Effective nuclear charge

The electrostatic repulsion among negatively charged electrons has a large affect on the energies of orbitals. So, the ionization energy of a neutral helium atom (two electrons) is 24.58 eV compared with the 54.40 eV for that of He+ (one electron). The influence of repulsion is explained as shielding or screening. The combined influence of attraction to the repulsion and nucleus from other electrons gives an effective nuclear charge Z_eff, that is less than that (Z) of the 'bare' nucleus. One quantitative definition is from orbital energy ε using the equation:

Where R is the Rydberg constant and n is the principal quantum number. For instance, applying this equation to He (n=1) gives Zeff=1.34.

The dissimilarity between the 'bare' and the effective nuclear charge is the screening constant σ:

For instance, σ=0.66 in He, showing that the influence of repulsion from one electron on another has an effect equal to the reducing the nuclear charge through 0.66 units.