What is the meaning of m and n in DOScorr(sp)_proj(i)_(m)_(n).dat?

[saeidjalali]

Dear All,

Description of the partial DOSs are given as follows:
DOScorr(sp)proj(i)(m)_(n).dat: Sames as above, but printed as orbitally resolved matrix in indices (m) and (n). For d orbitals, it gives separately the DOS for, e.g., dxy, dx2−y2, and so on.

I guess that the i index refers to the l-quntum number, i.e., 0 for s orbital, 1 for p orbital, an so on. But, it is not clear the definition of m and n indexes. For example, we expect to have 5=(2_2+1) partial DOSs for spin up d orbitals and 5=(2_2+1) partial DOSs for spin down d orbitals. So, totally 10 partial DOSs for d orbital. But, we ran LDA+DMFT for Ce and found 12 partial DOSs for d orbital.
We cannot correspond the m and n symbols to the partial DOSs so that we can distinguish which one is dxy or which one is dx^2-y^2.

Would you define the i, n, and m indexes more clearly?

Best,
S. Jalali

[aichhorn]

In fact, the routine does not only calculate the diagonal part of the density of states, but the full matrix, that is why we have indices m and n. To be precise, if you have 5 orbitals and are interested only in the diagonal part (the thing that you would normally call a DOS), then you look at the files *_0_0.dat, *_1_1.dat, *_2_2.dat, *_3_3.dat, and *4_4.dat. The off-diagonal parts are often zero by symmetry, but in some cases it can be useful to look at this, that is why it is implemented.
Be careful: The index i is not the quantum number l!!! It is just an index for an orbital shell. The range over which the indedx i runs depends on your inputfile case.indmftpr. In the lines where you define the correlated orbitals, you can put 0 (not included),1 (included), or 2 (included as correlated). As soon as you put 1 or 2, the atomic shell is included in the list of orbitals for which you can calculate the DOS. For instance, if you put 0 everywhere, except 2 for the f-shell in your Ce example, the you get only files like DOScorr(sp)proj0(m)(n).dat, where i is 0! And i runs also over non-equivalent atoms! So if you have too independet Ce atoms in the unti cell, then you should get indices i=0 and i=1 (obvioulsy with the same content).

[saeidjalali]

Dear Markus,
Thank you for your reply and explanation.
Let me check whether I understand all of your comments as you mean or not.
For fcc gamma-Ce case, we have only one nonequivalent atom. My Ce.indmftpr is as follows:
1 ! Nsort
1 ! Mult(Nsort)
3 ! lax
complex
1 1 1 2 ! l included for each sort
0 0 0 0 ! l included for each sort
0
-.40 0.40 ! Energy window relative to E_f

snort is set to 1, since the number of non-equivalent atomic is one for fcc gamma-Ce.
snort is set to 1, since the multiplicity of Ce in the case.struct is one for fcc gamma-Ce.
l_max is set to 3, since we include only the s,p,d and f orbitals.

spherical harmonics is considered to be complex, as it should be in general. But, Ce crystalizes in cubic. So, I am not sure whether I can select cubic or not. Anyway, complex seems to be more general than cubic(?).

lsort(l): (lmax+1) integers to describe the “treatment” of each orbital:
0 means that the corresponding orbital is not included
1 means that the orbital is included but no projector P��
lm,�(k) will be calculated for it.
2 means that the orbital is included and a projector P��
lm,�(k) will be calculated for it.

nb_irep(l): (lmax+1) integers to describe the number of irreducible representation (irep) to consider
for each orbital l.
0 means that the orbital is not correlated ; no projector P��
lm,�(k) will be calculated for it

I think, it is better to add spin-orbit for gamma-Ce, but here it is not included for simplicity.

I am laso not sure about the energy window. How should we estimate it?
Let's get back to the discussion.

