Hierarchical Response Theory of Electronegativity from Atomic Mean Inner Potential
Abstract
Electronegativity remains conceptually ambiguous: is it a fixed atomic constant, or does it depend on the chemical environment? We resolve this debate by recasting electronegativity as a continuous response function rooted in the Atomic Mean Inner Potential (AMIP). Building on the established static scale χAMIP,1/2, we expand the electronegativity in fractional positive charge δ. The first-order term defines the Electrostatic Rigidity ℛ, whose sign indicates whether an atom hardens or softens upon oxidation, and the second-order term defines the Electrostatic Anharmonic Modulus 𝒜. A logarithmic-derivative decomposition separates ℛ into an intrinsic, scale-independent response asymmetry 𝒟 ≡ ℛΩ/Ω0 − ℛf/f0, which governs the competition between electronic screening loss (softening) and geometric volume collapse (hardening). Applying this to all 102 elements reveals a systematic dichotomy between softening main-group elements and hardening d-block elements, two scaling laws within the transition series, and two anomalies at half-filled d5 configurations and in Ce. The framework resolves the Cs--Fr controversy through relativistic analysis, reproduces classical electronegativity scales and Lewis acidity trends, and provides three falsifiable experimental predictions. It transforms electronegativity into a predictive, hierarchically structured quantum descriptor.
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BibTeX
@misc{zheng2026hierarchical,
title = {{Hierarchical Response Theory of Electronegativity from Atomic Mean Inner Potential}},
author = {Jin-Cheng Zheng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29765},
eprint = {2610.29765},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29765},
}
RIS
TY - UNPB
TI - Hierarchical Response Theory of Electronegativity from Atomic Mean Inner Potential
AU - Jin-Cheng Zheng
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.29765
UR - https://arxiv.org/abs/2610.29765
AB - Electronegativity remains conceptually ambiguous: is it a fixed atomic constant, or does it depend on the chemical environment? We resolve this debate by recasting electronegativity as a continuous response function rooted in the Atomic Mean Inner Potential (AMIP). Building on the established static scale χ_AMIP,1/2, we expand the electronegativity in fractional positive charge δ. The first-order term defines the Electrostatic Rigidity ℛ, whose sign indicates whether an atom hardens or softens upon oxidation, and the second-order term defines the Electrostatic Anharmonic Modulus 𝒜. A logarithmic-derivative decomposition separates ℛ into an intrinsic, scale-independent response asymmetry 𝒟 ≡ ℛ_Ω/Ω_0 − ℛ_f/f_0, which governs the competition between electronic screening loss (softening) and geometric volume collapse (hardening). Applying this to all 102 elements reveals a systematic dichotomy between softening main-group elements and hardening d-block elements, two scaling laws within the transition series, and two anomalies at half-filled d^5 configurations and in Ce. The framework resolves the Cs--Fr controversy through relativistic analysis, reproduces classical electronegativity scales and Lewis acidity trends, and provides three falsifiable experimental predictions. It transforms electronegativity into a predictive, hierarchically structured quantum descriptor.
ER -