[Paper Review] First-Principles Electronegativity Scale from the Atomic Mean Inner Potential

Jin‐Cheng Zheng|arXiv (Cornell University)|Mar 11, 2026

Machine Learning in Materials Science0 citations

TL;DR

The paper introduces a first-principles electronegativity scale based on the atomic mean inner potential (AMIP), with three analytic formulations, validated against established scales and applied to bonding classification and predictive tasks.

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.

Motivation & Objective

• Motivate a physically rigorous electronegativity definition tied to a measurable quantum property (mean inner potential).
• Develop an AMIP-based electronegativity scale unifying atomic descriptors with clear units.
• Provide three analytic variants of the scale and normalize to hydrogen Pauling value for comparability.
• Demonstrate the scale’s agreement with established scales and its predictive capabilities across bonding types and environments.

Proposed method

• Define AMIP as the volume-averaged electrostatic potential linked to the second moment of total charge density.
• Express AMIP in terms of forward electron-scattering factor f^(e)(0) and atomic valence radius r_v to obtain v_0 for each atom.
• Construct three AMIP-based electronegativity scales: chi_AMIP,1, chi_AMIP,1/2, and chi_AMIP,1/2^H, with explicit analytic forms (no empirical parameters).
• Normalize chi_AMIP,1/2 to hydrogen’s Pauling value to yield a dimensionless scale comparable with conventional scales.
• All-electron DFT (revPBE-GGA) calculations provide f^(e)(0), r_v, and v_0 for elements 1–102; hydrogen serves as the reference.
• Compare AMIP-based scales against Pauling, Allen, Mulliken, TO, RZH, DOCZW, OK, and others to establish correlations.

Experimental results

Research questions

• RQ1 Can electronegativity be rigorously defined from a fundamental quantum property (AMIP) with clear units?
• RQ2 Do AMIP-derived scales correlate with established scales across main-group elements and beyond?
• RQ3 Can the AMIP framework robustly classify metals, metalloids, and nonmetals (the Si-rule) and predict bonding trends?
• RQ4 What predictive power does the AMIP electronegativity have for chemical reactivity descriptors and spectral widths?
• RQ5 Is the AMIP-based framework transferable to a wide range of coordination environments and bonding contexts?

Key findings

• The AMIP-based scales chi_AMIP,1 and chi_AMIP,1/2 are analytic and parameter-free; chi_AMIP,1/2 shows a strong linear correlation with the Pauling scale for main-group elements (as per Fig. 2b).
• chi_AMIP,1/2 correlates with multiple established scales, achieving R^2 values above 0.80 across main-group and all-element sets (Table 2).
• chi_AMIP,1/2 demonstrates high predictive power for Lewis acid strengths (R^2 = 0.93) across 14,000 coordination environments and for gamma-ray annihilation spectral widths across 36 elements (R^2 = 0.97).
• The AMIP framework reproduces the metalloid “Si rule,” correctly placing metalloid elements within a dedicated metalloid band, consistent with Pauling and Allen scales.
• Hydrogen serves as a robust reference point, enabling a dimensionless normalization chi_AMIP,1/2^H that aligns with the Pauling hydrogen value (2.20).