Molecular size insensitivity of optical gap of [n]cycloparaphenylenes (n = 3-16)

The first-principles GW+Bethe-Salpeter method is applied to [n]cycloparaphenylenes ([n]CPPs, n = 3-16) to explain why the experimental UV-vis absorption spectra for n = 7-16 are roughly size-insensitive, unlike the fluorescence spectra. Having confirmed that the calculated absorption spectra consistently exhibit size-insensitivity, the exciton properties are investigated in detail using a novel analysis method based on the two-particle picture. The size-insensitivity of large-sized [n]CPPs (n≥9) is found due to a common spatial distribution of the wave functions involved with the first dark exciton and the first bright exciton, which are characterized primarily by a number of the wave function nodes. The exciton wave function as well as other properties of smaller molecules of n = 7 and 8 is, on the contrary, size-sensitive, although and the peak positions are essentially size-insensitive because of the cancellation of size-dependence of exciton binding energy and orbital energy. Different size-sensitivity between absorption and fluorescence can thus be explained unless such cancellation also occurs for fluorescence.