Quantitative Interpretation of Projected DOS

[Franky]

Hi,
I have a question concerning the projected DOS (PDOS) using the LORBIT-Flag.
The QUALITATIVE picture remains unchanged if I use lorbit = 1 or 11. Only the absolute values of the lm-decomposed DOS vary depending on the setting of RWIGS due to the different radiuses. So far so good, but if you want to go beyond the qualitative to a QUANTITATIVE interpretation you get into trouble.

1. E.g., the relative size of the s-projected and p_z-proj. DOS are missleading (due to different radial extend of the s and p_z wavefct. you project on and a constant radius for all l-quantumnumbers). Increasing RWIGS does not seem to help. The charge inside the sphere does not converge to a constant value which in my eyes should happen.

2. The energy integral of the PDOS for every l-quantumnumber should be finite but it is not. If you increase NBANDS the PDOS does not drop to zero for higher eigenvalues. Analaytically, however, the value of the integrated PDOS should be the norm of the function you project on due to the completeness of the eigenfunctions.
This point leads you back to 1 since you dont know what the integral of the PDOS should be so that you could actually compare the absolute values of the PDOS for l = s,p,d,...

What am I missing?
Thanks alot.

[admin]

ad 1) please read the postings concerning partial charges and magnetic moments. This is inherent to all mixed- and PW basis set calculations. This has been discussed in the forum several times before.
ad 2) you must of course integrate up to the Fermi energy only, all states higher in energy are not occupied.

[Franky]

ad1)
Sorry, forget what I said about the charge inside the sphere.

ad2)
I am not quite sure that we are talking about the same thing.
I am talking about the integral of the PROJECTED DOS for a fixed quantum number L and M.
So, for example, you project all your kohn-sham wavefcts., that you obtain from a VASP run
(occupied and unocc, bound and unbound), onto a "p_z" wavefunction.
Now, if you integrate the resulting PDOS from -INF to INF you get the norm of the wavefunction
you projected on. This is an analytical fact and has nothing to do with the calculation.
In order to obtain this, you need the completeness relation for your kohn-sham wavefct..
The latter is why you need to integrate up to INF.
(A fermi disitribution is not necessary to define the PDOS.) Now, the integral that I obtain
with the VASP code doesnt converge. The PDOS for energies greater than the workfunction seem to resemble the free electron like DOS (?).
Integrating to the fermi energy gives you something like the charge associated with p_z - like orbitals in your calculation.
Lets say you evaluated the PDOS for some calcuation (some adsorbate on a metal surface, lets say)
that you perfomed. So, you plot the DOS projected onto s- and p_z - orbitals located at the adsorbate position.
Now, these curves will in general overlap. A peak at the same energy tells you that within that
energy region there are wavefcts. with alot of s and p_z admixtures. How do you decide wether the
wavefunction character is more s or p_z - like? The absolute values of the PDOS dont really help
since the integral from -INF to INF doesnt converge and thus you dont have the normalization to 1 or
the value of the integral over the wavefct. you project on restricted to a sphere with radius RWIGS.

Is there a way to normalize the s-projected DOS and the p_z -projected DOS relative to each other and thus allow
for a quantitative comparison?

Thanks alot.

[Franky]

I am still interested in an answer to my question.

How are the PDOS for different l and m to be quantitatively compared to each other?
And what do I have to do to get the correct normalization for the PDOS for a given l and m?
Both questions are obviously related.
Thank you very much.