Effective Nuclear Charge Calculator

Effective Nuclear Charge Calculator

The Effective Nuclear Charge Calculator estimates $Z_{eff}$, the net positive charge felt by a valence electron after shielding by inner electrons. It uses Slater's rules to approximate the shielding constant $S$ for any occupied orbital.

$$Z_{eff} = Z - S$$

where $Z$ is the nuclear charge (atomic number) and $S$ is the shielding constant. Slater's rules assign fractional shielding contributions from electrons in the same shell, the $(n-1)$ shell, and deeper shells depending on the selected orbital type.

For an $ns$ or $np$ electron with principal quantum number $n$:

• Other electrons in the same $(ns, np)$ group contribute 0.35 each (0.30 for $1s$).
• Electrons in the $(n-1)$ shell contribute 0.85 each.
• Electrons in $(n-2)$ or lower shells contribute 1.00 each.

For $nd$ or $nf$ electrons, all electrons in groups at or to the left of the selected orbital contribute 1.00 each.

Explore related tools: Atom Calculator and Bond Order Calculator.