Kinetic energy in density-functional theory

While Kohn-Sham theory uses the quantum-mechanical operator for kinetic energy, Thomas-Fermi theory replaces this with an effective local potential. If both theories are based on the exact universal density functional defined by Hohenberg-Kohn theory, it is an interesting question whether they should give the same results for N-electron ground states. This question is examined and answered in the negative. The inconsistency is resolved only by extending the definition of functional derivatives to encompass linear operators. An exact theory must incorporate one-electron energies and occupation numbers derived from Kohn-Sham theory.