Completely local relativistic density-functional theory: The role of the virial

Starting from a completely local relativistic density-functional theory, the total kinetic energy is first related to the virial plus contributions from the chemical potential of the electron cloud and classical potential-energy terms. Using the derivative of the Euler equation of the theory, the force term is then replaced in the virial by a function of the ground-state electron density. The theory is exemplified by two examples: (a) the relativistic Thomas-Fermi theory due to Vallarta and Rosen, and (b) heavy atoms in intense magnetic fields.