Dimensional crossover of the kinetic-energy electronic density functional - art. no. 014501

In the density-functional formalism (DFF), the ground state of any electron system is described by a unique universal energy functional of the density . Thus the functional has to describe properly the dimensional crossover (D C), i.e., the functional for a system confined in d-1 spatial dimensions mu st result from the functional for the d-dimensional system when its density profile becomes a delta function along one of the coordinates. As a first step in the study of DC within DFF for electron systems, we present a study of the ability of density kinetic-energy functionals to behave correctly a t the DC. We conclude that the weighted density approximation is the best s uited to describe the strict DC, but it fails to describe systems with a sm all, but finite, width along the constrained coordinate. In contrast, the a verage density approximations, which diverge at the strict DC, are the best functionals to describe these highly inhomogeneous systems close to the DC .