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.
Ground-state correlation energy of counterions at a charged planar wall: Gibbs-Bogoliubov lower-bound approach
