[Wien] q re: 'local coordinates' and px, py, pz

[Cormac McGuinness]

In this instance the local rotation matrix given by WIEN2k for the
oxygen sites is the identity matrix. 

I took it from the posting I referenced of Oct 2003 that WIEN2k uses
local coordinate systems as distinct from an additional rotation of
these coordinate systems by the local rotation matrix ? 
In my case the Cu-O-Ti2 planes in the crystal structure are at 6
distinct angles with respect to each other so the global x,y,z (or even
a simple rotation of this) would mean something very different at each
of these equivalent sites with respect to the local positioning of the
single Cu and two Ti atoms.

I think my question remains as to how this local coordinate system for
the oxygen is oriented for point group m (C_s). Is x directed towards
the Cu atom, or is z directed toward the Cu atom ?

Perhaps I could poke around in the code but I wouldn't know where to
begin to look ?

Thanks
Cormac

On Fri, 2004-07-30 at 12:07, Stefaan Cottenier wrote:
> Your question will be probably solved by looking at the local rotation
> matrix, that is given for each inequivalent position in case.struct. (I
> always forget whether this matrix transforms from global to local or from
> local to global axis system, and whether it is printed rowwise or
> columnwise -- but you can probably figure that out. Look also in the UG, at
> the end there is section on local rotation matrices).
> 
> Stefaan
> 
> ----- Original Message ----- 
> From: "Cormac McGuinness" <Cormac.McGuinness at tcd.ie>
> To: <wien at zeus.theochem.tuwien.ac.at>
> Sent: Friday, July 30, 2004 11:29 AM
> Subject: [Wien] q re: 'local coordinates' and px, py, pz
> 
> 
> > Dear Wien users,
> >
> > I am calculating a system where O atoms are on sites with point-group m
> > (C_s) bonding in a plane with 1 Cu and 2 Ti atoms. My question is what
> > are the 'local coordinates' i.e. in which directions are p_x p_y and p_z
> > oriented (this being the way that WIEN2k splits the p-states)
> >
> > >From the discussion in the archives of Oct 2003 with the subject "how to
> > calculate the DOS of p(sigma) or p(pi)":
> >
> > > P.Blaha wrote in response to Yushan Wang:
> > >
> > > a) WIEN usually selects the proper coordinate system for you (i.e. it
> > > introduces automatically a "local coordinate system" if necessary for
> > > "proper" analysis).
> > > A simple example of what is going on: Suppose you do a diatomic
> > > molecule with coordinates (0,0,0) and (x,x,0). In this case WIEN will
> > > introduce "local coordinates" and put the z axis along the (1,1,0)
> > > direction. Thus you will get an eigenvalue (orbital) which has p-z
> > > character (that's your sigma orbital), and other eigenvalues with
> > > px,py character (these are the pi orbitals in this case).
> > > Without the local coordinates the px orbital would be part of both,
> > > the sigma AND the pi orbitals.
> > >
> >
> > Is x oriented towards the Cu atom, y in the plane of the atoms and z out
> > of the plane ? or is z directed towards the Cu atom ?
> >
> > I should note that WIEN2k does not suggest a local rotation matrix but
> > does give in case.outputsgroup the following information
> >
> > Sort number: 4
> >   Names of point group: m      m      Cs
> >   New basis vectors for this point group:
> >     1.0000   0.0000  0.0000  <--- 1
> >    -1.0000   0.0000 -1.0000  <--- 2
> >     0.0000   1.0000  0.0000  <--- 3
> >
> > Perhaps I could also ask for an interpretation of the above ?
> >
> > Yours gratefully
> > Cormac
> > -- 
> > Dr. Cormac McGuinness, Lecturer, Physics Dept. Trinity College,
> > Dublin 2, Ireland.
> >
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> > Wien at zeus.theochem.tuwien.ac.at
> > http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien
> >
> 
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-- 
Dr. Cormac McGuinness, PhD. etc., Lecturer, Physics Dept. Trinity College,
Dublin 2, Ireland. Cormac.McGuinness at tcd.ie
Telephone: +353 1 6083547 Fax: +353 1 6711759 Office: SNIAM 3.17