[Wien] Cu-3d orbitals under the symmetry operations

[wmppemam@lg.ehu.es]

The space group symmetry of a crystal is the one of the atomic positions, 
as points, and also of its electron density as a whole. But it is not 
necessarily the symmetry of any local or extended basis of electron states 
that you may use or construct.

Regards,

J. Manuel Perez-Mato
=======================================================================
On Fri, 20 Feb 2009, katrusiat wrote:

> Dear Wien2k community,
>
> Suppose in a crystal of 139_I4/mmm space group there is a Cu atom at (x,y,z) = (0.5,0.5,z) (assuming that the (0,0,0) point is in the centre of the unit cell and x,y,z are in fractions of the unit vectors). Another, equivalent to this one, Cu atom would then be at (x,y,z) = (0.5,0.5,-z) as obtained from, for instance, (x,y,-z) or (y,x,-z) generators of the 139_I4/mmm space group. The (x,y,-z) generator is a mirror plane reflection about xy-plane, and the (y,x,-z) generator is this same reflection plus a subsequent reflection about the (x=y) plane going through (0,0,0).
>
> Now, I want to know how the "+" and "-" lobes of the Cu-3d_x2y2 orbital of the second Cu are oriented, when some reference orientation of the lobes of the first Cu is assumed. But here is the problem: when (x,y,-z) and (y,x,-z) generators are applied to the lobes, one gets different answers :(
>
> Which is the way to determine the orientation of the lobes in the Wien2k??
>
> Thank you very much!
>
> Kateryna Foyevtsova
>
>
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