Atomic size, ionization energy, polarizability, asymptotic behavior, and the Slater–Zener model

We employ the Slater–Zener model to relate effective atomic radius to ionization energy: r e = na 0 I H / I ¯ v ; n is the principal quantum number of the valence shell, a0 is the Bohr radius, IH is the ionization energy of the hydrogen atom, and I ¯ v is the average valence ionization energy. Along a given row in the periodic table, these semi-empirical radii correlate linearly with theoretical Hartree–Fock radii, semi-empirical radii derived from static dipole polarizability, and empirical covalent radii. Correlation of radii column by column is not as accurate, but still respectable. The asymptotic electron density varies as exp ( - 2 2 I ¯ v r ) , which reverts to exp ( - 2 2 I 0 r ) upon invoking the frozen orbital approximation.