I want to calculate the occupation of the d-orbitals for a specific atom in my structure in VASP. By setting LDAUPRINT=2 I get information on occupancies and eigenvectors in the OUTCAR. I cannot decipher the meaning of the matrices though.
I get something like:
atom = 24 type = 2 l = 2
onsite density matrix
spin component 1
0.7866 -0.0439 -0.0005 0.1847 -0.0004
-0.0439 0.6623 0.0003 -0.0030 0.1875
-0.0005 0.0003 0.9259 0.0006 -0.0003
0.1847 -0.0030 0.0006 0.6644 0.0467
-0.0004 0.1875 -0.0003 0.0467 0.7840
spin component 2
0.1135 0.0124 -0.0002 -0.0539 0.0000
0.0124 0.1502 0.0000 0.0011 -0.0550
-0.0002 0.0000 0.0756 -0.0004 0.0002
-0.0539 0.0011 -0.0004 0.1497 -0.0138
0.0000 -0.0550 0.0002 -0.0138 0.1141
occupancies and eigenvectors
o = 0.0727 v = 0.0000 0.0000 0.0000 0.0000 0.0000 0.2443 0.5045 0.0004 0.3020 0.7711
o = 0.0733 v = 0.0000 0.0000 0.0000 0.0000 0.0000 -0.7581 0.3002 -0.1800 -0.4961 0.2382
o = 0.0757 v = 0.0000 0.0000 0.0000 0.0000 0.0000 0.1398 -0.0555 -0.9837 0.0892 -0.0425
o = 0.1891 v = 0.0000 0.0000 0.0000 0.0000 0.0000 -0.5522 -0.4494 -0.0012 0.6713 0.2061
o = 0.1924 v = 0.0000 0.0000 0.0000 0.0000 0.0000 0.2029 -0.6710 0.0018 -0.4518 0.5517
o = 0.5189 v = -0.1786 0.6890 -0.0018 0.4214 -0.5619 0.0000 0.0000 0.0000 0.0000 0.0000
o = 0.5277 v = 0.5624 0.4199 0.0012 -0.6890 -0.1807 0.0000 0.0000 0.0000 0.0000 0.0000
o = 0.9253 v = -0.7359 -0.0934 -0.1430 -0.5760 -0.3122 0.0000 0.0000 0.0000 0.0000 0.0000
o = 0.9254 v = 0.3018 -0.5815 0.0994 0.0872 -0.7439 0.0000 0.0000 0.0000 0.0000 0.0000
o = 0.9259 v = 0.1383 -0.0459 -0.9847 0.0909 -0.0290 0.0000 0.0000 0.0000 0.0000 0.0000
What is the meaning of the above blocks of data?
Here is some comment on this issue:
https://www.vasp.at/wiki/index.php/NiO_LSDA+U
Regards, W.
It seems like this calculation is with LDAUTYPE = 2 means rotationally invariant approach to the LDA+U.
To understand this, if we consider the example given in this link https://www.vasp.at/wiki/index.php/NiO_LSDA+U
where eigenvectors matrices of all 10 orbitals with up as well as down spin is given, then if we need to calculate the orbital contribution of 'dxy' spin-up then it can be calculated as
o1*(v11)^2+o2*(v21)^2+o3*(v31)^2+......+o10*(v101)^2 .
where o1 is the occupancy of the first row, o2 is for the 2nd row, and so on
While v11 is the value of v in 1st row and 1st column (it is mainly the projection of orbitals on the orbitals in rotationally invariant space)
v21 is the value of v in the 2nd row and 1st column, and so on.
and the reason behind this can be understood by the following image I am attaching.
Hope this helps!
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