In this work, we show the advantages of using the Coulomb hole plus screened exchange (COHSEX) approach in the calculation of potential energy surfaces (PES). In particular, we demonstrate that, unlike perturbative GW and partial self-consistent GW approaches, such as eigenvalue self-consistent GW and quasi-particle (QP) self-consistent GW, the COHSEX approach yields smooth PES without irregularities and discontinuities. Moreover, we show that the ground-state PES obtained from the Bethe-Salpeter equation (BSE), within the adiabatic connection fluctuation dissipation theorem, built with QP 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 QP 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 the changes in the screening inside the BSE.