[Pw_forum] rotational ASR in nanotube

[WU Gang]

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. But What does this rule mean in nanotube?
And how can I apply this rule to the result force constant matrix?

Thank you very much!

Gang WU