How to get the reaction rate?

[hlzya]

Hi

After I use the method such as NEB and dimer, I can obtain the activation energy and prefactor. I want to konw how I can get the reaction rate at certain temperature using the above mentioned information.

Thanks!

[graeme]

The harmonic rate is R=v exp(-dE/kT) where dE is the activation energy and v is the prefactor.

[lanjh]

But how to calculate the prefactor?

[dano]

The harmonic prefactor looks like this:

v = Prod (vmin_i) /Prod (vsaddle_j)

where (vmin) is the normal modes at the minimum and i goes from i=1->3N
and (vsaddle) is the normal modes at the saddle and j goes from j=1->3N-1

The one imaginary mode at the saddle is not left out of the product

N is the number of degrees of freedom (ie. atoms that are not frozen)

[lanjh]

thanks, Sir!
I am still not very clear about what your reply. Do you mean that vmin_i and vsaddle_j are the normal modes of reactant and saddle? vmin_j denotes
one normal mode or more?
Furthermore, Prod represents what ?

I am eager to your reply, thanks very much!

[graeme]

These questions are a little basic for this forum. A short description of harmonic transition state theory can be found in the following class notes:
http://theory.cm.utexas.edu/statmech/notes/notes12.pdf

The equation that Dan gave you is 12.13 in these notes, and the text (along with any statistical mechanics textbook), describes the harmonic approximation.