[Pw_forum] phonon symmetry and mode

[Paolo Giannozzi]

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