Approximating the kinetic energy functional T s[ρ]: lessons from four-electron systems

Abstract

It is shown that for pairs of electron densities (ρα and ) obtained from mixing orbital densities in a spin-compensated four-electron system, the kinetic energy functional of the non-interacting reference system (T s[ρ]) satisfies the general inequality . This condition is discussed in the context of the gradient expansion approximation to T s[ρ] and its possible use in variational orbital-free calculations. In particular, it is shown that the second-order term of the analytic form given by von Weizsäcker violates this inequality for the considered pairs.