density of states

[brocks]

Dear Administrator,

I have a question for you.
I'm studying a system with d orbital giving an orbital ordering.
The unit cell of the system has its vectors along the usual x,y,z directions so:
A1=(a,0,0)
A2=(0,b,0)
A3=(0,0,c)
In the plane xy at z=0 there are two ions at
A=(a/2,0,0) and B=(0,b/2,0)
The orbital ordering is along the line connecting this two ions and i know this because i made a contour plot of the partial charge density already.
It is a d(3x'**2-r'**2) ordering along the direction connecting A and B on the ion A, d(3y'**2-r'**2) along the direction connecting C to A on the ion C, where x' is connecting A to B and y' A to C=(a/2,b/2,0).
Now i want to plot the density of state per angular momenta
in the basis of the ions (x',y') interested in the orbital ordering.
VASP naturally gives the density of states making the projection on the different d levels (dxy,dyz,dxz,dz**2,dx**2-y**2) using the coordinates x,y,z.
The quantity d(x**2-y**2) for example given by VASP is different from what i'm looking for because x,y,z are not connecting my ions.
The coordinates of the ions in this case are rotated of 45 degrees respect to the ones used by VASP.
So if i consider the trasformation:
x'=(1/sqrt(2))*(x+y)
y'=(1/sqrt(2))*(x-y)
z'=z

i can easily go from the cordinates of VASP to the coordinates of my ions and this brings me to have, for example, (we can forget about the normalization factors at this moment):

density_of_states_d(x'**2-y'**2) =
density_of_states_d(xy)_calculated_by_VASP

(i simply used the definition of local density of states to get it as integration in the sphere.........).
I'm really wondering if is possible to use this trick.

Thank you in advance.

[brocks]

..i wrote C=(a/2,b/2,0) but it is C=(a/2,b,0).....

[admin]

there are no 'local' coordinate systems in vasp, i.e. z is always along z of the cell, not along the line connecting the NNs. Hence, d_xy would be the orbital causing bonds between A and B.
The ordering of the l,m decomposed DOS in DOSCAR is
l,-m.... l,0, ... l,+m,
ie. s, p_y, p_z, p_x, d_xy, d_yz, d_z2-r2, d_xz, d_x2-y2
if you want to label the local partial DOS according to some local
coordinates, you can of course do so.