[Pw_forum] help me: how to calculate free energy
yuhailin_79 at msn.com
Tue Aug 22 16:39:32 CEST 2006
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)). 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)) to compute free energy and
attainted the same results with using Equ(1)(PRB,57,10421(1998)). 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?
Thank you very much!
the follow is my pragramme
double precision hi,k,T,Z,F,dos
double precision aSn(197),aSndos(197)
hi= 1.055 !
k=1.38 ! the Boltzman's constant
read(1,*)aSn(i),aSndos(i) ! the unit of omega is CM-1
Z=(hi*aSn(i)*0.029979*10.0)/(2*k*T) ! the value of (h*omega)/(2*K*T);
0.029979 is the coefficient of CM-1 ~THz
F=F+k*6.24151*(10.0E-5)*T*log(exp(z)-exp(-z))*aSndos(i) ! the sum of
!the unit of F is eV;
>From: Stefano Baroni <baroni at sissa.it>
>Reply-To: pw_forum at pwscf.org
>To: pw_forum at pwscf.org
>Subject: Re: [Pw_forum] help me: how to calculate free energy
>Date: Tue, 22 Aug 2006 13:09:32 +0200
>On Aug 22, 2006, at 5:14 AM, hailin yu wrote:
>> 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).
>>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.
>>Thanks a lot!
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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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