[Pw_forum] rotational ASR in nanotube

[WU Gang]

Dear Mr. Baroni,

Many thanks for your reply. With your kindly help, I have gotten the
criterion of rotational ASR and a formula which can check whether my
force constant matrix obeys this criterion. But how can I fix the
original force constant matrix to make it obey the rotational ASR? Do
I need to add a Lagrange constraint? But I have no idea how to add
this. Would you please give me some advice? Thank you very much!

Gang Wu

On Wed, 25 Aug 2004 12:44:55 +0200, Stefano Baroni <baroni at sissa.it> wrote:
> On Aug 25, 2004, at 12:22 PM, WU Gang wrote:
> 
> > Hello All.
> >
> > Recently I calculated the phonon-dispersion curves for nanotubes, but
> > I found that at Gamma point, there is always some imaginary phonon
> > frequencies, even when I applied translational acoustic summing rule
> > (ASR) on the final force constant matrix. After look up some
> > reference, a so-called rotational ASR seems to be important in reduce
> > these unstable frequencies.
> 
> Nice problem of physics!
> 
> >  But What does this rule mean in nanotube?
> 
> It simply means that you cannot pay any energy to twisting a tube
> around its axis.
> In free space, this is trivially rotational invariance. With periodic
> boundary conditions,
> of course, such a twist would correspond to a non-trivial periodic mode
> which has got
> zero frequencies. The same, by the way would hold or any molecule.
> 
> > And how can I apply this rule to the result force constant matrix?
> 
> Once you understand what physically this "rotational ASR" means,
> it should not be difficult to figure out how to impose it onto the
> dynamical matrix that
> you calculate. We would leave this to you as an exercice (Hint: figure
> out which atomic
> displavement pattern would correspond to a rigid twist of the tube and
> see how the ASR is
> imposed in the translational case).
> 
> > Thank you very much!
> 
> You are most welcome!
> 
> Stefano Baroni
> 
> ---
> Stefano Baroni    ---  SISSA  &  DEMOCRITOS National Simulation Center
> via Beirut 2-4 34014 Trieste Grignano / [+39] 040 3787 406 (tel) -528
> (fax)
> 
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> Why? See:  http://www.gnu.org/philosophy/no-word-attachments.html
> 
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