Variational Definition of Electronegativity from the Principle of Least Action

Electronegativity is a cornerstone of chemical theory, yet its traditional definitions remain empirical. Here, a variational definition of electronegativity (\( χ_V \)χV) is proposed, derived directly from the principle of least action. In this framework, the ratio between the effective nuclear charge (Zeff\( Z_eff \)) and the principal quantum number (\( n^* \)n*) quantifies the deviation of an atom from its stationary (minimal-action) configuration, yielding \( \) χV=κ[(Zeff/n* )2-1] , with a single universal constant (κ) fixed using fluorine. The scale reproduces periodic trends without empirical fitting and shows strong linear correlations with Pauling, Mulliken, and Allen electronegativities (r = 0.91–0.97, R² ≈ 0.9). χV also exhibits a nearly perfect proportionality with the first ionization energy (r = 0.9999) and an inverse-square dependence on atomic radius (R² = 0.904). When applied to 47 diatomic molecules, predicted bond-dissociation energies yield a mean absolute error of 15.8 kJ mol⁻¹—slightly lower than Pauling’s classical relation. These results demonstrate that electronegativity can be interpreted as a quantified deviation from the condition of least action, bridging atomic structure, energy, and reactivity within a unified physical framework.