On the interpretation of the OUTCAR file from LDA+U with LDAUPRINT=1

[joseph]

Dear all,
I have a compound with d atomic oribitals.
I did the calculation with LDAUL=2 for that atom.
The output of the occupancies for the d orbitals
is printed out as follows.

Could anyone kind give an detailed explanation
on the format of the output and simple physical interpretations for those quantities?


The coefficients of the eigenvector of d orbitals seems to depend on
the orientation of the local coordinate of the atom.
What are the corresponding coefficients in the d orbitals?

It's always confusing to me that how VASP determine
the orientation of the local coordinates because the value of
the coefficients really depend on it.

Sincerely

atom = 6 type = 3 l = 2

onsite density matrix

spin component 1

0.1428 0.0173 0.0059 0.0004 -0.0278
0.0173 0.0642 -0.0032 -0.0068 -0.0083
0.0059 -0.0032 0.1449 -0.0346 -0.0066
0.0004 -0.0068 -0.0346 0.0816 -0.0027
-0.0278 -0.0083 -0.0066 -0.0027 0.0715

spin component 2

0.1537 0.0269 0.0087 0.0021 -0.0281
0.0269 0.5097 0.0625 0.0962 0.3061
0.0087 0.0625 0.1661 -0.0238 0.0405
0.0021 0.0962 -0.0238 0.1077 0.0695
-0.0281 0.3061 0.0405 0.0695 0.2945

occupancies and eigenvectors

o = 0.0526 v = 0.0160 -0.7030 -0.2444 -0.4990 -0.4436 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
o = 0.0613 v = 0.0000 0.0000 0.0000 0.0000 0.0000 0.3854 -0.5026 -0.0574 -0.1419 0.7586 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
o = 0.0633 v = 0.3803 -0.4462 -0.0098 -0.0717 0.8069 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
o = 0.0704 v = 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0251 0.2579 -0.3822 -0.8870 -0.0112 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
o = 0.0725 v = -0.0097 0.5158 -0.3209 -0.7637 0.2181 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
o = 0.1516 v = 0.7475 0.1700 -0.5347 0.2610 -0.2415 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
o = 0.1638 v = 0.0000 0.0000 0.0000 0.0000 0.0000 0.7239 0.1798 -0.5574 0.2750 -0.2394 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
o = 0.1650 v = -0.5444 -0.1081 -0.7425 0.3073 0.2150 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
o = 0.1795 v = 0.0000 0.0000 0.0000 0.0000 0.0000 0.5715 0.1062 0.7256 -0.2951 -0.2203 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
o = 0.7567 v = 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0116 -0.7983 -0.1163 -0.1745 -0.5644 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000