The gas-phase Cn (n = 6–31) carbocyclic clusters were systematically investigated based on DFT using ABCluster software. In this work, two geometrical parameters, degree of circularity and the ratio of carbon atoms occupying the fitted circle, were defined for the geometrical circle formed by Cn (n = 6–31) carbocyclic by curve-fitting the coordinates of the carbon atoms, and it is found that even-numbered carbon rings are always more rounded than odd-numbered ones. The study of relative stability of Cn ring clusters, on the one hand, revealed that even carbon rings are always more stable than odd ones. On the other hand, it proved that cyclic shape carbon clusters are always more stable than cage-like structure ones. In addition, the density of states, simulated electron absorption spectra, polarization response to electrostatic field, π-electron population, and topological properties of bond critical points were compressively studied. This work effectively filled the lack of research on odd-numbered carbocycles, a member of the carbocyclic family, and showed readers the physical and chemical reasons for the relative deformation of odd-numbered carbocycles.
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