Atomic density functions: atomic physics calculations analyzed with methods from quantum chemistry

TL;DR

This paper reviews atomic density functions, introduces methods from quantum chemistry to analyze them, and demonstrates how these functions reveal chemical information and periodicity in the periodic table.

Contribution

It presents a comprehensive analysis of atomic density functions using quantum similarity and information theory, connecting atomic physics with quantum chemistry techniques.

Findings

Density functions can be expressed in multi-configuration Hartree-Fock scheme.

Quantum similarity measures effectively compare atomic density functions.

Information-theoretic concepts reveal periodicity in Mendeleev's table.

Abstract

This contribution reviews a selection of findings on atomic density functions and discusses ways for reading chemical information from them. First an expression for the density function for atoms in the multi-configuration Hartree--Fock scheme is established. The spherical harmonic content of the density function and ways to restore the spherical symmetry in a general open-shell case are treated. The evaluation of the density function is illustrated in a few examples. In the second part of the paper, atomic density functions are analyzed using quantum similarity measures. The comparison of atomic density functions is shown to be useful to obtain physical and chemical information. Finally, concepts from information theory are introduced and adopted for the comparison of density functions. In particular, based on the Kullback--Leibler form, a functional is constructed that reveals the periodicity in Mendeleev's table. Finally a quantum similarity measure is constructed, based on the integrand of the Kullback--Leibler expression and the periodicity is regained in a different way.