zeff

Zeff, short for effective nuclear charge, is a concept in atomic physics and chemistry that describes the net positive charge experienced by an electron in a many-electron atom. It accounts for the shielding effect of other electrons that reduce the pull of the nucleus on a given electron.

A common approximate expression is Zeff ≈ Z − S, where Z is the atomic number and S is the shielding constant representing the cumulative repulsion from other electrons. S depends on the electron's location (core vs valence) and the arrangement of all electrons. Inner-shell electrons shield more effectively than outer-shell electrons; consequently, outer electrons experience a larger Zeff than electrons closer to the nucleus.

Zeff is not directly observable but helps explain trends in atomic structure. It is correlated with ionization energy, electron affinity, atomic radius, and electronegativity. There are different ways to estimate Zeff. Slater's rules provide a simple, historically common method to assign S and thus Zeff. More sophisticated approaches use quantum-mechanical calculations (for example, the expectation value of the electron-nucleus interaction) within the Hartree-Fock or density functional theory frameworks.

Trends: across a period Zeff for valence electrons generally increases as Z increases while shielding remains similar, leading to higher ionization energies and smaller atomic radii. Down a group, additional shells increase shielding, often offsetting the Z increase and causing Zeff to rise more slowly or even decrease for outer electrons, contributing to the observed downward trend in ionization energy and increasing atomic size.