Inhomogeneous Electron Gas

This work is a generalization of the Hohenberg---Kohn---Sham theory of the inhomogeneous electron gas, with emphasis on spin effects. An argument based on quantum electrodynamics is used to express the ground-state energy of a system of interacting electrons as a functional of the current density. Expressions are derived for coefficients appearing in an expansion of the correlation functional in terms of the linear-response functions of the homogeneous system, for a gas of almost constant four-current density. The current density contains a spin-dependent term which leads, in the nonrelativistic limit, to a local potential which is also spin dependent. This potential is applied to the problems of spin splitting of energy bands in ferromagnets and spin-density-wave antiferromagnets. The relations between the present approach, that of Slater, and the collective electron theory of ferromagnetism of Stoner are described.