Functional derivative of the kinetic energy functional for spherically symmetric systems

Ensemble non-interacting kinetic energy functional is constructed for spherically symmetric systems. The differential virial theorem is derived for the ensemble. A first-order differential equation for the functional derivative of the ensemble non-interacting kinetic energy functional and the ensemble Pauli potential is presented. This equation can be solved and a special case of the solution provides the original non-interacting kinetic energy of the density functional theory. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3607313]