UT theoretical chemistry code forum

Hello:
Does the prefactor calculated using dymprefactor include the vibrational entropy term? S_vib ( which is calculated as a sum of harmonic oscillators). I am interested in calculating the bulk diffusion coefficient in a fcc crystal. I would like to include the S_vib term which is approximated by a summation over the frequencies at the minimum and the saddle point. Is there a utility to do this automatically?

Regards,
Priya

Yes, the dymprefactor script calculates the vibrational entropy term for diffusion. A low prefactor means that the minimum has more entropy than the saddle, and a high prefactor is the opposite case.

Dear Graeme,
Thanks for the reply. Just a quick question to clarify: While trying to calculating the diffusion coefficient, D=D0 exp(-Q/kbT), the factor D0 is approximated in the harmonic limit as:
D0 = 1/6 a^2 exp(-ds/Kb) v0 where v0 is the preexponential factor of the rate constant.

When I use dymprefactor, is it the v0 or v0*exp(-dS/Kb) which is being reported.

While estimating the diffusion coefficient using this formula, I am getting a difference of around 10^-3 with the reported values. I don't expect a good agreement with the experiments but this difference seems a bit large. Just wanted to be sure that I am using the correct parameters.

Regards,
PG.

It is v0*exp(-dS/Kb); the rate in the T->infinity limit.

Hi,
I'm having a fundamental question here. Please correct me if I'm wrong.

D=(a^2)*(Equilibrium concentration of vacancies)*(defect jump Rate).
Empirically it is given as D = Do * exp (-Q/KbT)
And all the temperature independent terms are clubbed together into Do.

Priya, I think the exp(dS/Kb) that you're talking to refers to the vibrational entropy of vacancy formation which comes in the Do because the equilibrium concentration of vacancies is given as Xv = exp(dS/Kb)*exp(-dH/KbT). Thus, this exp(dS/Kb) comes from here. And I'm not sure if this prefactor is accounted from the Dymprefactor.pl script.

Graeme, Please clarify me.
The exp(dS/Kb) that you're refering to is the migration entropy term [which is different from the vibration entropy of vacancy formation] and yes, as the Vineyard's paper describes, the ratio of the product of N frequencies at minimum to the N-1 frequencies at saddle point does include this term.

Thanks..

yes