Kohn-Sham Kinetic Energy Density in the Nuclear and Asymptotic Regions: Deviations from the Von Weizs'acker Behavior and Applications to Density Functionals

摘要

We show that the Kohn-Sham positive-definite kinetic energy (KE) densitysignificantly differs from the von Weizs\"acker (VW) one at the nuclear cusp aswell as in the asymptotic region. At the nuclear cusp, the VW functional isshown to be linear and the contribution of p-type orbitals to the KE density istheoretically derived and numerically demonstrated in the limit of infinitenuclear charge, as well in the semiclassical limit of neutral large atoms. Inthe latter case, it reaches 12 of the KE density. In the asymptotic region wefind new exact constraints for meta Generalized Gradient Approximation(meta-GGA) exchange functionals: with an exchange enhancement factorproportional to $\sqrt{\alpha}$, where $\alpha$ is the common meta-GGAingredient, both the exchange energy density and the potential are proportionalto the exact ones. In addition, this describes exactly the large-gradient limitof quasi-two dimensional systems.