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arXiv · 2608.22206

Unified Bonding Entropy Model for Kekul\'{e} Graphene Nanoflakes

Chang-Chun He·Yu-Jun Zhao·Xiao-Bao Yang
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Abstract

The open-shell character of Kekul\'{e} graphene nanoflakes (GNFs) is conventionally rationalized by the gain of Clar aromatic $\pi$-sextets upon electron unpairing. While this rule successfully explains many quinoidal diradicaloids, it treats only the maximum number of sextets and neglects the multiplicity and spatial distribution of resonance configurations that realize the same Clar count. Here, we identify a second route to open-shell stabilization in which the maximum Clar-sextet number remains unchanged while the number of accessible Clar resonators increases substantially. We term this mechanism \emph{Clar-number-invariant resonance-space expansion}. By enumerating closed-shell and open-shell Clar resonators and combining this analysis with a bonding entropy model (BEM), we show that electron unpairing can release closed-shell pairing constraints, enlarge the resonance manifold, and redistribute C--C bond occupancies away from localized single- and double-bond limits. The BEM-predicted number and spatial distribution of unpaired electrons correlate strongly with density-functional-theory diradical character, local magnetic moments, optimized C--C bond lengths, and relative energies across a broad set of GNFs. The resulting framework offers a graph-based and physically transparent route for screening open-shell carbon nanostructures and for designing tunable molecular spins without requiring an increase in the maximum Clar number.

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Chang-Chun He, Yu-Jun Zhao, Xiao-Bao Yang. 2026-08-23. Unified Bonding Entropy Model for Kekul\'{e} Graphene Nanoflakes. https://arxiv.org/abs/2608.22206

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