NOTES ON THE STATIC DIELECTRIC RESPONSE FUNCTION IN THE DENSITY-FUNCTIONAL THEORY

We discuss several aspects of the dielectric response theory applicati on to the density functional theory. This field has been an unceasing source of confusion during several decades. The most frequent reasons for this confusion are (a) uncritical transfer of the results, especia lly regarding so-called local field corrections, obtained in many-body perturbation theory onto density functional theory, and (b) mixing up the statements true for the exact density functional theory with thos e applicable to the local density approximation only. In these notes w e try to draw an appropriate lines between those theories. We also dis cuss a newly introduced (X. Gonze, Ph. Ghosez and R. W. Godby, Phys. R et,. Lett., 74, 4035, 1995) ''polarization + density functional'' and show that within a given (e.g., local density) approximation to the e xchange-correlation energy the Gonze et al. approach is exactly equiva lent to the conventional one.