Structures and bonding patterns of nanoannular carbon clusters (C₄–C₂₀) through AIM analyses

Abstract

Structures, binding energies, harmonic frequencies, dipole moments, HOMO–LUMO energy gaps and particularly atoms in molecules (AIM) analyses of some nanoannular carbon clusters (C₄–C₂₀) are investigated at B3LYP/6-31+G(d) level of theory. No correlation is found by plotting the calculated binding energies as a functional number of carbon atoms of carbon clusters. The calculated binding energies sharply increase from C₄ to C₁₀ while slowly from C₁₀ to C₂₀. The binding energies of C_4n+2 clusters including C₆, C₁₀, C₁₄, and C₁₈ have a clear increase when compared with others indicating their aromatic characters which is confirmed by results of HOMO–LUMO energy gaps and geometrical parameters. AIM analyses show that most of our carbon clusters are topologically normal (non-conflict) with stable structures. Nevertheless, the topological networks of small antiaromatic rings, C₄ and C₈, at their equilibrium geometries may change via molecular vibrations. The existence of straight bond paths in 3D molecular graphs of carbon clusters with n > 10 implies that ring strains are decreased as the ring sizes grow. Except for C₄ and C₈, the ellipticity values for the remaining carbon clusters are small indicating that the C–C bond is conserved in these clusters. Dipole moments of even-numbered structures are negligible, whereas odd-numbered ones have μ values of 0.09−0.73 D.