Abstract
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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Martin, R.M. (1998). Density polarization functional theory. In: Joubert, D. (eds) Density Functionals: Theory and Applications. Lecture Notes in Physics, vol 500. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0106734
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DOI: https://doi.org/10.1007/BFb0106734
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