Molecular tests of the random phase approximation to the exchange-correlation energy functional

The exchange-correlation energy functional within the random phase approximation (RPA) is recast into an explicitly orbital-dependent form. A method to evaluate the functional in finite basis sets is introduced. The basis set dependence of the RPA correlation energy is analyzed. Extrapolation using large, correlation-consistent basis sets is essential for accurate estimates of RPA correlation energies. The potential energy curve of ${\mathrm{N}}_2$ is discussed. The RPA is found to recover most of the strong static correlation at large bond distance. Atomization energies of main-group molecules are rather uniformly underestimated by the RPA. The method performs better than generalized-gradient-type approximations (GGA’s) only for some electron-rich systems. However, the RPA functional is free of error cancellation between exchange and correlation, and behaves qualitatively correct in the high-density limit, as is demonstrated by the coupling strength decomposition of the atomization energy of ${\mathrm{F}}_2.$ The GGA short-range correlation correction to the RPA by Yan, Perdew, and Kurth [Phys. Rev. B 61, 16 430 (2000)] does not seem to improve atomization energies consistently.