The behaviors of the positive definite Kohn-Sham kinetic energy density near the origin and at the asymptotic region play a major role in designing meta-generalized gradient approximations (meta-GGAs) for exchange in low-dimensional quantum systems. It is shown that near the origin of the parabolic quantum dot, the Kohn-Sham kinetic energy differs from its von Weizsäcker counterpart due to the p orbital contributions, whereas in the asymptotic region, the difference between the above two kinetic energy densities goes as . All these behaviors have been explored using the two-dimensional isotropic quantum harmonic oscillator as a test case. Several meta-GGA ingredients are then studied by making use of the above findings. Also, the asymptotic conditions for the exchange energy density and the potential at the meta-GGA level are proposed using the corresponding behaviors of the two kinetic energy densities.
Exploration of near the origin and the asymptotic behaviors of the Kohn-Sham kinetic energy density for two-dimensional quantum dot systems with parabolic confinement
Subrata Jana, Prasanjit Samal; Exploration of near the origin and the asymptotic behaviors of the Kohn-Sham kinetic energy density for two-dimensional quantum dot systems with parabolic confinement. J. Chem. Phys. 14 January 2018; 148 (2): 024111. https://doi.org/10.1063/1.5009495
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