Current-density functional theory of the response of solids

The response of an extended periodic system to a homogeneous field (of wave-vector $q=0)$ cannot be obtained from a $q=0\mathrm{}$ time-dependent density functional theory (TDDFT) calculation, because the Runge-Gross theorem does not apply. Time-dependent current–density functional theory is needed and demonstrates that one key ingredient missing from TDDFT is the macroscopic current. In the low-frequency limit, in certain cases, density polarization functional theory is recovered and a formally exact expression for the polarization functional is given.