Role of Vibronic Couplings and Energy Gap in the Internal Conversion Process of a Molecule

An analytical expression for the rate constant of internal conversion (IC) in a molecule was derived based on the crude adiabatic representation. All vibrational modes were considered to be on an equal footing in the rate constant expression. Based on this expression, we investigated the role of vibronic couplings and electronic energy gap in IC processes, using 9-fluorenone as an illustrative example. Vibrational modes with strong off-diagonal vibronic coupling constants (VCCs) give rise to non-radiative transitions. In contrast, vibrational modes with strong diagonal VCCs constitute the final vibronic states that accept the excess electronic energy between the initial and final electronic states. Therefore, vibrational modes are classified into promoting and accepting modes based on their roles. We identified important promoting modes responsible for one-phonon emission/absorption and accepting modes that contribute greatly to the final state. A Franck-Condon envelope, which describes the density of final vibronic states, explains the dependence of the rate constant on the electronic energy gap. VCC can be visualised as a spatial distribution of its density form, i.e., vibronic coupling density (VCD). The VCD concept is expected to facilitate the design of functional molecules with IC processes understood in terms of electronic states and vibrational modes.