Fully nonlocal exchange-correlation functionals derived from the adiabatic-connection fluctuation-dissipation theorem can go beyond local or gradient corrected functionals and include the van der Waals interaction. We implement three functionals of this class, in a pseudopotential plane-wave framework, (1) using the random-phase approximation (RPA), (2) adding to the RPA short-range correlations (RPA+), and (3) including density fluctuations through an exchange kernel. We find the binding energy of the H-2 and Be-2 molecules described, by all three functionals, within 0.1 eV accuracy.
Fuchs, M., & Gonze, X. (2002). Accurate density functionals: Approaches using the adiabatic-connection fluctuation-dissipation theorem. Physical review. B, Condensed matter and materials physics, 65(23), 235109:1-235109:4. https://doi.org/10.1103/PhysRevB.65.235109 (Original work published 2002)