A relativistic density functional formalism

A relativistic generalisation of the Hohenberg-Kohn-Sham density functional formalism is presented. Single-particle equations, analogous to those suggested for the non-relativistic formalism are introduced. These equations may take two forms, one analogous to the Dirac-Slater and the other analogous to Dirac-Fock relativistic self-consistent field equations. The complicated relativistic many-body effects are included in the formalism via energy functionals analogous to the exchange-correlation functionals of the non-relativistic formalism. The local density approximation for these functionals is discussed and explicit expressions are given for relativistic corrections. The relation of these corrections to the Breit interaction is mentioned. The description of magnetic effects in the relativistic formalism is discussed briefly.