Calculation of absorption and emission spectra of [n]cycloparaphenylenes: the reason for the large Stokes shift

Abstract

The electronic absorption and emission spectra of the [n]cycloparaphenylenes with n = 6,7,…,11 ([n]CP) have been studied at the time-dependent density functional theory level. The calculations show that the optical gap increases with increasing size of the ring due to reduced ring strain in the larger carbon nanohoops, whereas the energy of the first bright state follows the opposite trend for the studied [n]CPs. For the excited-state structures, the C–C bonds between the phenylene groups have a significant double-bond character giving rise to a continuous electron delocalisation pathway around the ring. The torsion angles between the phenylene moieties are much smaller for the excited state than for the ground state suggesting that the excited state has a stronger electron delocalisation around the carbon nanohoop than for the ground state. The double bond character of the phenylene C–C bonds declines and the phenylene torsion angle increases with increasing ring size. The aromatic stabilisation of the excited state due to the continuous electron delocalisation pathway is probably the main reason for the large Stokes shift. The excited state of the larger [n]CPs are less aromatic than the smaller ones explaining why the Stokes shift decreases with increasing size of the ring. For large [n]CPs, the excitation-energy spectrum forms bands making localisation of the excitons feasible. Localisation of the excitons probably leads to the observed ring-size independence of the electronic excitation spectra for large [n]CPs.