Potential energy surfaces without unphysical discontinuities: the Coulomb-hole plus screened exchange approach

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.