Pros and Cons of the Bethe-Salpeter Formalism for Ground-State Energies.

The combination of the many-body Green's function GW approximation and the Bethe-Salpeter equation (BSE) formalism has shown to be a promising alternative to time-dependent density functional theory (TD-DFT) for computing vertical transition energies and oscillator strengths in molecular systems. The BSE formalism can also be employed to compute ground-state correlation energies thanks to the adiabatic-connection fluctuation-dissipation theorem (ACFDT). Here, we study the topology of the ground-state potential energy surfaces (PESs) of several diatomic molecules near their equilibrium bond length. Using comparisons with state-of-art computational approaches (CC3), we show that ACFDT@BSE is surprisingly accurate and can even compete with lower-order coupled cluster methods (CC2 and CCSD) in terms of total energies and equilibrium bond distances for the considered systems. However, we sometimes observe unphysical irregularities on the ground-state PES in relation with difficulties in the identification of a few GW quasiparticle energies.