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 (DC), i.e., the functional for a system confined in $d-1$ spatial dimensions must result from the functional for the d-dimensional system when its density profile becomes a δ 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 at the DC. We conclude that the weighted density approximation is the best suited to describe the strict DC, but it fails to describe systems with a small, but finite, width along the constrained coordinate. In contrast, the average density approximations, which diverge at the strict DC, are the best functionals to describe these highly inhomogeneous systems close to the DC.

• Received 9 October 1998

DOI:https://doi.org/10.1103/PhysRevA.62.014501