Notes on the static dielectric response function in the density functional theory

TL;DR

This paper clarifies the application of dielectric response theory within density functional theory, addressing common confusions and comparing different approaches to improve understanding and correct usage.

Contribution

It distinguishes between the exact and local density approximation theories and shows the equivalence of a recent polarization+density functional approach to conventional methods.

Findings

Clarifies distinctions between theories to reduce confusion.

Shows equivalence of polarization+density functional to conventional approaches.

Highlights proper application of dielectric response in DFT.

Abstract

We discuss several aspects of the dielectric response theory application 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 tranfer of the results, especially 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 those applicable to the local density approximation only. In these notes we try to draw an appropriate lines between those theories. We also discuss a newly introduced (X. Gonze, Ph. Ghosez, and R.W. Godby, Phys. Rev. Lett., 74, 4035, 1995) "polarization+density functional" and show that within a given (e.g., local density) approximation to the exchange-correlation energy the Gonze et al approach is exactly equivalent to the conventional one.