As far as I understand from your comment on i-index, it should be 0, 1, and 2, as I have included the correlated f-orbital. My generated DOSs are as follows:
./Ce/DOScorrdown_proj2_0_4.dat
./Ce/DOScorrup_proj3_0_0.dat
./Ce/DOScorrup_proj1_1_2.dat
./Ce/DOScorrup_proj1.dat
./Ce/DOScorrdown_proj3_0_1.dat
./Ce/DOScorrdown_proj3_0_2.dat
./Ce/DOScorrdown_proj2.dat
./Ce/DOScorrdown_proj3_2_2.dat
./Ce/DOScorrup_proj2_2_3.dat
./Ce/DOScorrdown_proj2_3_3.dat
./Ce/DOScorrup_proj3_4_4.dat
./Ce/DOScorrdown_proj3_1_5.dat
./Ce/DOScorrup_proj3_2_3.dat
./Ce/DOScorrdown_proj3_1_2.dat
./Ce/DOScorrup_proj3_1_1.dat
./Ce/DOScorrdown_proj1.dat
./Ce/DOScorrdown_proj3_3_5.dat
./Ce/DOScorrdown_proj3_4_6.dat
./Ce/DOScorrup.dat
./Ce/DOScorrup_proj3_2_5.dat
./Ce/DOScorrup_proj3_5_6.dat
./Ce/DOScorrdown_proj2_3_4.dat
./Ce/DOScorrup_proj2_0_4.dat
./Ce/DOScorrdown_proj2_0_2.dat
./Ce/DOScorrup_proj2_3_4.dat
./Ce/DOScorrdown_proj3_2_4.dat
./Ce/DOScorrdown_proj2_0_1.dat
./Ce/DOScorrup_proj3_1_6.dat
./Ce/DOScorrup_proj2_0_0.dat
./Ce/DOScorrdown_proj3_0_0.dat
./Ce/DOScorrup_proj3_6_6.dat
./Ce/DOScorrup_proj1_1_1.dat
./Ce/DOScorrdown_proj0_0_0.dat
./Ce/DOScorrup_proj2_1_2.dat
./Ce/DOScorrup_proj1_2_2.dat
./Ce/DOScorrup_proj2_3_3.dat
./Ce/DOScorrup_proj3_0_2.dat
./Ce/DOScorrup_proj1_0_2.dat
./Ce/DOScorrup_proj3_3_5.dat
./Ce/DOScorrup_proj3_2_4.dat
./Ce/DOScorrdown_proj3_2_6.dat
./Ce/DOScorrup_proj3_4_6.dat
./Ce/DOScorrup_proj2_4_4.dat
./Ce/DOScorrdown_proj3_1_4.dat
./Ce/DOScorrdown_proj3.dat
./Ce/DOScorrdown_proj3_5_5.dat
./Ce/DOScorrup_proj3_1_2.dat
./Ce/DOScorrdown_proj1_0_0.dat
./Ce/DOScorrup_proj2_0_3.dat
./Ce/DOScorrup_proj2_1_4.dat
./Ce/DOScorrdown_proj1_1_2.dat
./Ce/DOScorrdown_proj3_0_5.dat
./Ce/DOScorrdown_proj2_2_3.dat
./Ce/DOScorrdown_proj3_3_6.dat
./Ce/DOScorrup_proj1_0_1.dat
./Ce/DOScorrup_proj2_2_4.dat
./Ce/DOScorrup_proj3_3_4.dat
./Ce/DOScorrup_proj3_0_1.dat
./Ce/DOScorrdown_proj0.dat
./Ce/DOScorrup_proj3_0_4.dat
./Ce/DOScorrup_proj3_4_5.dat
./Ce/DOScorrdown_proj2_0_3.dat
./Ce/DOScorrdown_proj1_0_1.dat
./Ce/DOScorrdown_proj3_6_6.dat
./Ce/DOScorrup_proj2_0_1.dat
./Ce/DOScorrup_proj3_0_5.dat
./Ce/DOScorrup_proj3_5_5.dat
./Ce/DOScorrdown_proj3_1_1.dat
./Ce/DOScorrdown_proj2_2_4.dat
./Ce/DOScorrdown.dat
./Ce/DOScorrup_proj3_3_6.dat
./Ce/DOScorrup_proj3.dat
./Ce/DOScorrdown_proj2_4_4.dat
./Ce/DOScorrdown_proj3_2_5.dat
./Ce/DOScorrup_proj3_0_6.dat
./Ce/DOScorrup_proj2_0_2.dat
./Ce/DOScorrdown_proj2_1_2.dat
./Ce/DOScorrup_proj0_0_0.dat
./Ce/DOScorrdown_proj2_1_3.dat
./Ce/DOScorrdown_proj2_1_4.dat
./Ce/DOScorrup_proj2_2_2.dat
./Ce/DOScorrup_proj3_1_5.dat
./Ce/DOScorrdown_proj1_0_2.dat
./Ce/DOScorrup_proj2_1_3.dat
./Ce/DOScorrdown_proj3_5_6.dat
./Ce/DOScorrdown_proj3_1_3.dat
./Ce/DOScorrdown_proj3_4_4.dat
./Ce/DOScorrdown_proj3_2_3.dat
./Ce/DOScorrdown_proj1_1_1.dat
./Ce/DOScorrup_proj3_3_3.dat
./Ce/DOScorrdown_proj1_2_2.dat
./Ce/DOScorrup_proj1_0_0.dat
./Ce/DOScorrdown_proj3_3_4.dat
./Ce/DOScorrdown_proj3_3_3.dat
./Ce/DOScorrup_proj0.dat
./Ce/DOScorrup_proj2_1_1.dat
./Ce/DOScorrdown_proj3_4_5.dat
./Ce/DOScorrup_proj3_0_3.dat
./Ce/DOScorrup_proj3_1_3.dat
./Ce/DOScorrdown_proj3_0_6.dat
./Ce/DOScorrdown_proj2_1_1.dat
./Ce/DOScorrdown_proj2_2_2.dat
./Ce/DOScorrup_proj2.dat
./Ce/DOScorrup_proj3_2_2.dat
./Ce/DOScorrup_proj3_2_6.dat
./Ce/DOScorrdown_proj3_0_4.dat
./Ce/DOScorrdown_proj3_1_6.dat
./Ce/DOScorrdown_proj2_0_0.dat
./Ce/DOScorrdown_proj3_0_3.dat
./Ce/DOScorrup_proj3_1_4.dat

As far as I understand, only diagonal DOS's are the regular DOSs, for which m=n. *_0_0.dat, *_1_1.dat, *_2_2.dat, *_3_3.dat are my interested DOSs. As far as I know these are called TOTAL DOS. I need to have partial DOSs too.
But, I cannot correspond them to the partial DOSs generated by WIEN2k. In WIEN2k, depending on the point group of the system, we have pz, pay, dx^2_y^2, and so on. These are standard and everybody are familiar with them.

Would you tell me how can I correspond the *.dat files to partial DOSs of WIEN2k?

But, as you see I have *_4_4.dat. This is in the case that in my Ce.indmftpr I set l_max to 3! So, why is *_4_4.dat also generated?

Best,
Saeid.