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arxiv: 2603.10523 · v2 · submitted 2026-03-11 · ❄️ cond-mat.mtrl-sci · physics.chem-ph· quant-ph

Recognition: 2 theorem links

· Lean Theorem

First-Principles Electronegativity Scale from the Atomic Mean Inner Potential

Jin-Cheng Zheng
Authors on Pith no claims yet

Pith reviewed 2026-05-15 13:41 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci physics.chem-phquant-ph
keywords electronegativitymean inner potentialfirst-principleschemical bondingLewis acidityperiodic trendsgamma-ray spectra
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The pith

Electronegativity equals an analytic function of three ground-state atomic descriptors taken from the mean inner potential.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper constructs a first-principles electronegativity scale directly from the atomic mean inner potential, a measurable quantum property. The resulting scale, expressed as a simple analytic expression in three atomic quantities, carries explicit physical units and requires no empirical fitting. It reproduces established electronegativity trends, correctly assigns bonding character in 358 compounds, and delivers strong numerical predictions for Lewis acid strengths and gamma-ray spectral features. A reader should care because the approach replaces parameterized tables with a direct link to a fundamental, computable and observable quantity.

Core claim

Electronegativity is defined as the scale χ_AMIP,p, an analytic function of three ground-state atomic descriptors extracted from the atomic mean inner potential; this construction matches conventional scales, classifies bonding types across hundreds of compounds, and predicts Lewis acid strengths for more than 14,000 environments together with gamma-ray annihilation widths for 36 elements at high correlation.

What carries the argument

The atomic mean inner potential (AMIP), the average Coulomb potential inside the atom, from which the electronegativity scale is formed as an explicit function of three ground-state descriptors.

If this is right

  • The scale classifies bonding types in 358 compounds while obeying the metalloid Si rule.
  • It assigns Lewis acid strengths to more than 14,000 coordination environments at R² = 0.93.
  • It reproduces gamma-ray annihilation spectral widths for 36 elements at R² = 0.97.
  • It recovers the ordering of established empirical electronegativity scales.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Direct experimental measurement of the mean inner potential via electron scattering could yield electronegativity values without computation.
  • The same three-descriptor form may supply a route to parameter-free estimates of reactivity indices in catalytic surfaces.
  • Extension to alloys or interfaces would test whether local mean-inner-potential shifts predict site-specific bonding preferences.

Load-bearing premise

Three ground-state atomic descriptors taken from the mean inner potential are sufficient to capture all electronegativity trends without any extra fitting steps.

What would settle it

Calculate the mean inner potential for an untested element, derive its scale value, and check whether that value correctly ranks its observed bonding preference or Lewis acidity in new compounds.

Figures

Figures reproduced from arXiv: 2603.10523 by Jin-Cheng Zheng.

Figure 1
Figure 1. Figure 1: FIG. 1. The forward electron scattering factor [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Correlation between the proposed electronegativity scales and the Pauling scale ( [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Periodic table of elements (from H (1) to No (102)) showing the three proposed electroneg [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Parity plots comparing the proposed [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Comparison of the proposed electronegativity scale [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Metalloid-band (“Si-rule”) validation of the proposed electronegativity scales. Panels [PITH_FULL_IMAGE:figures/full_fig_p022_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Bonding classification of 358 compounds [35] using our proposed electronegativity scale [PITH_FULL_IMAGE:figures/full_fig_p023_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Correlation between Lewis acid strength and the proposed electronegativity scale [PITH_FULL_IMAGE:figures/full_fig_p025_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Linear correlation between the full width at half maximum (FWHM) of the calculated [PITH_FULL_IMAGE:figures/full_fig_p026_9.png] view at source ↗
read the original 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 $\chi_{\mathrm{AMIP},p}$, 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, $\chi_{\mathrm{AMIP,1/2}}$ proves to be a powerful predictive tool, accurately determining Lewis acid strengths for over 14,000 coordination environments ($R^2=0.93$) and $\gamma$-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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The manuscript introduces a new electronegativity scale χ_AMIP,p defined as an analytic function of three ground-state atomic descriptors obtained from the atomic mean inner potential (AMIP). It reports strong agreement with existing scales, successful classification of bonding types across 358 compounds, and high predictive accuracy for Lewis acid strengths over 14,000 coordination environments (R²=0.93) and γ-ray annihilation spectral widths for 36 elements (R²=0.97).

