[Pw_forum] my understanding about ASR

[stewart at cnf.cornell.edu]

Hi Stefano, 

You raise a good point and perhaps I should have been more careful in my 
previous statement.  I agree that based on symmetry, the total forces on the 
system should be zero and there should be a set of zero mode.  Applying the 
acoustic sum rule reinstates this fact.  From my practical experience, I 
recall having greater problems with negative frequencies at the Gamma point 
for systems that had the lattice constant greater than the equilibrium value 
(expanded system).  This occurred for direct calculations at small q and 
also based on interpolating the phonon dispersion from the q grid.  Here you 
get phonon softening which shifts the phonon dispersion curves down and 
perhaps this leads to problems with calculating the phonon dispersion from 
the given q grid near Gamma.  I took this as an indication of the 
instability of the expanded structure, but perhaps this is not the best way 
to view it. 

Best regards, 

Derek 


Stefano Baroni writes: 

> 
> On Jun 19, 2008, at 4:17 PM, stewart at cnf.cornell.edu wrote: 
> 
>> Fig 2 (D. A. Stewart, New. J. Phys. 10 043025 (2008)).  Of course, the
>> difference you get between ASR results and direct calculations will  
>> depend
>> strongly on how well relaxed your structure is.
> 
> hmmm: this may well be the case, but if this is so, it must be for a  
> nontrivial reason (which, if true, would qualify the "of course" as  
> slightly misplaced). 
> 
> the total force acting on any isolated system is of course zero, even  
> though the system is not at equilibrium ("not well relaxed"). in  
> particular, this total force is invariant ("invariantly zero!") with  
> respect to a homogeneous translation of the system. therefore, the  system 
> must have a zero mode (actually three of them: one for each  cartesian 
> coordinate), irrespective on how well (or how bad) the  internal degrees 
> of freedom have been optimized. 
> 
> is this wrong? 
> 
> SB 
> 
>>  
>> 
>> http://dx.doi.org/10.1088/1367-2630/10/4/043025 
>> 
>> Best regards, 
>> 
>> Derek 
>> 
>> 
>> Paolo Giannozzi writes: 
>> 
>>> xwzhang at uestc.edu.cn wrote: 
>>> 
>>>> are there any problem that the slope of the phonon around Gamma is
>>>> incorrect, because ASR cure the problem of k=0, but what about other
>>>> points near it?
>>> 
>>> for phonons at k/=0, the error due to ASR violation seems to be
>>> usually negligible. I never tried to make calculations with
>>> very small q, though. 
>>> 
>>> Paolo
>>> -- 
>>> Paolo Giannozzi, Democritos and University of Udine, Italy
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>>> 
>>  
>> 
>> 
>> ################################
>> Derek Stewart, Ph. D.
>> Scientific Computation Associate
>> http://www.people.cornell.edu/pages/das248/
>> 250 Duffield Hall
>> Cornell Nanoscale Facility (CNF)
>> Ithaca, NY 14853
>> stewart (at) cnf.cornell.edu
>> (607) 255-2856
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> 
> ---
> Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center -  
> Trieste
> [+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype) 
> 
> La morale est une logique de l'action comme la logique est une morale  de 
> la pensée - Jean Piaget 
> 
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> 
>  
> 
> 
 


################################
Derek Stewart, Ph. D.
Scientific Computation Associate
250 Duffield Hall
Cornell Nanoscale Facility (CNF)
Ithaca, NY 14853
stewart (at) cnf.cornell.edu
(607) 255-2856