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The random phase approximation (RPA) for the correlation energy functional ofdensity functional theory has recently attracted renewed interest. Formulatedin terms of the Kohn-Sham (KS) orbitals and eigenvalues, it promises to resolvesome of the fundamental limitations of the local density and generalizedgradient approximations, as for instance their inability to account fordispersion forces. First results for atoms, however, indicate that the RPAoverestimates correlation effects as much as the orbital-dependent functionalobtained by a second order perturbation expansion on the basis of the KSHamiltonian. In this contribution, three simple extensions of the RPA areexamined, (a) its augmentation by an LDA for short-range correlation, (b) itscombination with the second order exchange term, and (c) its combination with apartial resummation of the perturbation series including the second orderexchange. It is found that the ground state and correlation energies as well asthe ionization potentials resulting from the extensions (a) and (c) for closedsub-shell atoms are clearly superior to those obtained with the unmodified RPA.Quite some effort is made to ensure highly converged RPA data, so that theresults may serve as benchmark data. The numerical techniques developed in thiscontext, in particular for the inherent frequency integration, should also beuseful for applications of RPA-type functionals to more complex systems.

Random-phase-approximation-based correlation energy functionals: Benchmark results for atoms