# [Pw_forum] rotational ASR in nanotube

WU Gang wugaxp at gmail.com
Fri Aug 27 13:36:25 CEST 2004

```Dear Mr. Baroni,

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)
>
> Please, if possible, don't  send me MS Word or PowerPoint attachments
> Why? See:  http://www.gnu.org/philosophy/no-word-attachments.html
>
> _______________________________________________
> Pw_forum mailing list
> Pw_forum at pwscf.org
> http://www.democritos.it/mailman/listinfo/pw_forum
>

```