Random-phase approximation correlation methods for molecules and solids

Abstract

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.

Keywords:

• random-phase approximation
• density functional theory
• time-dependent density-functional theory
• correlation energy
• RPA

Acknowledgements

We gratefully acknowledge the funding of the German Research Council (DFG), which, within the framework of its ‘Excellence Initiative’, supports the Cluster of Excellence ‘Engineering of Advanced Materials’ (www.eam.uni-erlangen.de) at the University of Erlangen-Nuremberg. We are grateful to Wim Klopper for providing us with 31 prior to its publication.