Analytic energy gradients for the self-consistent direct random phase approximation

Analytic energy gradients with respect to nuclear coordinates are derived and implemented for the self-consistent direct random phase approximation (sc-dRPA) method. In contrast to the more common non-self-consistent dRPA methods, the sc-dRPA method does not require a choice for the approach to generate the Kohn-Sham orbitals and eigenvalues serving as input for the dRPA correlation functional. The fact that the sc-dRPA total energy is variational facilitates the calculation of analytic gradients. The analytic gradients are tested against numerical ones and then used to calculate equilibrium geometries and vibrational frequencies for various molecules including weakly bonded dimers and transition metal compounds. The sc-dRPA method can compete in accuracy with Møller-Plesset perturbation theory of second order and with conventional density-functional methods within the generalized gradient approximation or of hybrid type. Indeed, sc-dRPA geometries and vibrational frequencies are most accurate in many cases. Moreover, the sc-dRPA method is robust in the sense that it is applicable to all considered molecules, whereas conventional density-functional methods are not applicable to dispersion bonded dimers, and Møller-Plesset perturbation theory of second order erroneously predicts a number of molecules to be unbound and yields completely wrong vibrational frequencies in some cases. The coupled cluster singles doubles methods yield geometries and vibrational frequencies of a quality that is inferior to that of the other considered methods.