Transmission coefficient in reaction rate theory

[dsigg]

This question relates to rate constants of transition events. The transmission coefficient κ reduces the value of the rate constant compared to the transition state theory (TST) value. I understand κ to be defined as the probability that a reaction coordinate q will proceed to product given that is has positive velocity at the transition state. In TST, there are no frictional forces to hold q back and κ = 1.

With increasing friction, there are recrossings, and κ is reduced. My question is how does k ever fall below the value of 0.5? Naively speaking, in the limit of very large friction the velocity is quickly randomized and the probabilities of falling back to reactant or moving forward to product should both be 0.5. Yet, Kramers theory and the more general Grote-Hynes theory allow for much smaller values of κ.

My thoughts are either that the stated definition of κ is wrong or if κ < 0.5 a greater number of transition events "bounce-back" to the reactant state than proceed to product. Neither option seems very appealing.

Can anyone set me straight?

 

[DrDu]

I don't know Kramers theory too well, but I could imagine that for very high friction, the particle is effectively stopped at the TS. Then it has a high probability to go back to the educts.
Also without friction, you can get a small kappa due to quantum mechanical effects:
http://en.wikipedia.org/wiki/Rectangular_potential_barrier