Efficient calculation of exact exchange and RPA correlation energies in the adiabatic-connection fluctuation-dissipation theory

Recently there has been a renewed interest in the calculation of exact-exchange and random-phase approximation (RPA) correlation energies for realistic systems. These quantities are main ingredients of the so-called EXX/RPA+ scheme which has been shown to be a promising alternative approach to the standard local-density-approximation/generalized-gradient-approximation density-functional theory (LDA/GGA DFT) for weakly bound systems where LDA and GGA perform poorly. In this paper, we present an efficient approach to compute the RPA correlation energy in the framework of the adiabatic-connection fluctuation-dissipation formalism. The method is based on the calculation of a relatively small number of eigenmodes of RPA dielectric matrix, efficiently computed by iterative density response calculations in the framework of density functional perturbation theory. We will also discuss a careful treatment of the integrable divergence in the exact-exchange energy calculation which alleviates the problem of its slow convergence with respect to Brillouin-zone sampling. As an illustration of the method, we show the results of applications to bulk Si, Be dimer, and atomic systems.