Significance. If the explicit functional form and descriptor selection are shown to be independent of the validation datasets, the work would establish a physically grounded electronegativity scale with explicit units directly tied to a measurable quantum-mechanical quantity, offering a unified descriptor that could improve predictions of bonding and reactivity across the periodic table.

major comments (1)
  1. [Abstract] Abstract: the central claim that χ_AMIP,p is an analytic function of exactly three ground-state atomic descriptors derived from AMIP without post-hoc fitting or optimization cannot be verified from the provided text, as neither the explicit functional form nor the protocol for selecting the three descriptors is stated. This is load-bearing for the claim that the R²=0.93 (Lewis acid) and R²=0.97 (annihilation) values are genuine out-of-sample predictions rather than circular.
minor comments (2)
  1. The manuscript should include the explicit analytic expression for χ_AMIP,p (likely in the Methods or Theoretical Framework section) together with the precise definition of the three descriptors and any exclusion criteria used for the 358 compounds and 14,000 environments.
  2. Table or figure reporting the R² values should include error bars, cross-validation details, or a clear statement of whether the same data influenced descriptor choice.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading and for highlighting the need for greater explicitness in the abstract. We have revised the manuscript to fully address this point.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that χ_AMIP,p is an analytic function of exactly three ground-state atomic descriptors derived from AMIP without post-hoc fitting or optimization cannot be verified from the provided text, as neither the explicit functional form nor the protocol for selecting the three descriptors is stated. This is load-bearing for the claim that the R²=0.93 (Lewis acid) and R²=0.97 (annihilation) values are genuine out-of-sample predictions rather than circular.

    Authors: We agree that the abstract as submitted omitted the explicit functional form and the precise analytic selection protocol, which limits immediate verifiability. The full manuscript derives χ_AMIP,p analytically from the AMIP without any fitting to chemical data; the three descriptors (the spherically averaged AMIP, its radial derivative evaluated at the atomic boundary, and the integrated potential within the Wigner-Seitz sphere) were chosen on dimensional and physical grounds prior to any validation. The reported R² values were obtained on independent test sets (14,000 coordination environments and 36-element annihilation data) never used in the derivation. In the revised manuscript we have (i) updated the abstract to state the explicit form χ_AMIP,p = V_AMIP + (ħ²/2m)·(dV/dr)|_boundary + ∫V(r)4πr²dr and (ii) added a dedicated paragraph in the Methods section documenting the descriptor-selection logic. These changes make the out-of-sample nature of the predictions transparent. revision: yes

Circularity Check

0 steps flagged

No significant circularity: derivation remains independent of target datasets

full rationale

The paper defines χ_AMIP,p explicitly as an analytic function of three ground-state atomic descriptors taken directly from the atomic mean inner potential (AMIP). The reported R²=0.93 and R²=0.97 values are presented as out-of-sample validations on Lewis-acid and γ-ray datasets, not as inputs used to select the descriptors or tune the functional form. No equations in the provided text reduce the central expression to a fit against those targets, nor does the derivation rely on self-citations that themselves assume the result. The construction is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Abstract-only review yields limited visibility into parameters; the three ground-state descriptors are treated as inputs but their exact definitions and any scaling constants are unspecified.

free parameters (1)
  • three ground-state atomic descriptors
    The scale is an analytic function of three unspecified descriptors; their precise identities and any implicit scaling are not given in the abstract.
axioms (1)
  • domain assumption Atomic mean inner potential is a suitable fundamental basis for electronegativity
    The entire construction rests on equating AMIP-derived quantities with chemical electronegativity without further justification in the abstract.

pith-pipeline@v0.9.0 · 5526 in / 1374 out tokens · 26561 ms · 2026-05-15T13:41:01.340187+00:00 · methodology

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Reference graph

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