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The response of an infinite, periodic, insulating, solid to aninfinitesimally small electric field is investigated in the framework ofDensity Functional Theory. We find that the applied perturbing potential is nota unique functional of the periodic density change~: it depends also on thechange in the macroscopic {\em polarization}. Moreover, the dependence of theexchange-correlation energy on polarization induces an exchange-correlationelectric field. These effects are exhibited for a model semiconductor. We alsoshow that the scissor-operator technique is an approximate way of bypassingthis polarization dependence.Comment: 11 pages, 1 Fig

Density-Polarization Functional Theory of the Response of a Periodic Insulating Solid to an Electric Field