An optimized-effective-potential method for solids with exact exchange and random-phase approximation correlation

We present a new density-functional method which does not exploit the local density approximation (LDA). In this method, we use an exchange-correlation energy which consists of the exact exchange (EXX) energy and the correlation energy in the random-phase approximation (RPA). A static approximation is used in the evaluation of the functional derivative of the RPA correlation energy. The self-consistent results for solid Cu, Fe, Co, Ni, Si, and MnO (type-II antiferromagnets) are presented. For the transition metals Cu, Fe, Co, and Ni, it is shown that the correlation potential gives rise to a large contribution which has the opposite sign to the exchange potential. The resulting eigenvalue dispersions and the magnetic moments are very close to those of the LDA and experiments. On the other hand, the Fermi-contact parts of the hyperfine field are rather different from the LDA results, and are in better agreement with experiments. The band gap obtained for Si is larger than the LDA value by similar to 0.2 eV. For MnO, the density of states shows good correspondence with data obtained by x-ray photoelectron spectroscopy and bremsstrahlung isochromat spectroscopy.