It is apparent that the ISC and RISC processes are facilitated by negligible energy gap (∆E ST ) and large SOC matrix element (SOCME) between the first singlet and triplet excitedstates. These two conditions are usually rather controversial. However, in recent few years, the sufficiently fast RISC processes have been found in many systems with the sizable ∆E ST and vanishingly small SOCME. For these systems, their RISC mechanism has not been well understood. That's for sure that the high-order factors like the vibronic coupling should play a crucial role on their ISC/RISC processes. Unveiling the mechanism underlying that fast RISC process presents a challenge. Powerful computing resources and effective algorithms provide a way to resolve this challenge. Like the calculations of molecular vibronic spectra, the rate calculations with the inclusion of vibronic coupling effect require us to account for simultaneous changes in the vibrational and electronic states. One thus has to combine both the electronic structure theories and quantum dynamics methods to obtain the structure parameters and to describe the nuclear dynamics, respectively. The earliest research examples to characterize the vibronic properties were to calculate the phosphorescence of small aromatic hydrocarbons such as benzene. Later, the vibronic effects were involved in the calculations of ISC rates of some small organic molecules, and were demonstrated to be significant for the RISC rates of some TADF materials. One of the vibronic effects is captured by spin-vibronic coupling (SVC), represented by the third and fourth terms in RHS of Eq. (7), which require to calculate the other, intermediate excited-states and nonadiabatic coupling (NAC) elements between the excited states. The NACs between the low-lying singlet and triplet excited-states open the possibility for significant second-order coupling effects. Many previous theoretical works have found that the second-order SVC could assist the triplet-to-singlet up-conversion and increase RISC rates by a few orders of magnitude in some TADF emitters. Therefore, a full secondorder SVC model was adopted to calculate S-T crossing rates (e.g. Refs 25-29). Usually, the second-order vibronic coupling effect in most cases is much smaller than the first-order one. However, due to a vibronic resonance that orchestrates the low-lying electronic states (S 1 , T 1 , T 2 ) together, S 1 -T n crossings may play a major role in enhancing ISC and RISC, especially for some MR-type TDAF emitters. Except the SVC, there is another vibronic coupling effect known as Herzberg-Tellertype vibronic coupling (HTVC). This effect has been recognized and incorporated in the simulation of molecular vibronic specra. Along this line, we have developed the timedependent correlation function approach to account for the sumultaneous changes in the vibrational and electronic states and calculated the electronic absorption and emission spectra and resonant Raman scattering spectra, including the Franck-Condon (FC), HTVC, and Duschinsky rotation (DR) effects. This method could be naturally extended to calculate the ISC and RISC rates. It should be interesting to see what proportion of its ISC/RISC rate can be covered by the HTVC effect for a MR-type emitter. We aim to provide a demonstration in this work.