Density Functionals: Theory and Applications Proceedings of the Tent
This book is an excellent introduction to density functional theory for electrons. Largely written in review style, it will also serve as an excellent overview of recent developments. Nonrelativistic and relativistic approaches are discussed and conventio
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A b s t r a c t . At the center of density functional theory (DFT) are the proofs by Hohenberg and Kohn, which show that all properties of quantum many-body systems are functionals of the ground state density, and the Kohn-Sham construction, in which the exchange-correlation energy is a functional only of the density. DFT has been widely assumed to apply directly to the static dielectric properties of insulators. However, in 1995, Godby, Ghosez, and Godby pointed out that the assumptions of HK do not strictly apply to the case of a crystal in a finite electric field, since there is no ground state, and they argued that the description of intrinsic bulk dielectric phenomena in a crystal requires a functional of both the bulk density and the polarization. Here we summarize the status of recent work, especially a detailed exposition given elsewhere by the present author and G. Ortiz. The primary goal is to construct a density-polarization functional theory that will provide a fundamental basis for the theory of dielectrics, which is formulated in terms of polarization and electric fields. The consequences of the ideas presented here are: 1) it is essential to use polarization in order to describe the long wavelength limit; 2) physically meaningful changes in polarization can be derived directly from the wavefunction; and 3) DFT must be generalized to a density-polarization functional theory in order to fully describe the dielectric behavior of materials.
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Introduction
The purpose of these lecture notes is to survey recent work that brings together two of the basic aspects of the theory of condensed matter: the description of dielectric phenomena [1-4] and density functional theory [5-8]. The consequence of this analysis is that in order to describe intrinsic bulk dielectric properties of an insulator in terms of only properties defined in the bulk, even in the static low frequency limit, the bulk density alone is not sufficient;
in general, the state of the many-electron quantum system is a functional not only of the bulk density, but also of the macroscopic polarization. Since the exchange and correlation are in general functionals of the polarization as well as the density, this also leads to changes in the form of the Kohn-Sham (KS) [6] equations needed to describe polarized dielectrics. Since this is a controversial idea for a conference on density functional theory, it is important to review the ideas and state clearly the particular circumstances in which it is argued that the density is not sufficient. In the opinion of the author, this exercise is especially valuable because it requires a thorough analysis of the assumptions behind density functional theory, as well as the problems associated with the theory of dielectrics, which deepens our understanding of
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Richard M. Martin
both areas. This summary is based primarily upon work with G. Ortiz which is described in more detail in a set of papers, [9-12] especially a paper by Martin and Ortiz to be published in 1997 which will be referred to here as
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