Title: Role of Kohn-Sham Kinetic Energy Density in Designing Asymptotically Correct Semilocal Exchange-Correlation Functionals in Two Dimensions,
Abstract: The positive definite Kohn-Sham kinetic energy(KS-KE) density plays crucial
role in designing semilocal meta generalized gradient approximations(meta-GGAs)
for low dimensional quantum systems. It has been rigorously shown that near
nucleus and at the asymptotic region, the KE-KS differ from its von
Weizsäcker(VW) counterpart as contributions from different orbitals (i.e.,
s and p orbitals) play important role. This has been explored using two
dimensional isotropic quantum harmonic oscillator as a test case. Several
meta-GGA ingredients with different physical behaviors are also constructed and
further used to design an accurate semilocal functionals at meta-GGA level. In
the asymptotic region, a new exchange energy functional is constructed using
the meta-GGA ingredients with formally exact properties of the enhancement
factor. Also, it has been shown that exact asymptotic behavior of the exchange
energy density and potential can be attained by choosing accurately the
enhancement factor as a functional of meta-GGA ingredients.