Does variational transition state theory provide an upper bound to the rate in dissipative systems

By comparing variational transition state theory (VTST) against exact numerical calculations for the Brownian motion of a reactive particle, we uncover the unexpected result that VTST does not provide a rigorous upper bound to the least nonvanishing eigenvalue of the corresponding Fokker–Planck equation, a quantity which can be shown to correspond to the phenomenological rate constant. This result is tied to deviations between the reactive flux rate and the least nonvanishing eigenvalue which arise for intermediate to low barriers.