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

Abstract.

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: where λ(r) is the local-scaling transformation function, T _W[ρ] is the von Weiszäcker term and τ^l _N (r _l ) and κ^l _N (r _l ) are the radial and angular enhancement factors, respectively, within an atomic domain Ω_I. The terms τ^C _N (r _l ) and τ^C _N (r _l ) (where C stands for “complement of I”) contain all contributions to the radial and angular enhancement factors within Ω_I coming from the “tails” of functions centered on nuclei outside Ω_I. 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 T _s[ρ].