Revisiting the Z-dependence of the electron density at the nuclei

TL;DR

This paper introduces a new formula relating electron density at the nucleus to atomic number, providing more accurate predictions than previous models and simplifying related atomic equations.

Contribution

A novel formula for rho(0,Z) that outperforms previous models in accuracy and simplifies atomic correlation energy equations.

Findings

New formula fits ab initio data more precisely

Reduces error by an order of magnitude

Simplifies equations involving atomic properties

Abstract

A new formula that relates the electron density at the nucleus of atoms,rho(0,Z), and the atomic number,Z, is proposed. This formula,rho(0,Z)=a(Z-bZ^(0.5))^3, contains two unknown parameters (a,b) that are derived using a least square regression to the ab initio derived rho(0,Z) of Koga dataset from He (Z=2) to Lr (Z=103) atoms (Theor Chim Acta 95, 113 (1997)). In comparison to the well-known formula,rho(0,Z)=aZ^b, used for the same purpose previously, the resulting new formula is capable of reproducing the ab initio rho(0,Z) dataset an order of magnitude more precisely without introducing more regression parameters. This new formula may be used to transform the equations that relate correlation energy of atoms and rho(0,Z) into simpler equations just containing the atomic number as a fundamental property of atoms.