[Pw_forum] The choice of Acoustic Sum Rule for crystal

[Matteo Cococcioni]

Dear Baoling,

I will try to address some of your questions.



On Jan 15 2007, naivebamboo Huang wrote:

>Dear PWscf users,
>       I am trying to calculate the phonon eigen modes of Bi2Te3 crystal 
> at gamma point. The fraction of one Te atom has two different reported 
> values in the literature (x1=0.792, x2=0.7905). 


This sounds pretty obscure to me: what is the fraction of one Te atom? are 
you considering two different compositions?


I want to know which 
> value is more appropriate. I calculated the energy of the cell and found 
> the configure with x=0.7905 has a very slightly lower energy(0.001% 
> lower, does this mean the well is flat?). I also calculated the 
> frequency. Both of the configurations give 14 positive frequencies and 1 
> negative frequency (totally 15 modes). I just thought this may be due to 
> the acoustic sum rule. I impose asr='simple' and used dynmat.x to get the 
> frequency. Only x=0.792 gives 12 positive frequencies and 3 zero 
> frequency. But if I set asr='crystal', both configures can produce 12 
> positive frequencies and 3 zero frequency. After checking with the gamma 
> point of experimental dispersion curve at 300 K, the configure x=0.792 
> and asr='crystal' give the best results. My questions are
>          (1) which ASR  should I use, since the different ASR give 
>different frequencies (10% difference for x=0.792 configure)

Here is the explanation I have found in dynmat.f90:

!  asr   character   indicates the type of Acoustic Sum Rule imposed
!                     - 'no': no Acoustic Sum Rules imposed (default)
!                     - 'simple':  previous implementation of the asr used
!                     (3 translational asr imposed by correction of
!                     the diagonal elements of the dynamical matrix)
!                     - 'crystal': 3 translational asr imposed by optimized
!                     correction of the dyn. matrix (projection).
!                     - 'one-dim': 3 translational asr + 1 rotational asr
!                     imposed by optimized correction of the dyn. mat. (the
!                     rotation axis is the direction of periodicity; it
!                     will work only if this axis considered is one of
!                     the cartesian axis).
!                     - 'zero-dim': 3 translational asr + 3 rotational asr
!                     imposed by optimized correction of the dyn. mat.
!                     Note that in certain cases, not all the rotational asr
!                     can be applied (e.g. if there are only 2 atoms in a
!                     molecule or if all the atoms are aligned, etc.).
!                     In these cases the supplementary asr are cancelled
!                     during the orthonormalization procedure (see below).
!                     Finally, in all cases except 'no' a simple correction
!                     on the effective charges is performed (same as in the
!                     previous implementation).


It sounds to me like: asr = 'simple' should work in most cases; probably 
'crystal' is more accurate and works better. However I would expect that 
only the frequencies close to 0 will differ. Corrections on the others 
should be small.


>           (2) how can I trust the results I calculated? Does the positive 
>eigen frequency indicate a stable structure? I guessed at 300 K, the 
>frequencies should be different from those of the relax structure.
>

I would say yes. If frequencies are positive as in your case I would trust 
the crystal is in a local minimum at least. You could even check comparing 
the energy of the relaxed ionic configuration (at which I guess you are 
computing phonons) with that obtained imposing the distorsion pattern of 
one of the vibrational mode you want to check and making sure the former is 
lower than the latter.

At 300K in principle you should take into account thermal expansion (e.g. 
with the quasi harmonic approximation) and compute phonons from the finite 
T free energy. I wouldn't expect however a very large difference from the 
0K result you are considering.

Hope this helps.

Matteo

>Thanks very much
>
>Baoling
>
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Matteo Cococcioni
Department of Chemical Engineering and Materials Science
University of Minnesota
151 Amundson Hall
421 Washington Av. SE
Minneapolis, MN 55455
Tel. +1 612 624 9056    Fax +1 612 626 7246
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