Complexity in atoms: an approach with a new analytical density

TL;DR

This paper introduces a new analytical density model inspired by the Tietz potential to calculate atomic complexity, revealing its increase with atomic number due to relativistic effects, and fits well with non-relativistic Hartree-Fock results.

Contribution

A novel analytical density based on the Tietz potential model is proposed for atomic systems, incorporating relativistic corrections and fitting non-relativistic Hartree-Fock data.

Findings

Complexity increases with atomic number due to relativistic effects.

The analytical density accurately reproduces non-relativistic Hartree-Fock results.

Relativistic corrections significantly impact the complexity trend.

Abstract

In this work, the calculation of complexity on atomic systems is considered. In order to unveil the increasing of this statistical magnitude with the atomic number due to the relativistic effects, recently reported in [A. Borgoo, F. De Proft, P. Geerlings, K.D. Sen, Chem. Phys. Lett., 444 (2007) 186], a new analytical density to describe neutral atoms is proposed. This density is inspired in the Tietz potential model. The parameters of this density are determined from the normalization condition and from a variational calculation of the energy, which is a functional of the density. The density is non-singular at the origin and its specific form is selected so as to fit the results coming from non-relativistic Hartree-Fock calculations. The main ingredients of the energy functional are the non-relativistic kinetic energy, the nuclear-electron attraction energy and the classical term of the electron repulsion. The relativistic correction to the kinetic energy and the Weizsacker term are also taken into account. The Dirac and the correlation terms are shown to be less important than the other terms and they have been discarded in this study. When the statistical measure of complexity is calculated in position space with the analytical density derived from this model, the increasing trend of this magnitude as the atomic number increases is also found.