Due to the initial success of the classical description of molecules interacting with cavity photon modes, the next natural question is how quantum effects (of the cavity mode or molecular vibrations) will influence the theoretical predictions. Along these lines, Ref. 377 attempted to add (approximate) quantum corrections to the GH rate theory to describe cavity-modified chemical kinetics. Two possible quantum corrections 377 are added, including (i) replacing the classical partition function with their quantum counterpart using the quantum transition state theory (QTST) 404 and (ii) adding tunneling effect using the formalism of the centroid TST (CTST). Using the QTST 377 that only includes the quantum correction in (i), the total rate constant is written as