Ab initio scaling of the second hyperpolarizabilities of carbon cages

Abstract

A sum over molecular orbitals scheme in an ab initio 6-31G* basis set is used to calculate the static second hyperpolarizabilities, γ, of the eight carbon cages now available in macroscopic quantities: C60, C70, one isomer of C76, three isomers of C78, and two isomers of C84. For C60 and C70, there is good agreement between calculations and available experimental data. The range of nuclearities is extended to cover the most stable isomers of C40 and C100. It is found that γ increases as a nonlinear function of both the number of atoms and the number of partial double bonds (hexagon–hexagon edges). Two proposed scaling laws lead to very different values of γ for systems with large numbers of carbon atoms but, even for the less steeply rising function, comparison with experimental data shows that, weight for weight, fullerenes should have a larger response than polyenic systems.