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Dear VASP master,

I have a question about Gaussian smear. I hope you can help me to understand it more.

The question is that we want to calculate the electron occupation (the number of electrons) in one d-orbital, say dz2 orbital. The OUTCAR can give us the number of electrons in total d-orbital, but not in each of the five d-orbitals.

It seems that we can calculate the number of electrons in dz2 from the decomposed DOSCAR, which gives the orbital decomposed DOS at every energy point for each atom. It seems that we can do an integral to get the number of electrons in dz2, provided that we can know the occupation function or filling function. It seems that when we set ISMEAR=0, we use Gaussian smearing, then the Gaussian smearing will give the occupation function or filling function. Is this understanding correct?

If this understanding is correct, then what is the math formula for the occupation function? If it is a Gaussian function, then we still don't know how it is applied to each energy point. We know that the DOS below the Fermi level is supposed to be occupied. Only states around the Fermi level will be partially occupied. How is the Gaussian function applied?

Please help me about this. I really appreciate your help very much.

Best,
Hong Tang

Dear hong_tang1,

I would recommend you to take a look at our tutorial pages.
wiki/index.php/CO_partial_DOS
This tutorial shows how to compute partial DOS files and
how to analyze them with p4vasp.
Alternatively to p4vasp you can also use the py4vasp
software to analyze your data

py4vasp/latest/data/dos/#py4vasp.data.Dos.plot

As you are expecting you can compute the number of electrons
with a certain orbital character dz2 by an integral over the partial DOS file.
I hope this helps

All the best Jonathan

Dear Jonathan,

Thank you so much for helping.
Maybe I did not make my question clear enough.

I know the DOSCAR and PROCAR. From partial DOS, you can know the dos for each orbital.
HOWEVER, DOSCAR does not tell you the occupation. In order to calculate the number of electrons in one particular orbital, we need also know the occupation information. Apparently, DOSCAR cannot give you this kind of information.

So, it seems we have to look at PROCAR. PROCAR does have occupation information for each k point and each band. But that occupation information is a total occupation for that k point and that band. My question is: is it legitimate to calculate the occupation for a particular orbital, say dz2, at that k and that band, by proportionality? I mean the proportionality is the ratio of the projection of the dz2 over the total projection of all orbitals at that k point and that band.

Even you think this is ok, But how about the noncollinear case with spin-orbit coupling? In this case, those projections shown in the PROCAR are understood as spin magnetic moment decomposition, right? Can we use the ratio of magnetic moment decomposition to prorate the occupation?

I hope you can understand my questions.

Best,
Hong

Dear Hong,

I am not 100 percent sure if I understand correctly what you mean.
What I understand you want to understand the occupancy of certain bands and their
occupancy. IN principle this would be described here.
https://www.vasp.at/wiki/index.php/PROCAR

So what you see in the PROCAR file following the example in the link is.
The different k-points and for every k-point the bands are listed. For every
band you have a occupancy written as # occ. 1.00000000 in the file.
This means there is a single electron in this state. What vasp does to compute
the band characters is to project the band on spherical harmonics giving the s,px,py,pz...
orbitals. This projection is done within a cutoff radius RWIGS. https://www.vasp.at/wiki/index.php/RWIGS

Then when looking at the line tot and column tot there is a value of 0.740 written in the PROCAR file example
of the link. So vasp is not finding a charge of 1.00 within RWIGS but only 0.740. Now to compute the
contribution of let's say the s orbital to the band you have to compute the ratio 0.727/0.740=0.982.
And the pz orbital would contribute 0.013/0.740=0.018 to the band.

About the second question.
Yes in the non-collinear case the PROCAR file will be decomposed into the different contributions of the spin directions as described in the link
https://www.vasp.at/wiki/index.php/PROCAR.

To my knowledge you can use those coefficients to decompose the orbital into spin contributions. Bu it is not allowed
to do a decomposition at the same time in x and y for example. This is because the commutator between the Pauli matrices is non zero.
And is for example for the x and y direction [\sigma_{x},\sigma_{y}]=2i\sigma_{z}.
So you can only choose one spin direction at a time (x,y or z) to use for your decomposition of the bands.

I hope this answers your questions or gives a hint on how to proceed.
Otherwise just ask again.

All the best Jonathan