How to Detect Low-Energy Isomers of Fullerenes Using Clar Covers

We demonstrate that the energetic stability of carbon (5,6)-fullerene isomers can, to a large extent, be inferred from two topological invariants: the Kekulé count K and the Clar count C. Although neither invariant alone exhibits a strong correlation with the total electronic energy at equilibrium geometry, the application of a min–max principle (maximizing C while minimizing K) proves effective in identifying the lowest-energy subset of Cn isomers for n= 50–100. This finding substantially reduces the complexity of determining the most stable isomer among larger fullerenes.