Summary and Future Directions. We applied a variety of MQC approaches to simulate the VSC-influenced reaction rate constant. These MQC simulations treat the key vibrational levels associated with the reaction coordinate in the quantum subsystem (as quantum states), whereas all other DOFs are treated inside the classical subsystem. We find that as long as we have the quantum state descriptions for the vibrational DOFs, one can correctly describe the VSC resonance condition in Eq. 1 regardless of the specific MQC methods one used. The results suggest that the MQC approaches can generate semi-quantitative agreement with the numerically exact HEOM results for k/k 0 when changing the cavity frequency ω c , the light-matter coupling strength η c , or the cavity lifetime τ c .