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First-Principles Electronegativity Scale from the Atomic Mean Inner Potential

Jin-Cheng Zheng

Abstract

Electronegativity is a cornerstone of chemical intuition, essential for rationalizing bonding, reactivity, and material properties. However, prevailing scales remain empirically derived, often relying on parameterized models or composite physical quantities. In this work, we introduce a universal electronegativity scale founded on the atomic mean inner potential (AMIP), also known as the average Coulomb potential, a fundamental, quantum-mechanical property accessible through both first-principles computation and electron-scattering experiments. Our scale, denoted $χ_{\mathrm{AMIP},p}$, is an analytic function of just three ground-state atomic descriptors and carries explicit physical units. It demonstrates excellent agreement with established scales and successfully classifies bonding types across 358 compounds, including adherence to the metalloid ``Si rule". Beyond replicating known trends, $χ_{\mathrm{AMIP,1/2}}$ proves to be a powerful predictive tool, accurately determining Lewis acid strengths for over 14,000 coordination environments ($R^2=0.93$) and $γ$-ray annihilation spectral widths for 36 elements ($R^2=0.97$), outperforming previous methods. By linking electronegativity directly to a measurable quantum property, this work provides a unified and predictive descriptor for electronic structure and chemical behavior across the periodic table.

First-Principles Electronegativity Scale from the Atomic Mean Inner Potential

Abstract

Electronegativity is a cornerstone of chemical intuition, essential for rationalizing bonding, reactivity, and material properties. However, prevailing scales remain empirically derived, often relying on parameterized models or composite physical quantities. In this work, we introduce a universal electronegativity scale founded on the atomic mean inner potential (AMIP), also known as the average Coulomb potential, a fundamental, quantum-mechanical property accessible through both first-principles computation and electron-scattering experiments. Our scale, denoted , is an analytic function of just three ground-state atomic descriptors and carries explicit physical units. It demonstrates excellent agreement with established scales and successfully classifies bonding types across 358 compounds, including adherence to the metalloid ``Si rule". Beyond replicating known trends, proves to be a powerful predictive tool, accurately determining Lewis acid strengths for over 14,000 coordination environments () and -ray annihilation spectral widths for 36 elements (), outperforming previous methods. By linking electronegativity directly to a measurable quantum property, this work provides a unified and predictive descriptor for electronic structure and chemical behavior across the periodic table.
Paper Structure (17 sections, 29 equations, 9 figures, 3 tables)

This paper contains 17 sections, 29 equations, 9 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Results
  3. Mean Inner Potential
  4. Electronegativity from the Atomic Mean Inner Potential
  5. Comparison with other electronegativity scales
  6. Applications
  7. Classification of Metals and Nonmetals
  8. Bonding Classification via Electronegativity
  9. Correlation with Lewis Acid Strength
  10. Correlation with $\gamma$-Ray Spectral Width
  11. Discussions
  12. Dependence of the AMIP-Based Electronegativity on the Exchange--Correlation Functional
  13. Relation to Electronegativity as Electronic Chemical Potential
  14. Experimental accessibility and uncertainty of AMIP
  15. Prospects for Pressure-Dependent Electronegativity
  16. ...and 2 more sections

Figures (9)

  • Figure 1: The forward electron scattering factor $f^{(e)}(0)$ (a), the valence radius $r_{v}$ (b), and atomic mean inner potential $v_{0}$ (c) for elements across the entire periodic table (from H (1) to No (102)).
  • Figure 2: Correlation between the proposed electronegativity scales and the Pauling scale ($\chi_P$) for main-group elements. (a) $\chi_P$ versus $\chi_{\mathrm{AMIP},1}$, fitted to a function of the form $a\sqrt{x}+c$, revealing a nonlinear relationship. (b) $\chi_P$ versus $\chi_{\mathrm{AMIP},1/2}$, fitted to a linear function $a x + c$ ($a=0.519$, $c=0.349$), demonstrating a strong linear correlation.
  • Figure 3: Periodic table of elements (from H (1) to No (102)) showing the three proposed electronegativity scales, $\chi_{\mathrm{AMIP}}$ (V), $\chi_{\mathrm{AMIP},1/2}$ (V$^{1/2}$), and $\chi_{\mathrm{AMIP},1/2}^H$ (dimensionless).
  • Figure 4: Parity plots comparing the proposed $\chi_{\text{AMIP},1/2}$ scale with various established electronegativity scales for main-group elements. The fitting results are listed below: $\chi_{\text{P}}$ = 0.519382$\chi_{\text{AMIP},1/2}$ + 0.349086, $\chi_{\text{A}}$ = 0.546745$\chi_{\text{AMIP},1/2}$ + 0.262706, $\chi_{\text{AR}}$ = 0.521839$\chi_{\text{AMIP},1/2}$ + 0.261769, $\chi_{\text{M}}$ = 1.2617$\chi_{\text{AMIP},1/2}$ + 0.985428, $\chi_{\text{TO}}$ = 0.350907$\chi_{\text{AMIP},1/2}$ + 1.70328, $\chi_{\text{RZH}}$ = 3.0165$\chi_{\text{AMIP},1/2}$ + 1.94308,
  • Figure 5: Comparison of the proposed electronegativity scale $\chi^{\mathrm{H}}_{\mathrm{AMIP},1/2}$ with classical electronegativity scales: (a) Pauling, (b) Allen, and (c) Mulliken, for elements across the entire periodic table (from H (1) to No (102)). The coefficients of determination ($R^2$) between $\chi^{\mathrm{H}}_{\mathrm{AMIP},1/2}$ and the Pauling, Allen, and Mulliken scales are 0.8836, 0.9670, and 0.8732, respectively, as shown in panels (d)–(f). Note that the Mulliken scale has been rescaled to Pauling units. The $R^2$ values between $\chi^{\mathrm{H}}_{\mathrm{AMIP},1/2}$ and more recent electronegativity scales are also shown: (g) Rahm–Zeng–Hoffmann (RZH), 0.9169; (h) Dong–Oganov–Cui–Zhou–Wang (DOCZW), 0.8402; and (i) Oganov–Kostenko (OK), 0.8581.
  • ...and 4 more figures