Unified bonding entropy model to determine magnetic properties in graphene nanoflakes

Graphene nanoflakes (GNFs) exhibit rich magnetic behaviors arising from two primary mechanisms: geometry frustration in non-Kekul\'e structures and electron delocalization-driven aromatic stabilization in Kekul\'e-type systems. Herein, we develop a unified bonding entropy model (BEM) to quantitatively characterize the magnetic properties in GNFs within a statistical framework, providing an entropy-based criterion for understanding and predicting bond occupancy numbers and unpaired electron distributions. While non-Kekul\'e systems naturally favor high-spin configurations due to topological frustration, the BEM reveals that even Kekul\'e-type GNFs can exhibit magnetic character when the entropy gain from unpaired electrons outweighs the loss of aromatic stabilization. The model predictions show excellent agreement with density functional theory calculations in terms of spin density distributions and unpaired electron counts. Our results establish bonding entropy as a general guiding principle for designing carbon-based magnetic materials with tunable magnetic properties.