[Pw_forum] help me: how to calculate free energy
Stefano Baroni
baroni at sissa.it
Tue Aug 22 13:09:32 CEST 2006
On Aug 22, 2006, at 5:14 AM, hailin yu wrote:
> Dear all:
> In recently, I have calculated the phonon dispersion and
> phonon density of states of alpha-Sn using PWSCF. And our results
> are very agreement with previously work(PRB 57,10421(1998), phonon
> dispersion and phonon density of states).
very good
> But when I calucalte the free energy, our results are very
> different from the previously work, and our results are too large.
> So I want to konw there have any programme to calculate the free
> energy F(T) when attainted the phonon density of states.
The vibrational free energy can ben calculated from the vibrational
DOS using Eq. (1) of the above paper and replacing the sum over
normal modes with an \int n(\omega) d\omega. This results in a simple
one-dimensional integral over a finite range. Are you sure you want
us to send you a 10-lines piece of code doing just this?
If you have already written down your own 10-lines code and still
find wrong results, you may want to:
1) Check that your 10-lines code give correct results when used to
integrate functions that you can integrate analitically. Beware that,
due to Van Hove singularities, the DOS may have to be sampled at a
rather large number of points in order to obtain sensible numerical
results.
2) Check the normalization of the DOS. In order for the \int n
(\omega) d\omega to give the same result as in Eq. (1), The integral
of the DOS must be equal to the number of normal modes per unit cell,
i.e. 3N, N being the number of atoms. With this normalization, Eq.
(1) will give the free energy per unit cell.
Hoper this helps.
Stefano B.
>
> Thanks a lot!
>
> yuhailin
>
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---
Stefano Baroni - SISSA & DEMOCRITOS National Simulation Center -
Trieste
[+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype)
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