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

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.