[Pw_forum] my understanding about ASR

[xwzhang at uestc.edu.cn]

Dear Eduardo and Stefano,
Thank you for clear and careful explaination of my phonon problem. I am now doing some tests and getting more experiences, because I am a freshman in phonon calculation. 
It seems to me that ASR can "force" the acoustic phonon at Gamma point to zero. A naive thought is that can we just ignore it? In this case, 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?  
Regards
Wenxu Zhang
State Key Lab. of thin films and integrated devices ,
Univ. of Elec. Sci. & Tech. of China.
Chengdu, 610054, China
>Eduardo Ariel Menendez Proupin wrote:
>> This happens because
>> a) 0 frecuencies at Gamma occurs because the energy is is invariant 
>> with respect to arbitrary translations of the whole crystal (the same 
>> translation for all atoms). From this assumption the accoustic sum 
>> rule (ASR) is obtained theoretically.
>> b) The plane wave DFT calculations do not have this invariance 
>> exactly, because of the plane wave cutoff. The energy is invariant not 
>> for arbitrary translations, but for translations in the FFT grid.
>> c) I guess that the absolute translation invariance is lost in the 
>> back and forth FFTs of the exchange-correlation potential, which is 
>> non linear, and probably in some part related with the ultrasoft 
>> pseudopotentials. Someone correct me if I am wrong, please.
>everything correct, except for the clarification of a detail.
>The problem is actually not in the finite kinetic energy cutoff but in 
>the fact that the exchange and correlation energy is computed in real 
>space on a discrete grid and hence the total energy is invariant (as you 
>said) only for translation in the FFT grid.
>Increasing the charge density cutoff increases the grid density thus 
>making the integral more exact thus reducing the problem.... 
>unfortunately rather slowly...
>This problem is usually more severe for GGA  than with LDA because the 
>GGA functionals have functional forms that vary more strongly with  the 
>position; particularly so for isolated molecules or system with 
>significant portions of "vaccum" because in the exponential tail of the
>charge density a) the finite cutoff  (hence there is an effect due to 
>cutoff) induces oscillations in rho and b) the reduced gradient is diverging
>
>stefano
> 
>> You may increase the density cutoff (ecutrho) and see if the first 
>> three frequencies get closer to zero. First do it with one of the 
>> ESPRESSO examples, that run in minutes. I guess that I made that test 
>> some years ago.
>> Using larger cutoffs increase a lot the calculation time. That is why 
>> you have the tricky option to impose the ASR in postprocessing (matdyn.x).
>>
>> Practical way. If your "wrong" frecuencies are smaller than 50 cm^-1, 
>> this is normal. Apply the ASR in the input for matdyn. Check that the 
>> other frequencies do not change more than 1 or 2 cm^-1. Then, if  this 
>> makes you happy, go to write your report
>>
>> >I have another question about the output: What is the >difference 
>> between the total magnetic moment and the >absolute magnetic moment.
>> This has been asked in the forum before. Please, google for this. If I 
>> remember well, the absolute magnetic moment is the integral of the 
>> absolute value of the magnetization.
>>
>> Regards
>> Eduardo Menendez
>>
>> On Sat, Jun 14, 2008 at 2:57 AM, >> > wrote:
>>
>>     Dear my pwscf friends,
>>
>>     Recently, I am trying to do phonon calculations in Heusler. As a
>>     first step, I tried to reproduce the results of a paper by
>>     Zayak(PRB, 72, 054113, 2005). I choose Ni2MnGe as an example. To
>>     my surprise, the acoustic branches at Gamma point gives a
>>     frequency of about 1 THz, which should be zero. Other branches
>>     agree with the published data.
>>
>>     I wonder what might be the reason? I attached my scf, and phonon
>>     input files, and the phonon out put files.
>>
>>     I have another question about the output: What is the difference
>>     between the total magnetic moment and the absolute magnetic moment.
>>
>>     Thank you and wish you a happy weekend!
>>
>>     Wenxu Zhang
>>
>>
>> ------------------------------------------------------------------------
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