[Pw_forum] help me: how to calculate free energy

Stefano Baroni baroni at sissa.it
Tue Aug 22 21:43:15 CEST 2006

On Aug 22, 2006, at 4:39 PM, hailin yu wrote:

> Dear Stefano B:
>      Thank you for your advice.
> I have writen a programme to compute the free energy according to  
> Equ(1)(PRB,57,10421(1998)).

"eq 1"

> And I have checked the normalization of the DOS and found the  
> integral of the DOS  equal to 5.932386, agreement with 3*2 (2  
> atomic per unit cell, is unit cell or primitive cell?? ). I also  
> have using Equ(3)( Chem. Phys. Lett. 417,272-276(2005))

"eq 2"

> to compute free energy and attainted the same results with using Equ 
> (1)(PRB,57,10421(1998)).

I am confused. The equations that you cite are the same, but for the  
fact that in the first one calculates the free energies directly by  
sampling phonon frequencies in the BZ, whereas in the second one  
makes explicit use of the density of states. It thus seems that,  
while using the first equation, you do *NOT* use any DOS, but just  
the phonon frequencies calculated by PHONON. But then you should have  
*TWO* ten-lines fortran codes, don't you? If you really use the first  
eq as is and the second as is, the fact that you obtain the same  
result is good news: your two 10lines codes are likely to be almost  

> but our results is still different with the previous work (PRB, 
> 57,10421(1998)). At the range of 0~400 K, our results ( free  
> energy) decrease nearly 6 eV,  while the previous work is about  
> 0.26 eV. Where are wrong?

difficult to say. may be units, but you may want to post the  
calculated DOS in a sensible format (e.g., two columns: first  
frequency (specify units, second DOS)

Also, see a recent post by Eyvaz Isaev who seems eager to share some  
of the codes he has written to calculate thermodynamic properties  
using QHA/DFPT.

Cheers - SB

Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center -  
[+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype)

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