Fully parameter-free calculation of optical spectra for insulators, semiconductors and metals from a simple polarization functional

We present a fully parameter-free density-functional approach for the accurate description of optical absorption spectra of insulators, semiconductors and metals. We show that this can be achieved within time-dependent current-density-functional theory using a simple dynamical polarization functional. We derive this functional from physical principles that govern optical spectra. Our method is truly predictive because not a single parameter is used. In particular, we do not use an \textit{ad-hoc} material-dependent broadening parameter to compare theory to experiment as is usually done. Our approach is numerically efficient; the cost equals that of a calculation within the random-phase approximation.