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The frequency-dependent exchange-correlation potential, which appears in theusual Kohn-Sham formulation of a time-dependent linear response problem, is astrongly nonlocal functional of the density, so that a consistent local densityapproximation generally does not exist. This problem can be avoided by choosingthe current-density as the basic variable in a generalized Kohn-Sham theory.This theory admits a local approximation which, for fixed frequency, is exactin the limit of slowly varying densities and perturbing potentials.

Current-Dependent Exchange-Correlation Potential for Dynamical Linear Response Theory