Random-phase approximation correlation methods for molecules and solids

Random-phase approximation (RPA) correlation methods based on Kohn-Sham density-functional theory and Hartree-Fock are derived using the adiabatic-connection fluctuation dissipation theorem. It is shown that the correlation energy within the adiabatic-connection fluctuation-dissipation theorem is exact in a Kohn-Sham framework while for Hartree-Fock reference states this is not the case. This shows that Kohn-Sham reference states are probably better suited to describe electron correlation for use in RPA methods than Hartree-Fock reference states. Both, Kohn-Sham and Hartree-Fock RPA methods are related to each other both by comparing the underlying correlation functionals and numerically through the comparison of total energies and reaction energies for a set of small organic molecules.