Grote-Hynes correction

The factor Ao/cob is the classical (Grote-Hynes) correction to the TST result Eq. (4). The quantum enhancement factor 5 is equal to... 

Known as the Grote-Hynes correction (Hynes, 1985a, 1985b). See Problem F. 

The quantum thermodynamic factor S is the quantum correction to the Kramers-Grote-Hynes classical result in the spatial diffusion limited regime, derived by Wolynes " ... 

There are in principle dynamical recrossing corrections to the normal mode TST rate constant Equation (3.127) itself due to solvent frictional effects, which can be calculated via Grote-Hynes theory [81,82] when the time-dependent frictions on the three... 

In the previous sections a model of the frequency-dependent collisional friction has been derived. Because the zero-frequency friction for a spherical particle in a dense fluid is well modeled by the Stokes-Einstein result, even for particles of similar size as the bath particles, there has been considerable interest in generalizing the hydrodynamic approach used to derive this result into the frequency domain in order to derive a frequency-dependent friction that takes into account collective bath motions. The theory of Zwanzig and Bixon, corrected by Metiu, Oxtoby, and Freed, has been invoked to explain deviation from the Kramers theory for unimolec-ular chemical reactions. The hydrodynamic friction can be used as input in the Grote-Hynes theory [Eq. (2.35)] to determine the reactive frequency and hence the barrier crossing rate of the molecular reaction. However, the use of sharp boundary conditions leads to an unphysical nonzero high-frequency limit to Ib(s). which compromises its utility. 

The second key insight into the dynamical corrections to the TST was provided by the Grote-Hynes theory... 

We shall present here an equilibrium simulation of the transport of a solute across a liquid-liquid interface, which permits to measure the rate constant. This work has been done with the same rationale than other recent molecular dynamics studies of chemical kinetics /5,6/. The idea is to obtain by simulation, at the same time, a computation of the mean potential as a function of the reaction coordinate and a direct measure of the rate constant. The mean potential can then be used as an input for a theoretical expression of the rate constant, using transition state /7/, Kramers /8/ or Grote-Hynes /9/ theories for instance. The comparaison can then be done in order to give a correct description of the kinetics process. A distinct feature of molecular dynamics, with respect to an experimental testing of theoretical results, is that the numerical simulations have both aspects, theoretical and experimental. Indeed, the computation of mean potentials, as functions of the microscopic models used, is simple to obtain here whereas an analytical derivation would be a heavy task. On the other hand, the computation of the kinetics constant is more comparable to an experimental output. 

Kramers (11) correction to the one-dimensional TST rate came from consideration of the properties of the Fokker-Planck equation in the vicinity of the barrier in the presence of ohmic friction. As noted in the previous section, if one considers only the parabolic barrier limit, the Fokker-Planck equation may be solved analytically. Grote and Hynes (23) and Hanggi and Mojtabai (65) generalized Kramers result to include the case of memory friction and the GLE. A different approach (31) would be to consider the Hamiltonian equivalent, Equation (29), for space-independent coupling (g(q) = q in Eq. (29)) in the parabolic barrier limit. 

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