The expression given by Fatemeh Keshavarz, due to Shavitt (please give a reference) appears to be missing some essential features, for instance the (reduced) mass of the particle. Surely a proton tunnels more easily than a carbon or other heavy particle. Also the width of the barrier should play a role. An expression for the tunneling correction was developed by R.P. Bell (of "The Proton in Chemistry" fame), which does include both these features. A very nice overview of his results, and his correction to the Arrhenius expression can be found in the lecture by Carrera on the website:

http://www.princeton.edu/chemistry/macmillan/group-meetings/DEC_tunneling.pdf

(although I would replace dependence on particle "size" by particle "mass"). The  lecture should give you sufficient literature references to see if it applies your own system.

If you tell me which Truhlar reference you are looking for, maybe I can find it for you.

Hi,

A simple expression for the tunneling correction is suggested by Shavitt:

Qtunneling= 1+ 1/24(h.nu*/kB.T)^2 . (1+kB.T/E0)

Where "nu*" is the imaginary frequency of the activated complex at the top of the barrier, and kB and h are Boltzmann's and Plank's constants, respectively, and E0 is the barrier height corrected for zero point energy for the reaction (Energy (TS) -Energy (Intermediate)).

nu* is the negative energy in frequency results of your TS which only its value should be used (I mean don't put its negative sign in the equation). Let me know if you need further help.

Hello Fatemeh,

I tried the equation but the second part of equation its too much small, in order of 1E-22 in front of 1. My reaction is a bimolecular reaction without intermediates. It is valid in this case or simply Qtuneelling is 1 in this case and have meaning?

Thank you very much for answer and your time,

Joaquim Mª Rius Bartra

The expression given by Fatemeh Keshavarz, due to Shavitt (please give a reference) appears to be missing some essential features, for instance the (reduced) mass of the particle. Surely a proton tunnels more easily than a carbon or other heavy particle. Also the width of the barrier should play a role. An expression for the tunneling correction was developed by R.P. Bell (of "The Proton in Chemistry" fame), which does include both these features. A very nice overview of his results, and his correction to the Arrhenius expression can be found in the lecture by Carrera on the website:

http://www.princeton.edu/chemistry/macmillan/group-meetings/DEC_tunneling.pdf

(although I would replace dependence on particle "size" by particle "mass"). The  lecture should give you sufficient literature references to see if it applies your own system.

If you tell me which Truhlar reference you are looking for, maybe I can find it for you.

Dear Joaquim,

The file mentioned by Gert is great and seemed so helpful. But, what program have you used for your rate calculations? One of the most commonly used packages is POLYRATE (http://comp.chem.umn.edu/polyrate/) for bimolecular reactions with no intermediates. If you have used that, it has the option to compute tunneling through several methods mentioned in its manual. It reports the rate constants with and without tunneling.

Dear,

The article that my principle article suggest to apply at similar system that I am studying is " Skodje, R. T.; Truhlar, D. J. Chem. Phys. 1981, 85 624. " 

About the  web page, I tried but I am not sure about the values of distance "a" and "m". My reaction imply the formation of H-Cl bond and H-OH break. All these calculation have been performed in Gaussian09 with DFT and coupled-cluster correction at  CBS limit. I suppose that I must calculate the rate constant with correction manually but now I have require a POLYRATE license and I will check it.

Thank you very much for your time and answers,

Joaquim Rius

Dear Joaquim,

I don't understand from your answer if you have access to Truhlar's paper or not. I attached it in case you don't. It is a relatively simple calculation relating the rate not to the Arrhenius rate but to a classical particle with enough energy to fly directly over the barrier. I am not convinced that you can just apply it to compare to Arrhenius, or transition state theory, since for the calculation of those rates you also have sufficient thermal energy to go closer to the barrier top, at which point tunneling could take place, so it is more of a competition. But I am sure other people have done so. 

The parameters (and shape of the barrier) is a very tricky question indeed. In Bell's derivation a is just the width of the inverted parabolic potential at the point where you truncate it (leaving to you to decide where to do that). I guess Bell took the mass as the mass of hydrogen (he gives a value 1.66x10^-16, but leaves out units), but properly it should be the reduced mass for motion along the the reactive coordinate. Actually Bell approximated the truncated parabola by an Eckhart potential for which an exact solution is available.

I believe that calculating the potential barrier by quantum mechanical methods is often done incorrectly (for instance by having the whole molecule in equilibrium with an instantaneous position of the hydrogen or proton).  In Truhlar's paper also parabolic barriers are used, and more realistic (?) barriers fitted to such a parabola.  I am not an expert in quantum chemical methods, however, and will refrain from further comments on that topic. I assume that you can play with the POLYRATE program until you get an answer that satisfies you.

If your reaction takes place in water or other polarizable media you have numerous additional worries. Check out the work of J.T. Hynes, who did a lot of work on the behavior of protons in polar (and aqueous) media. 

Thank you very much for your answer and paper. With this one and POLYRATE I have enough material to start working properly. I think that I have found correct transition structures with high accuracy methods, but even so, there are some differences in Ea in comparison to experimental one. I've made the representation of k vs 1/T and there are a range of temperatures that shows a clear tunnelling effect and it is very interesting to me perform these corrections to make computational prediction of similar systems with maximum accuracy possible.

Thank you very much for your time and dedication,

Joaquim Mª Rius Bartra

Universitat Autònoma de Barcelona