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In the presence of a (time-dependent) macroscopic electric field the electrondynamics of dielectrics cannot be described by the time-dependent density only.We present a real-time formalism that has the density and the macroscopicpolarization P as key quantities. We show that a simple local function of Palready captures long-range correlation in linear and nonlinear opticalresponse functions. Specifically, after detailing the numerical implementation,we examine the optical absorption, the second- and third-harmonic generation ofbulk Si, GaAs, AlAs and CdTe at different level of approximation. We highlightlinks with ultranonlocal exchange-correlation functional approximationsproposed within linear response time-dependent density functional theoryframework.

Dielectrics in a time-dependent electric field: a real-time approach based on density-polarization functional theory