Exchange and correlation effects beyond the LDA on the dielectric function of silicon

local-field effects into account. The results, compared with those obtained in the local-density approximation, show a limited reduction of the well-known overestimation of the macroscopic dielectric constant. Results obtained for optical and energy loss spectra are also presented. @S0163-1829~99!00344-6# I. INTRODUCTION Density-functional theory 1‐3 provides a formally exact tool for the description of all the ground-state properties of many-electron systems at zero temperature, starting from first principles. The only essential approximation introduced in actual calculations is in the exchange-correlation term of the energy functional, since its exact form is unknown. The most widely used expression for the exchange-correlation functional is obtained in the local-density approximation ~LDA!, 3 which, over the past 20 years, has been shown to yield results for crystal structures, lattice constants, elastic constants, and phonon frequencies within a few percent from the experiment, for a wide class of materials. 4,5 A remarkable exception is the static macroscopic dielectric constant « M , whose value is substantially overestimated by density-functional theory ~DFT! LDA. 6‐8 The exact amount of such an overestimate depends on the lattice constant used in the calculation ~and on other factors as pseudopotential types, basis sets, etc. ! but it ranges always between 12% and 18%. This point deserves an accurate discussion. The macroscopic dielectric constant of a system is related to the change in the electronic ground state induced by an external perturbing electrostatic potential dVext . Since, within DFT, the ground-state density r can be computed ~at least in principle! exactly, for both the unperturbed and perturbed systems, the difference dr5(r pert2r 0) can also be obtained exactly. Hence, treating adequately the variation of the external potential ~either by a direct approach or by using perturbation theory!, the dielectric constant should come out correctly within DFT. The large discrepancy with the experiments seems hence to be uniquely due to the LDA. However, it has been recently argued that this is not necessarily true. 9‐11 On the other hand, Levine and Allan 12 performed calculations of « M within a quasiparticle scheme, i.e., in the framework of an excited-state theory. They obtained a value of « M for Silicon within 3% from experiment. However, as pointed out by Dal Corso, Baroni, and Resta, 13 there is no immediate justification for the failure of DFT.