Optical Excitations in Cycloparaphenylene Molecules of Various Sizes

Cycloparaphenylene ([$n$]CPP) molecule can be imagined as $n$ benzene molecules connected in a periodic chain. [$n$]CPPs with even number of links have alternating dihedral angles of $+$/- 34 degrees, whereas odd-numbered [$n$]CPPs cannot adopt such a high symmetry configuration, so they have a ``defect'': one of the rings is connected to its neighbors by dihedral angles of about 20 degrees. This ``defect'' plays a role of a localization site for an exciton. In this work we show that in [$n$]CPPs with $n$\textgreater 8 the exciton is localized on 5-6 rings, which strongly reduce their dihedral angles, while preserving the ground state geometry on the rest of the rings. This occurs both in odd-numbered and, surprisingly, in even-numbered [$n$]CPPs. We use electronic structure theory to address the spatial extent/properties of electronic wavefunctions and resulting electronic functionalities in [$n$]CPP molecular chromophores. Localization of excitonic states due to electron-phonon coupling in cycloparaphenylenes invalidates Condon approximation and breaks optical selection rules, making these materials to be efficient emitters. The effect of solvent is also discussed.