[Pw_forum] my understanding about ASR

[Stefano Baroni]

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
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---
Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center -  
Trieste
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