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: T <inf>s</inf>[ρ] = T<inf>w</inf>[ρ] + ∑<inf>I</inf> ∫ <inf>ΩI</inf> d³r<inf>I</inf>ρ^5/3(r <inf>I</inf>)[1 + r<inf>I</inf> · ▽<inf>rI</inf> 1n λ(r <inf>I</inf>)]^-2/3 × [3 + r<inf>I</inf> · ▽ <inf>rI</inf> 1n λ(r<inf>I</inf>)]²[τ<inf>N</inf> ^I(r<inf>I</inf>) + τ<inf>N</inf>^C(r<inf>I</inf>) + κ<inf>N</inf>^I(r<inf>I</inf>) + κ<inf>N</inf> ^C(r<inf>I</inf>)], where λ(r) is the local-scaling transformation function, T<inf>w</inf>[ρ] is the von Weiszäcker term and τ<inf>N</inf>^I(r<inf>I</inf>) and κ<inf>N</inf> ^I(r<inf>I</inf>) are the radial and angular enhancement factors, respectively, within an atomic domain Ω<inf>I</inf>. The terms τ <inf>N</inf>^C(r<inf>I</inf>) and τ<inf>N</inf>^C(r <inf>I</inf>) (where C stands for "complement of I") contain all contributions to the radial and angular enhancement factors within Ω <inf>I</inf> coming from the "tails" of functions centered on nuclei outside Ω<inf>I</inf>. 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<inf>s</inf>[ρ].

Año de publicación:

2003

Keywords:

• DFT
• Local-scaling transformations
• Kinetic energy functional

Fuente:

scopus