Non-local and non-adiabatic effects in the charge-density response of solids: a time-dependent density functional approach

The charge-density response of extended materials is usually dominated by the collective oscillation of electrons, the plasmons. Beyond this feature, however, intriguing many-body effects are observed. They cannot be described by one of the most widely used approaches for the calculation of dielectric functions, which is time-dependent density functional theory (TDDFT) in the adiabatic local density approximation (ALDA). Here we propose an approximation to the TDDFT exchange-correlation kernel which is non-adiabatic and non-local. It is derived in the homogeneous electron gas and implemented in the real system in a simple mean density approximation. This kernel contains effects that are completely absent in the ALDA; in particular, it correctly describes the double plasmon in the dynamic structure factor of sodium, and it shows the characteristic low-energy peak that appears in systems with low electronic density. It also leads to an overall quantitative improvement of spectra.