Dynamical aspects of correlation corrections in a covalent crystal

A central problem in one-electron band calculations is the proper inclusion of exchange and correlations. We have performed a first-principles calculation by utilizing the Green's-function method with an energy-dependent nonlocal self-energy operator obtained by replacing the Coulomb potential in the exchange operator by a dynamically screened interaction. Diamond was chosen as a prototype of covalent materials. To be consistent with a variety of experimental facts, we have taken the dielectric matrix of the medium within the time-dependent screened Hartree-Fock approximation, thereby including both local-field and electron-hole (excitonic) effects. Previous calculations along similar lines have been restricted either to a random-phase-approximation frequency-independent dielectric function or to a plasmon-pole approximation. We have investigated for the first time the role of a realistic frequency and wave-vector-dependent dielectric matrix, and examined the relative importance of the electron-hole excitations and of the plasma resonance across the range of the valence and conduction bands. The correlated band structure was calculated by diagonalizing the quasiparticle equation of motion in a local orbital basis in order to exploit the local character of both the self-energy operator and the orbitals spanning these bands. We have found that the plasma resonance does not contribute appreciably in the energy range about the band gap while it contributes significantly to the valence bandwidth. Our values of 7.4 eV (band gap) and 25.2 eV (valence band-width) are in good agreement with reflectivity and photoemission experiments. Implications for the local-density and the energy-independent Coulomb-hole plus screened-exchange approximations are discussed. In addition, our method, by utilizing an energy-dependent self-energy, has also enabled us to calculate quasiparticle damping times (specifically, intraband Auger decay rates) that are consistent with photoemission spectra.