Dependence of Radiationless Decay Rates in Polyatomic Molecules upon the Initially Selected Vibronic State: General Theory and Application

Abstract

A general scheme for calculating relative nonradiative decay rates of initially selected vibronic levels in polyatomic molecules is developed. Here we are concerned only with relative rates corresponding to initial vibronic states in some particular electronic manifold decaying into some other particular electronic manifold. Therefore we need only consider the exact density-of-states-weighted-Franck—Condon factor accounting for the vibrational contribution to the over-all nonradiative decay rate. This contribution is calculated approximately in the large molecule (statistical) limit by deriving the appropriate (modified) energy gap law. The contributions of ``special'' modes (e.g., optically excited modes, and modes with large geometry and/or frequency shifts) are partitioned from those of the other modes by techniques similar to ones developed earlier to treat cis—trans isomerism and are calculated explicitly. Excellent agreement with the recent low pressure experimental results of Spears, Abramson, and Rice for the S1→ T1 intersystem crossing rates from individual vibronic states in benzene and perdeuterobenzene is obtained, but only by taking proper account of the effects of geometry and frequency changes of the various vibrational modes involved in the transition. The sharp dependence of the relative nonradiative rates for a progression in an optical mode upon the frequency shift in that mode leads to the possibility of evaluating the vibrational frequencies in an electronic state by measuring the radiationless decay rate into that electronic state (e.g., in the benzene case determining T1 vibrational frequencies from S1→ T1 decay rates). Finally, we comment upon recent low pressure experimental results for β-naphthylamine, monofluorobenzene, and upon some observed temperature dependences of radiationless transition rates in matrices.