[Pw_forum] help me: how to calculate free energy

[Stefano Baroni]

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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