# Kinetic and Exchange Energy Densities near the Nucleus

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## Abstract

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## 1. Introduction

## 2. Kinetic and Exchange Energy Densities at the Nuclear Cusp in Spherical Systems

#### 2.1. Hydrogenic Shells

#### 2.2. Ten-Electron Hydrogenic Model

#### 2.3. The Asymptotic Neutral Atom with an Infinite Number of Electrons

#### 2.4. 1s-Shell Model

#### 2.5. Real Atoms

## 3. Non-Local Approximations for Exchange and Kinetic Energies, at and near the Nucleus

#### 3.1. Kinetic Energy

#### 3.2. Exchange Energy

## 4. Conclusions

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Error on the kinetic enhancement factor ${F}_{s}-{F}_{s}^{exact}$ versus the scaled radial distance $r/R$ near the nucleus of the Kr atom.

**Figure 2.**Kinetic energy enhancement factor ${F}_{s}$ at the nuclear cusp, for the noble atoms ($2\le Z\le 2022$); see the text for details.

**Figure 3.**Exchange enhancement factors ${F}_{x}$ at the nucleus, for the noble atoms ($2\le Z\le 2022$); see the text for details.

**Figure 4.**The scaled lengths ${\lambda}_{F}/R$ and ${\lambda}_{W}/R$, versus the scaled distance $r/R$, for noble atoms (He-Rn).

**Figure 6.**Kinetic energy enhancement factors ${F}_{s}$ versus scaled radial distance, for the Ar atom (upper panel) and the Rn atom (lower panel).

**Figure 7.**Exchange enhancement factors ${F}_{x}$ near the nucleus versus scaled radial distance, for the Ne atom (upper panel) and the Kr atom (lower panel).

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Constantin, L.A.; Fabiano, E.; Della Sala, F.
Kinetic and Exchange Energy Densities near the Nucleus. *Computation* **2016**, *4*, 19.
https://doi.org/10.3390/computation4020019

**AMA Style**

Constantin LA, Fabiano E, Della Sala F.
Kinetic and Exchange Energy Densities near the Nucleus. *Computation*. 2016; 4(2):19.
https://doi.org/10.3390/computation4020019

**Chicago/Turabian Style**

Constantin, Lucian A., Eduardo Fabiano, and Fabio Della Sala.
2016. "Kinetic and Exchange Energy Densities near the Nucleus" *Computation* 4, no. 2: 19.
https://doi.org/10.3390/computation4020019