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

Jing Li,Valerio Olevano,Xavier Blase,Ivan Duchemin

doi:10.21468/scipostphys.8.2.020

Abstract

Since the ’30s the interatomic potential of the beryllium dimer Be_22 has been both an experimental and a theoretical challenge. Calculating the ground-state correlation energy of Be_22 along its dissociation path is a difficult problem for theory. We present ab initio many-body perturbation theory calculations of the Be_22 interatomic potential using the GWGW 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 GWGW corrections already improves the energy even at the level of the random-phase approximation. At the level of the BSE on top of the GWGW 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.

Highlights

The beryllium dimer Be2 has a long scientific history, with hundreds of experimental and theoretical investigations [1, 2]
We present the theoretical curve that we calculated at the level of the direct random-phase approximation (RPA) approximation on top of Density-functional theory (DFT) in the PBE [53] approximation (RPA@PBE) by the trace formula (TF) formula Eq (6) or equivalently Eq (8) which, we checked, provide the same result within numerical precision
We show the same RPA@PBE curve calculated by the adiabatic-connection fluctuation-dissipation theorem (ACFDT) formula

Summary

Introduction

The beryllium dimer Be2 has a long scientific history, with hundreds of experimental and theoretical investigations [1, 2]. Later studies [2, 7] pointed to a possible van der Waals binding with a shallow energy minimum at large (∼ 5 Å) distance, while other studies yielded a double minimum, at short and long distance separation [2, 8]. Be2 remained elusive till the ’70s [9], and only in the ’80s first rotovibrational spectra were measured [10] and reliable calculations [11] were made, both pointing to a single short-bond minimum at ∼ 2.5 Å. Be2 remains a severe workbench to check many-body theories, and this is the purpose of this work

Methods

Results

Conclusion