Radiationless Transitions in Polyatomic Molecules. II. Triplet-Ground-State Transitions in Aromatic Hydrocarbons

The theory of Part I is applied to nonradiative transitions from the lowest triplet state to the ground state of aromatic hydrocarbons. A previously communicated empirical relation between triplet energy, triplet lifetime, and the relative number of hydrogen atoms per molecule is substantiated and its physical implications are discussed. It is transformed into a relation between the Franck-Condon factor of the transitions and the triplet energy. In this form it can be compared with the theoretical expressions derived in Part I. No satisfactory theoretical representation of the empirical formula could be obtained on the basis of a harmonic-oscillator description of the normal modes of the molecules. However, introduction of anharmonicity leads to excellent agreement between theory and experiment. A one-parameter formula is derived which accounts with good accuracy for the dependence of the triplet lifetime on the triplet energy and the number of carbon and hydrogen atoms in the molecule. This formula shows that the Franck-Condon factors relevant to the radiationless triplet-ground-state transition are governed by CH or CD stretching modes, which behave in this respect as completely degenerate for a given molecule. The single adjustable parameter is related to the anharmonicities of these modes in the ground and triplet state. The analysis confirms that the purely radiative triplet lifetime of most if not all aromatic hydrocarbons is close to 30 sec and that the Franck-Condon factor is the only parameter in the expression for the nonradiative triplet decay constant which varies considerably between different aromatic hydrocarbons. Finally the temperature dependence of the Franck-Condon factors is considered. A theoretical treatment indicates a very small temperature dependence below 400°K. This result seems to be borne out by an analysis of recent experiments, leading to the conclusion that the observed temperature effects are associated with bimolecular processes. A notable exception is benzene, where the triplet lifetime is temperature-dependent down to very low temperatures, possibly due to a Jahn-Teller distortion.