## Vinyard formula in Arrhenius Eq. dymprefactor.pl

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microomran
Posts: 28
Joined: Fri Aug 03, 2018 7:06 am

### Vinyard formula in Arrhenius Eq. dymprefactor.pl

Dear Dr.Graeme,

Currently I am calculating the rate constant for elementary reactions.I am using the simple harmonic TS theory and calculating the prefactor using dymprefactor.pl

for that I use the simple form k(T)=A exp (-Ea/KbT) where A is prefactor form the script and Ea is the energy barrier from cNEB/Dimer calculations.

I have a couple of concerns :

1-Is that approach is OK? or I am missing something.I compare to literature and I found an alternative method utilizing partition function q=1/sum (1-exp(-hv/KbT) then A=KbT/h * Q1/Q2 (where Q1 for TS and Q2 for initial state) ,Are these approaches equivalent?

2-In both ways I did not see the ZPE correction /entropic effect included.When they are preferred to include them? (e.g specific Temperature range..etc?)
Thank you
Regards
Attachments
1406.3621.pdf
graeme
Posts: 1999
Joined: Tue Apr 26, 2005 4:25 am
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### Re: Vinyard formula in Arrhenius Eq. dymprefactor.pl

The Arrhenius expression uses the classical harmonic partition function q_cl = kT/hw. You can certainly replace this with the quantum partition function, which is close to what you wrote: q_qm = exp(-hw/2kT) / (1-exp(-hw/kT). At high temperature, this converges to the classes partition function and at low temperature, -kT ln q_qm will give you the zero point energy, hw/2. The full quantum partition function is indeed more accurate and important at low temperature (kT<hw). At high temperature (kT>hw) the classical expression is nice because it yields a constant prefactor that does not change with temperature, and a linear Arrhenius relation. Entropic effects are included in both expressions, within the harmonic approximation.
microomran
Posts: 28
Joined: Fri Aug 03, 2018 7:06 am

### Re: Vinyard formula in Arrhenius Eq. dymprefactor.pl

Thank you for the explanation.
In fact, I am working with temperature 800-1000K (that is considered in high Temperature,is n't it?) so I used that simple classical form k(T)=A exp (-Ea/KbT) where A is from dymprefactor.pl/Vineyard and I plug in the Ea directly from NEB results for few calculation.Values -up till now- are within range compared with literature results with only minor differences.

I also came across dymeffbar.pl and dymrate.pl ,What is the initial and final temperatures? Is it the reaction range such as above range of 800-1000K?
(Note:dymrate.pl is not updated in scripts page http://theory.cm.utexas.edu/vtsttools/scripts.html ,I am not clear with output)
graeme