  In this work we show the advantages of using the Coulomb-hole plus
screened-exchange (COHSEX) approach in the calculation of potential energy
surfaces. In particular, we demonstrate that, unlike perturbative $GW$ and
partial self-consistent $GW$ approaches, such as eigenvalue-self-consistent
$GW$ and quasi-particle self-consistent $GW$, the COHSEX approach yields smooth
potential energy surfaces without irregularities and discontinuities. Moreover,
we show that the ground-state potential energy surfaces (PES) obtained from the
Bethe-Salpeter equation, within the adiabatic connection fluctuation
dissipation theorem, built with quasi-particle energies obtained from
perturbative COHSEX on top of Hartree-Fock (BSE@COHSEX@HF) yield very accurate
results for diatomic molecules close to their equilibrium distance. When
self-consistent COHSEX quasi-particle energies and orbitals are used to build
the BSE equation the results become independent of the starting point. We show
that self-consistency worsens the total energies but improves the equilibrium
distances with respect to BSE@COHSEX@HF. This is mainly due to changes in the
screening inside the BSE.

Chemical Physics