| Abstract: | A non-local generalization K( r, r' ) of the kinetic energy t( r ) such that t( r ) = ∫K( r, r' ) dr' is defined using the idempotency property of the Hartree–Fock first-order density matrix. This is, in turn, related by means of an explicit differential equation to the non-local exchange energy density X( r, r' ). The relationship is illustrated for a couple of examples: with the Fermi-hole in a uniform electron gas, of importance in the local density version of density functional theory, and with inhomogeneous electron systems. |
