Ground-state correlation energy of beryllium dimer by the Bethe-Salpeter equation

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.

Can Popular DFT Approximations and Truncated Coupled Cluster Theory Describe the Potential Energy Surface of the Beryllium Dimer?

The potential energy surface (PES) of the ground state of the beryllium dimer poses a significant challenge for high-level ab initio electronic structure methods. Here, we present a systematic study of basis set effects over the entire PES of Be2 calculated at the full configuration interaction (FCI) level. The reference PES is calculated at the valence FCI/cc-pV{5,6}Z level of theory. We find that the FCI/cc-pV{T,Q}Z basis set extrapolation reproduces the shape of the FCI/cc-pV{5,6}Z PES as well as the binding energy and vibrational transition frequencies to within ~10 cm−1. We also use the FCI/cc-pV{5,6}Z PES to evaluate the performance of truncated coupled cluster methods (CCSD, CCSD(T), CCSDT, and CCSDT(Q)) and contemporary density functional theory methods (DFT) methods for the entire PES of Be2. Of the truncated coupled cluster methods, CCSDT(Q)/cc-pV{5,6}Z provides a good representation of the FCI/cc-pV{5,6}Z PES. The GGA functionals, as well as the HGGA and HMGGA functionals with low percentages of exact exchange tend to severely overbind the Be2 dimer, whereas BH&HLYP and M06-HF tend to underbind it. Range-separated DFT functionals tend to underbind the dimer. Double-hybrid DFT functionals show surprisingly good performance, with DSD-PBEP86 being the best performer. Møller–Plesset perturbation theory converges smoothly up to fourth order; however, fifth-order corrections have practically no effect on the PES.