Vinyard formula in Arrhenius Eq. dymprefactor.pl

[microomran]

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

[graeme]

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]

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]

800-1000K is almost for sure high-temperature. You really need to compare kT to hw for the highest frequencies in your system, but most phonons are excited at 1000K.

Those two scripts do evaluate rates with the quantum partition function. I guess they were used to make Arrhenius-like plots, so you can give a range of temperatures over which the rate will be calculated. You can use any range including 800-1000K, but it would be good to plot to a sufficiently low temperature so you can see where the rate deviates from the classical Arrhenius form. This will be around a temperature where kt=hw.