A Density Functional Formalism for Condensed Matter Systems

Abstract

A very large part of research in condensed matter physics may be considered as investigations of inhomogeneous electron systems. The inhomogeneities are due to nuclear charges located in certain geometrical forms (single nuclear charge for an atom, a small number of several nuclear charges distributed spatially to form small molecules, or a large number of nuclei arranged in a regular spatial three-dimensional array to form a solid etc.). We will not be interested here in amorphous systems even though a density functional scheme is being used in the liquid state research. Also we will not be interested in the detailed properties of the nuclei themselves and treat them as merely positively charged entities with no intrinsic character to them. One class of questions concerns the electronic properties including its spin effects and our main attention will be focussed on these. There have been some attempts to examine nuclear motions (molecular vibrations and phonons in solids) using density functional formalism; but this has not yet been explored fully as will be pointed out later. The central theme in the original density-functional formalism was that the ground state (equilibrium) properties depend only on the ground state (equilibrium) density of the electrons and the nuclei. Stated in this way, we may think of these problems as another facet of Relativistic Quantum Electrodynamics of many electrons and structureless charge compensating nuclei, which for all practical purposes can be treated as classical objects.