  Recent experiments in polariton chemistry have demonstrated that reaction
rates can be modified by vibrational strong coupling to an optical cavity mode.
Importantly, this modification only occurs when the frequency of the cavity
mode is tuned to closely match a molecular vibrational frequency. This sharp
resonance behavior has proved difficult to capture theoretically. Only
recently, Lindoy et al. reported the first instance of a sharp resonant effect
in the cavity-modified rate simulated in a model system using exact quantum
dynamics. We investigate the same model system with a different method,
ring-polymer molecular dynamics (RPMD), which captures quantum statistics but
treats dynamics classically. We find that RPMD does not reproduce this sharp
resonant feature at the well frequency, and we discuss the implications of this
finding for future studies in vibrational polariton chemistry.
