Monocyclic carbon clusters have two kinds of p-molecular orbitals, namely, out-of-plane p-molecular orbitals and in-plane p-molecular orbitals. We studied the double aromaticity/antiaromaticity in monocyclic carbon clusters from the geometry criterion and electron count criterion. The B3LYP method was used to obtain the optimized structures for monocyclic carbon clusters. We found that (1) monocyclic carbon clusters C_4n+2 are doubly aromatic, (2) C_4n are doubly anti-aromatic, and (3) C_4n+1 and C_4n+3 are out-of-plane aromatic and in-plane anti-aromatic.

We also calculated the NICS values for the monocyclic carbon clusters to evaluate the aromaticity. The obtained NICS values show that (1) monocyclic carbon clusters C_4n+2 are aromatic, (2) C_4n are anti-aromatic, and (3) C_4n+1 are anti-aromatic while C_4n+3 are aromatic .

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