Radiationless Transitions in Polyatomic Molecules. III. Anharmonicity, Isotope Effects, and Singlet-to-Ground-State Transitions in Aromatic Hydrocarbons

Abstract

The work on Franck–Condon factors for radiationless transitions in polyatomic molecules, as reported in Parts I and II of this series, is extended and generalized, starting from the theoretical expression for Franck–Condon factors in aromatic hydrocarbons, which was derived and applied to triplet-to-ground-state transitions in Part II. The role played in this expression by the anharmonicity and symmetry of CH-stretching modes is clarified. As a preliminary step towards application of this expression to singlet-to-ground-state transitions in aromatic hydrocarbons, the appropriate Franck–Condon factors are studied spectroscopically by measuring the long-wavelength part of the fluorescence spectra of anthracene-h10 and -d10. These experimental Franck–Condon factors are used to determine the anharmonicity parameter in the theoretical expression for the singlet-to-ground-state radiationless-transitions rate constant. Theoretical rate constants for the transition calculated on this basis compare favorably with the scarce experimental data. They tend to justify the commonly made assumption that these transitions contribute a negligible amount (about 1% or less) to singlet decay in most simple aromatic hydrocarbons, but with some notable exceptions. Thus, for benzene and tetracene, and possibly also for coronene, contributions of about 10% are obtained, whereas in azulene and all of its known derivatives, the transition dominates the other decay processes of the first excited singlet state. The calculations also account qualitatively for the broadening of the first singlet absorption system and the anomalous fluorescence of azulenes. The isotope rule derived in Part I is corrected for anharmonicity. In its new form it does not account quantitatively for the observed deuterium effects. This indicates that CD-stretching modes, which are much less efficient in taking up electronic energy than CH-stretching modes, have about the same efficiency as some of the skeletal modes, so that these skeletal modes will contribute substantially to the Franck–Condon factors of perdeuterated aromatic hydrocarbons. The analysis of singlet-to-ground-state transitions leads to rate constants of 1013–1014 sec−1 for transitions between closely spaced electronic energy levels of the same multiplicity. Comparison with the results for triplet-to-ground-state transitions indicates a spin-prohibition factor of 108. The dependence of spin-prohibition factors on the energy of the electronic states involved in the transition is briefly discussed.