Hierarchical Response Theory of Electronegativity from Atomic Mean Inner Potential

Abstract

Electronegativity, introduced by Pauling nearly a century ago, remains chemistry's most widely used yet conceptually ambiguous quantity: is it a fixed atomic constant, or does it depend on chemical environment? We resolve this debate by recasting electronegativity as a continuous response function rooted in the Atomic Mean Inner Potential (AMIP), a quantum-mechanical observable accessible through first-principles calculation and, ultimately, electron holography. Expanding the AMIP with respect to fractional electron removal defines a hierarchy of physically distinct coefficients: the static electronegativity $χ_0$, the Electrostatic Rigidity $\mathcal{R}$---whose sign indicates whether an atom hardens or softens upon oxidation---and the Electrostatic Anharmonic Modulus $\mathcal{A}$. A logarithmic-derivative decomposition links these coefficients to two competing microscopic channels, electronic screening loss and geometric volume collapse, whose balance governs the response of all 102 elements. This competition produces a systematic dichotomy between softening main-group elements and hardening d-block elements, two scaling laws within the transition series (closed-shell stiffening and principal quantum softening), and two anomalies: a pronounced exchange-driven effect at half-filled d$^{5}$ configurations and a near-perfect cancellation in Ce. It also resolves the long-standing Cs--Fr controversy, identifying Fr as a critical element whose near-boundary response is amplified fivefold by relativistic contraction of the 7s orbital. The framework reproduces the classical Allen, Pauling, and Mulliken scales as well as Lewis acidity trends, and makes three falsifiable experimental predictions. It transforms electronegativity from a lookup-table number into a predictive, hierarchically structured quantum descriptor.