In this study, an analytical expression for the rate constant of the internal conversion (IC) in a molecule was derived based on the crude adiabatic representation. All vibrational modes were considered to be on 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. Contrastingly, vibrational modes with strong diagonal VCCs constitute the final vibronic states that accept the excess 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 the one-phonon emission/absorption and accepting modes that contribute greatly to the final state. A Franck-Condon (FC) envelope describes the final density of vibronic states and explains the dependence of the rate constant on the energy gap. VCC can be visualized as a spatial distribution of its density form, i.e., vibronic coupling density (VCD), obtained from the electronic wave functions and vibrational modes. Using the concept of VCD, the IC process can be understood and controlled in terms of the electronic states and vibrational modes. This approach provides new chemical insights into IC processes. It has the advantage that the VCD concept facilitates the design of functional molecules with IC processes controlled.
Role of Vibronic Couplings and Energy Gap in the Internal Conversion Process of a Molecule
Supplementary materials: Theoretical details and supplementary computational results.