Accurate density functionals: Approaches using the adiabatic-connection fluctuation-dissipation theorem
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 $(\mathrm{RPA}+),$ and (3) including density fluctuations through an exchange kernel. We find the binding energy of the ${\mathrm{H}}_{2}$ and ${\mathrm{Be}}_{2}$ molecules described, by all three functionals, within 0.1 eV accuracy.