We report a critical analysis and comparison of a variety of random-phase-approximation (RPA) based approaches to determine the electronic ground-state energy. Interrelations between RPA variants are examined by numerical examples with particular attention paid to the role of spin-flipped excitations and the behaviour of the adiabatic-connection integrands where appropriate. In general, it is found that RPA variants that include Hartree–Fock exchange contributions are unsuitable as generally applicable methods for the determination of correlation energies. Of the remaining methods only the direct RPA and RPA with second-order screened exchange are recommended for general use.
Chemical Physics Letters, 2011, Vol 510, Issue 1-3, p. 147-153