[Pw_forum] About zero point energy

[oulihui666]

Dear all,
  I have a question about zero point energy calculation. According to a article called "Tutorial on calculating phonons: comparing the linear response and the small displacement methods", author states that we can calculate zero point energy use the results obtained with linear response method, i.e phonon code in pwscf. Calculated steps as follows(for example Al):
(1) > pw.x < Al.scf (This generates the self-consistent wave-function)
(2) > ph.x < Al.ph.in (This generate the dynamic matrices)
(3) > q2r.x < q2r.in (Obtaining force constant matrix)
(4) > matdyn.x < matdyn.in (Calculating the phonon dispersions)
(5) > matdyn.x < phdos.in (Calculating phonon density of states)
and this will produce a file called "Al.phdos" which contains the phonon density of states. Now by typing:
    awk '{e=e+2*1/2}END{print e/33.357*4.1357/1000}' Al.phdos
and you should see that the zero point energy. The question is, I do not understand the meaning of "{e=e+2*1/2}END{print e/33.357*4.1357/1000}", is this appropriate for the calculation of zero point energy? 
    In addition, In mail list, by calculating phonons all over the Brillouin zone (in practice, on a regular grid), and zero point energy by calculating {\hbar\over 2} \sum_{{\bf q},\nu} \omega_{{\bf q},\nu}. I do not understand the meaning of {\hbar\over 2} \sum_{{\bf q},\nu} \omega_{{\bf q},\nu} well. Anyone who help me will be appreciated.
 
Many thanks 
Best regards
Lihui

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Lihui Ou
PH.D Candidate in Electrochemistry                      
College of Chemistry and Molecular Science            
Wuhan University,430072,Hubei Province,China 
E-mail:oulihui666 at 126.com
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