[Wien] how to calculate the DOS of p(sigma) or p(pi)

[Peter Blaha]

> 	Onderwerp: [Wien] how to calculate the DOS of p(sigma) or p(pi)

> Whether this is possible, depends on your system.  Eg. I've done it myself for systems like graphite.  What you have to do is decompose the DOS not only w.r.t. L but also w.r.t. M.
> Eg. in the case of graphite, if you choose the z axis perpendicular to the graphitic planes and x,y in the planes, then the pi-component is equal to the L=1,M=0 DOS, and the sigma is equal to the sum of 0,0 and 1,-1 and 1,1.
> To get the l,m decomposed DOS:
> * finish a SCF calculation
> *go into case.struct and set isplit to 99 (this is not in w2web structgen, you have to edit the file - be careful, it's formatted!  So if you replace 4 by 99, delete a white space)
> *run lapw2 -qtl
> *now select the correct columns in case.int to get 0,0;1,0 etc.
> *add the columns yourself
> *publish a pi,sigma paper yourself :-)
>
> Careful : your coordinate system is important!  Be aware of local rotation matrices etc.

The recipie given above is ok and the most "general" solution.
However, in MOST (if not all) cases it is much simpler and WIEN provides
nearly an "automatic" way to get "pi" or "sigma" DOS.
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.

Of course, what is sigma and pi depends on the system under investigation.
The graphite example mentioned above has only ONE pi-orbital (pz in this case),
while px,py are the sigma orbitals.

b) Just look at the top of case.qtl. In almost all cases WIEN2k "splits"
the p-states properly according to the respective point symmetry, and
you will find for instance a pz and px+py DOS which correspond to your
desired pi and sigma (or sigma and pi).



                                      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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