Vibration correlation function formalism of radiative and non-radiative rates for complex molecules

General radiative and non-radiative rates formalisms are derived using the vibration correlation function method for the transition from the excited singlet to ground singlet states by considering the Duschinsky rotation and Herzberg-Teller effects at finite temperature. For the non-radiative transition process, the conventional assumption of (single) “promoting-mode” is abandoned and a promoting-mode free formula is presented. Using this new rate formalism, we re-examine the well-established photophysical properties of anthracene. Both the calculated radiative and non-radiative rates are in good agreement with the available experimental measurements and previous theoretical values. Furthermore, we rationalize the exotic aggregation induced emission phenomenon in 9-[(o-Aminophenyl)phenylmethylene]-9H-fluorene molecule: the roles of low-frequency phenyl ring twist motions and their Duschinsky mode mixings are found to be crucial, especially for the temperature dependence. The present rate theory can quantitatively describe the excited-states dynamic processes in large molecules and is a powerful tool for the design of new high-efficiency light-emitting materials.