Molecular static third-order polarizabilities of carbon-cage fullerenes and their correlation with three geometric properties: symmetry, aromaticity,and size

The static third-order polarizabilities (gamma) of C-60, C-70, five isomers of C-78 and two isomers of C-84 were analyzed in terms of three properties , from a geometric point of view: symmetry; aromaticity; and size. The pola rizability values were based on the finite field approximation using a semi empirical Hamiltonian (AMI) and applied to molecular structures obtained fr om density functional theory calculations. Symmetry was characterized by th e molecular group order. The selection of six-member rings as aromatic was determined from an analysis of bond lengths. Maximum interatomic distance a nd surface area were the parameters considered with respect to size. Based on triple linear regression analysis, it was found that the static linear p olarizability (alpha) and gamma in these molecules respond differently to g eometrical properties: alpha depends almost exclusively on surface area whi le gamma is affected by a combination of number of aromatic rings, length a nd group order, in decreasing importance. In the case of alpha, valence ele ctron contributions provide the same information as all-electron estimates. For gamma, the best correlation coefficients are obtained when all-electro n estimates are used and when the dependent parameter is ln(gamma) instead of gamma. Published by Elsevier Science B.V.