[Pw_forum] phonon symmetry and mode

[yumin qian]

thanks for your reply

2008/9/27 Paolo Giannozzi <giannozz at democritos.it>

> On Sep 26, 2008, at 11:01 , yumin qian wrote:
>
> > The group of S(q) is a subgroup of crystal lattice symmetry group S
> > (L),
>
> S(q) is the subgroup of the point group S of the crystal, that
> comprises all
> symmetry operations that leave q unchanged ("small group of q"). S may
> be smaller than the symmetry group of the lattice alone.
>
> > how to determine S(q) from S(L)?
>
> by applying the definition. It is automatically done by the code.
>
> > so is this subgroup of S(q) determines the phonon mode at point q  ?
>
> it determines the symmetry of phonon modes at point q, according to
> group theory.
>
> The symmetry in the phonon codes works this way:
> - for each q wavevector, the S(q) group is found
> - a new IBZ (Irreducible Brillouin Zone) is determined, using the S(q)
>   symmetry instead of the symmetry S of the crystal point group
> - the irreproducible representations (irreps) of S(q) are found.
>   Irreps are typically 1 to 3-dimensional (although there are a few
> cases
>   of 4- and even of 6-dimensional irreps)
> - the 3N-dimensional representation generated by the 3N coordinates of
>   the N atoms in the unit cell are decomposed into irreps. Linear-
> response
>   calculations are performed for displacements along these irreps .
> - all sums over the IBZ are performed using the k-points in the IBZ of
>   S(q) (typically larger than the IBZ used for the scf calculation,
> so more
>   k-points are needed)
> - symmetrization of the potential and of the dynamical matrix is
> performed,
>   using the S(q) group and the fact that each irrep transforms into
> itself
> - Finally, dynamical matrices at a different q in the star of q (i.e.
> all vectors
>   generated by applying operations of S to q) are generated, by
> applying
>   operations of S to the dynamical matrix
>
> Why is it so complicated? because it is a compromise between CPU and
> memory requirements.
>
> Disclaimer: I didn't write that part, so what written above reflects my
> present understanding and may not bear any resemblance with reality
>
> Paolo
> ---
> Paolo Giannozzi, Dept of Physics, University of Udine
> via delle Scienze 208, 33100 Udine, Italy
> Phone +39-0432-558216, fax +39-0432-558222
>
>
>
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-- 
Sincerely Y. M. Qian
Lab.of Condensed Matter Theory and Materials Computation
Institute of Physics
Chinese Academy of Sciences
Tel:  + 8610 8264 9147
E-Mail:yuminqian at gmail.com <E-Mail%3Ayuminqian at gmail.com>
P.O.Box 603   Beijing 100190
China
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