[Pw_forum] phonon symmetry and mode
Paolo Giannozzi
giannozz at democritos.it
Fri Sep 26 22:54:44 CEST 2008
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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