[Pw_forum] Re: phonon modes assignment and others

[Stefano de Gironcoli]

Please take a book on group theory and look for irreducible 
representations ...

If you have a set of patterns that belong to an irreducible 
representation (say U^mu_i, where i is the atom index and mu the
partner index in the representation)  what you need to do in general is 
to compute the way they transform under
symmetry operations.
If S is the symmetry operation , its action on a given pattern will 
transform it in a linear combination of its partners
S ( U^mu_i)  =  \sum_nu  D(S)_mu,nu  U^nu_i

Compute the trace of D(S) (the characteristics of the representation) 
and apply the orthogonality theorem you find in
group theory books to discover which representation you are dealing with.

stefano

W. YU wrote

>Any further remarks on the method you used would be
>much appreciated.! It seems completely two different
>things for me to have a space group in mind and know
>what irreducible representations are associated with
>it or on the contrary, to have a set of mormal vectors
>for specific lattice mode and find to which
>irreducible representation they belongs.
>
>  
>