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Coronene and corannulene are popular structures that have provided the basis for the investigation of extended carbon-based structures, like graphene, fullerene and their derivatives. Here we address the Jahn-Teller (JT) effects in electron paramagnetic resonance (EPR) spectroscopy of such molecules in ionic form. By density functional theory (DFT) and a Monte Carlo based sampling of the potential energy surface, we obtain three and five symmetry-related JT equivalent conformers in coronene and in corannulene ions, respectively. The structure and the interconversion between the JT distorted forms are discussed for their implication in EPR spectroscopy. The calculation of the g-tensor by DFT methods has also been benchmarked to serve as methodological approach for the investigation of more extended graphene molecules.