Total energy of solids: An exchange and random-phase approximation correlation study

Total energies of solids are calculated by an ab initio method based on the Green's-function theory. Green's function is constructed from one-body wave functions and eigenvalues obtained in the local-density approximation (LDA) to density-functional theory, and the correlation energy is estimated within the random-phase approximation. The scheme is applied to Na and Si. In both cases, the equilibrium lattice constants are in reasonable agreement with experiments. The role of the exchange-correlation energy in the total-energy curve is discussed in detail in comparison with the LDA.