)

Dear Editor,
we resubmit a new version of the manuscript following remarks by the Referees.
We in particular tried to clarify an apparent contradiction remarked by Referee 2 in the relation between ACFDT and Trace formulas.
And we better discuss the comparison with RSH methods, including the RSH+MP2 from a paper that was suggested by Referee 1.
Best regards.

### List of changes

Page 1, last 6 lines: clarification of the ACFDT TF relationship.
Page 3, 1st column, penultimate paragraph: same issue.
Page 4, 2nd column, penultimate paragraph: widening of the discussion on RSH metthods including RSH+MP2.
Page 5: addition of two new references, [60] (pointed to us by Referee 1) and [61] (related to the same topic).

### Submission & Refereeing History

Resubmission 1812.00932v3 on 17 January 2020
Submission 1812.00932v2 on 13 November 2019