<div dir="ltr">thanks for your reply<br><br>
<div class="gmail_quote">2008/9/27 Paolo Giannozzi <span dir="ltr"><<a href="mailto:giannozz@democritos.it">giannozz@democritos.it</a>></span><br>
<blockquote class="gmail_quote" style="PADDING-LEFT: 1ex; MARGIN: 0px 0px 0px 0.8ex; BORDER-LEFT: #ccc 1px solid">On Sep 26, 2008, at 11:01 , yumin qian wrote:<br><br>> The group of S(q) is a subgroup of crystal lattice symmetry group S<br>
> (L),<br><br>S(q) is the subgroup of the point group S of the crystal, that<br>comprises all<br>symmetry operations that leave q unchanged ("small group of q"). S may<br>be smaller than the symmetry group of the lattice alone.<br>
<div class="Ih2E3d"><br>> how to determine S(q) from S(L)?<br><br></div>by applying the definition. It is automatically done by the code.<br>
<div class="Ih2E3d"><br>> so is this subgroup of S(q) determines the phonon mode at point q ?<br><br></div>it determines the symmetry of phonon modes at point q, according to<br>group theory.<br><br>The symmetry in the phonon codes works this way:<br>
- for each q wavevector, the S(q) group is found<br>- a new IBZ (Irreducible Brillouin Zone) is determined, using the S(q)<br> symmetry instead of the symmetry S of the crystal point group<br>- the irreproducible representations (irreps) of S(q) are found.<br>
Irreps are typically 1 to 3-dimensional (although there are a few<br>cases<br> of 4- and even of 6-dimensional irreps)<br>- the 3N-dimensional representation generated by the 3N coordinates of<br> the N atoms in the unit cell are decomposed into irreps. Linear-<br>
response<br> calculations are performed for displacements along these irreps .<br>- all sums over the IBZ are performed using the k-points in the IBZ of<br> S(q) (typically larger than the IBZ used for the scf calculation,<br>
so more<br> k-points are needed)<br>- symmetrization of the potential and of the dynamical matrix is<br>performed,<br> using the S(q) group and the fact that each irrep transforms into<br>itself<br>- Finally, dynamical matrices at a different q in the star of q (i.e.<br>
all vectors<br> generated by applying operations of S to q) are generated, by<br>applying<br> operations of S to the dynamical matrix<br><br>Why is it so complicated? because it is a compromise between CPU and<br>memory requirements.<br>
<br>Disclaimer: I didn't write that part, so what written above reflects my<br>present understanding and may not bear any resemblance with reality<br><br>Paolo<br>---<br>Paolo Giannozzi, Dept of Physics, University of Udine<br>
via delle Scienze 208, 33100 Udine, Italy<br>Phone +39-0432-558216, fax +39-0432-558222<br><br><br><br>_______________________________________________<br>Pw_forum mailing list<br><a href="mailto:Pw_forum@pwscf.org">Pw_forum@pwscf.org</a><br>
<a href="http://www.democritos.it/mailman/listinfo/pw_forum" target="_blank">http://www.democritos.it/mailman/listinfo/pw_forum</a><br></blockquote></div><br><br clear="all"><br>-- <br>Sincerely Y. M. Qian <br>Lab.of Condensed Matter Theory and Materials Computation <br>
Institute of Physics <br>Chinese Academy of Sciences<br>Tel: + 8610 8264 9147<br><a href="mailto:E-Mail%3Ayuminqian@gmail.com">E-Mail:yuminqian@gmail.com</a> <br>P.O.Box 603 Beijing 100190<br>China <br><br></div>