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Ground-state correlation energy of beryllium dimer by the Bethe-Salpeter equation
by Jing Li, Ivan Duchemin, Xavier Blase, Valerio Olevano
This is not the current version.
|As Contributors:||Valerio Olevano|
|Arxiv Link:||https://arxiv.org/abs/1812.00932v2 (pdf)|
|Date submitted:||2019-11-13 01:00|
|Submitted by:||Olevano, Valerio|
|Submitted to:||SciPost Physics|
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.
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Submission & Refereeing History
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Reports on this Submission
Anonymous Report 2 on 2019-12-19 Invited Report
- Cite as: Anonymous, Report on arXiv:1812.00932v2, delivered 2019-12-19, doi: 10.21468/SciPost.Report.1403
1 - original approach
2- interesting results
1 - relation/equivalence between trace-formula and adiabatic-connection fluctuation-dissipation theorem formula not entirely clear
This is a well-written manuscript presenting very interesting results for researchers working in the fields of electronic structure methods and simulations. The introduction sets clearly the problem, the approach and the key results obtained. The theory part is accurate and precise and points clearly the approximations that are introduced. The results part compares various level of approximations.
I'd like the authors to provide clarifications on the relation between TF and ACFDT. In the introduction, the authors refer to a work which shows the equivalence between the methods within RPA and TDDFT. However, in the Method part they contrast the in-principle exact ACFDT with the TF relying on the boson approximation- which seems to contradict the previous statement.
Also, it would be interesting if the authors could argue more on the stark difference due to the starting point. Is it possible to identify the shortcoming with the PBE one-particle solutions that causes the bump (e.g. self-interaction, double counting ...). I think this could be a useful addition.
1 - clarify apparent contradiction (see report)
The addition (see report) is desirable not requested. On the other hand, I think a more careful analysis on the effect of the basis set choice should be added as pointed in the other referee's report.
Anonymous Report 1 on 2019-11-28 Invited Report
- Cite as: Anonymous, Report on arXiv:1812.00932v2, delivered 2019-11-28, doi: 10.21468/SciPost.Report.1344
2-comparisons with state of the art techniques
3-explanations of the discrepancies
1-Basis set dependency is missing
2-missing BSSE estimates
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.