The Oxygen Exchange Anisotropy Ratio (OEAR): A Reproducible Exchange-Driven Descriptor in Open-Shell Oxygen

Abstract

This short report identifies a reproducible electronic pattern in oxygen-centered open-shell species.

Across multiple radicals and anions—including O•, O⁻, and O₂⁻—the ratio between α and β frontier-orbital energies consistently falls within a narrow interval near 1.23, while closed-shell molecules collapse precisely to 1.00.

The ratio is defined as:

\mathrm{OEAR} = \frac{|\varepsilon_\alpha|}{|\varepsilon_\beta|}

and extracted directly from unrestricted B3LYP/def2-TZVP simulations performed via an external AI computation engine (Grok). Additional checks using HF and PBE0 confirm that the value remains stable within ±0.02.

This structured progression forms a monotonic scale from 1.00 → 1.28, separating into three reproducible regimes:

• 1.00 — closed-shell isotropy

• 1.16–1.20 — heteronuclear damping (HO•, NO•, ONO•)

• 1.23–1.28 — oxygen-centered open-shell anisotropy

The stability of this ratio suggests a compact exchange-driven motif associated with oxygen’s 2p manifold.

While preliminary, the results are consistent across species, charge states, and computational methods, offering a simple organizing parameter for interpreting open-shell oxygen chemistry.

All numerical values, figures, and methodological details (CAT workflow, simulation settings, reproducibility notes) are included in the report.