A density-functional approximation for relativistic kinetic energy

A density-functional approximation for the relativistic kinetic energy of a many-electron system is introduced, depending on the total particle density and the (nonrelativistic) kinetic energy density. The resulting scalar variational orbital equation is similar to Schrödinger’s nonrelativistic equation, but includes relativistic mass-velocity effects to all orders in p. We test the theory by computing relativistic orbitals in the uranium atom and comparing their energies and mean radii with Dirac and zeroth-order regular approximation results.