Transmission coefficient in reaction rate theory

In summary, the question is about the relationship between the transmission coefficient κ and the rate constant of transition events. κ is defined as the probability of a reaction coordinate q proceeding to product given positive velocity at the transition state. In the absence of friction, κ is equal to 1, but with increasing friction, it decreases due to recrossings. The question is how κ can fall below 0.5, and whether this is due to a wrong definition or a higher number of transition events "bouncing back" to the reactant state. The possibility of high friction causing the particle to effectively stop at the transition state and quantum mechanical effects may also contribute to a lower κ. Clarification on this matter is requested.
  • #1
dsigg
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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?
 
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  • #2
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
 

What is the transmission coefficient in reaction rate theory?

The transmission coefficient in reaction rate theory is a measure of the efficiency with which reactant molecules overcome the energy barrier to form products. It represents the fraction of collisions between reactant molecules that result in a successful reaction.

How is the transmission coefficient calculated?

The transmission coefficient is calculated by taking the ratio of the rate constant for the reaction to the rate constant for the corresponding uncatalyzed reaction. This can also be expressed as the ratio of the number of successful collisions to the total number of collisions between reactant molecules.

What factors influence the transmission coefficient?

The transmission coefficient is influenced by several factors, including the temperature, the activation energy of the reaction, and the presence of a catalyst. Higher temperatures and lower activation energies typically result in a higher transmission coefficient, while the presence of a catalyst can greatly increase the efficiency of the reaction.

Why is the transmission coefficient important in reaction rate theory?

The transmission coefficient is important because it helps to explain the rate at which reactions occur. It provides insight into the efficiency of a reaction and can help predict how changing certain variables, such as temperature or catalyst concentration, will affect the rate of the reaction.

How does the transmission coefficient differ from the reaction rate constant?

The transmission coefficient and the reaction rate constant are related but distinct concepts. While the transmission coefficient represents the fraction of successful collisions, the reaction rate constant is a measure of the speed at which the reaction occurs. The transmission coefficient is an important factor in determining the reaction rate constant, but they are not interchangeable terms.

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