Exact and approximate forms of the kinetic energy functional Ts[ρ] for molecules obtained via local-scaling transformations

By means of a constructive procedure based on local-scaling transformations, we have obtained the following exact form for the noninteractive kinetic energy functional of general molecular systems: [inline-graphic not available: see fulltext] where λ(r) is the local-scaling transformation function, TW[ρ] is the von Weiszäcker term and τlN(rl) and κlN(rl) are the radial and angular enhancement factors, respectively, within an atomic domain ΩI. The terms τCN(rl) and τCN(rl) (where C stands for “complement of I”) contain all contributions to the radial and angular enhancement factors within ΩI coming from the “tails” of functions centered on nuclei outside ΩI. Also, in the context of an “atoms-in-a-molecule” approach, we discuss the construction of approximations to the kinetic energy enhancement factors appearing in the previous expression for Ts[ρ].