We extend the capabilities of correlation energy functionals based on the adiabatic-connection fluctuation-dissipation theorem by implementing the analytical atomic forces within the random phase approximation (RPA), in the context of plane waves and pseudopotentials. Forces are calculated at self-consistency through the optimized effective potential method and the Hellmann-Feynman theorem. In addition, non-self-consistent RPA forces, starting from the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation, are evaluated using density functional perturbation theory. In both cases, we find forces of excellent numerical quality. Furthermore, for most molecules and solids studied, self-consistency is found to have a negligible impact on the computed geometries and vibrational frequencies. The RPA is shown to systematically improve over PBE and, by including the exact-exchange kernel within RPA $+$ exchange (RPAx), through finite-difference total energy calculations, we obtain an accuracy comparable to advanced wave-function methods. Finally, we estimate the anharmonic shift and provide accurate theoretical references based on RPA and RPAx for the zone-center optical phonon of diamond, silicon, and germanium.

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• Electronic structure
• Phonons
• Diamond structure
• Molecules
• Density functional theory
• Random phase approximation