[Wien] meaning of G vectors for local orbitals

[Peter Blaha]

The LOs are connected to ONE SINGLE plane wave in order to guarantee symmetry constrains
(eg. the LO for Si at the first site must be symmetrized and have inversion symmetry for
the Si atom at the equivalent site.

Note, that am Alm(G) in LAPW is connected to ALL G vectors and the G-vector determines the
value of Alm(G),
while the LO just has attached a phase factor  exp(iGr_at) to it and this G is listed.

See Singh book for more details.

katrusiat schrieb:
> Dear Wien2k community, dear Prof. Blaha,
> 
> What is the meaning of the lattice vectors G for local orbitals? The local orbitals have nothing to do
> with the plane waves that are characterized by G, but still when the expansion coefficients
> for the eigenvectors are made written in case.output1, one can see that each local orbital has a corresponding G.
> For instance, for the userguide example TiC:
> 
>    0   0   0
>                   -0.697973   0.000000   0.000000   0.000000  -0.002222   0.000000   0.000000   0.000000   0.000000       REALPART
>   -1  -1  -1
>                    0.000000   0.001306  -0.000071   0.007838   0.000000   0.000000   0.000000   0.000000   0.083386       REALPART
>    1  -1  -1
>                    0.000000   0.003939   0.005111  -0.004638   0.000000   0.000000   0.000000   0.000000  -0.044888       REALPART
>   -1   1  -1
>                    0.000000  -0.003836   0.006109  -0.003333   0.000000   0.000000   0.000000   0.000000   0.028094       REALPART
>    0   0   0
>                    0.007391   0.000000   0.000000   0.000000  -0.010230   0.000000   0.000000   0.000000   0.000000       REALPART
> 
> is the list of expansion coefficients for LO's for the first ten energy eigenvalues. The G vectors are listed in the left.
> 
> Thank you very much,
> 
> Kateryna Foyevtsova
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-- 

                                       P.Blaha
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Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
Phone: +43-1-58801-15671             FAX: +43-1-58801-15698
Email: blaha at theochem.tuwien.ac.at    WWW: http://info.tuwien.ac.at/theochem/
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