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

[Stefaan Cottenier]

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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