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Abstract
We investigate the behavior of the kinetic and the exchange energy densities near the nuclear cusp of atomic systems. Considering hydrogenic orbitals, we derive analytical expressions near the nucleus, for single shells, as well as in the semiclassical limit of large non-relativistic neutral atoms. We show that a model based on the helium iso-electronic series is very accurate, as also confirmed by numerical calculations on real atoms up to two thousands electrons. Based on this model, we propose non-local density-dependent ingredients that are suitable for the description of the kinetic and exchange energy densities in the region close to the nucleus. These non-local ingredients are invariant under the uniform scaling of the density, and they can be used in the construction of non-local exchange-correlation and kinetic functionals.
Highlights
Kohn–Sham (KS) density functional theory (DFT) [1,2,3] can be considered the most used method in electronic calculations of quantum chemistry and condensed matter physics
We demonstrate that the 1s-shell model (1SM) approach is remarkably accurate for both kinetic and exchange energies, in the case of real atoms
This model system has been largely used in DFT [68,70,71,72], is very important for semiclassical physics [70,73,74] and has been used as a main reference system in recent generalized gradient approximation (GGA) functionals [20,55]
Summary
Kohn–Sham (KS) density functional theory (DFT) [1,2,3] can be considered the most used method in electronic calculations of quantum chemistry and condensed matter physics. We recall that while in real atoms the electrons far from the nucleus experience a screened nuclear charge so that the corresponding orbitals differ from the hydrogenic ones, for large atoms or very positive ions, this screening effect becomes vanishingly small, and the simple model of hydrogenic orbitals becomes exact [69] This model system has been largely used in DFT [68,70,71,72], is very important for semiclassical physics [70,73,74] and has been used as a main reference system in recent GGA functionals [20,55]
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