[Wien] Meaning of EORB

[Laurence Marks]

You are going to have to take a step back and look at the original
papers for the on-site DFT+U papers and the on-site exact exchange
method which are cited in the user-guide. Two key points:

a) While DFT+U and exact-exchange are similar, they are not the same
and at a deeper level quite different. DFT+U requires a semi-empirical
U value (perhaps J) which depends upon the local environment so the
user has to "adjust" it for each different environment. It can be
estimated (see the FAQ, but this is tricky.) In contrast the
exact-exchange method, for a given fraction of exact-exchange (also
semi-empirical) gives an effective U/J value which automatically will
change as a function of environment. For the later perhaps look at
Surf. Sci. 603, 2179 (2009), and for how one might determine the
fraction of exact-exchange Surf. Sci. 604, 155 (2010).

b) :EORB is just a double-counting correction (see vldau.f in SRC_orb)
and a large fraction of the energy is in the eigenvalues produced by
lapw1 (try x lapw1 -up ; then x lapw1 -up -orb and compare).

My personal opinion is that the on-site method is much better than
DFT+U. However, it does not work well for oxygen and some other atoms
where a full exact-exchange method is known to be better, but this is
not presently in Wien2k.

2011/8/12 David Tompsett <dat36 at cam.ac.uk>:
> Dear All,
>
> I am trying to understand the meaning of the :EORB terms that are printed in
> the scf file. Specifically I am trying to compare results between DFT+U and
> on-site PBE0.
>
> For the relevant ion in PBE0 I obtain:
> :EORB:   0.78998998
> :EORB:   0.00187235
>
> For DFT+U=5.5 J=1.2 (a U value comparable to that from PBE0)
> :EORB:   3.50441505
> :EORB:  -2.13956456
>
> Firstly, why are there separate values for each spin? I though they had spin
> off-diagonal Hund's contributions and so there should be just one value?
>
> Secondly, why are the values from PBE0 so different to those from DFT+U. The
> F^0 Slater integral was 24 eV which is 6eV if we multiply by 25%. Therefore
> I don't understand why things are so different since the density matrix is
> similar in both cases (see below). Is it because we are yet to subtract off
> double counting corrections etc?
>
> Thanks,
> David.
>
> For PBE0:
> Density matrix UPUP block, real part.  L= 2
>          0.72230  0.00000 -0.16986  0.00000 -0.20538
>          0.00000  0.64110  0.00000  0.27822  0.00000
>         -0.16986  0.00000  0.76498  0.00000 -0.16986
>          0.00000  0.27822  0.00000  0.64110  0.00000
>         -0.20538  0.00000 -0.16986  0.00000  0.72230
>  Density matrix DNDN block, real part.  L= 2
>          0.16036  0.00000  0.05754  0.00000  0.03920
>          0.00000  0.19403  0.00000 -0.08197  0.00000
>          0.05754  0.00000  0.11826  0.00000  0.05754
>          0.00000 -0.08197  0.00000  0.19403  0.00000
>          0.03920  0.00000  0.05754  0.00000  0.16036
>
> For DFT+U:
>  Density matrix UPUP block, real part.  L= 2
>          0.75404  0.00000 -0.14997  0.00000 -0.18121
>          0.00000  0.68074  0.00000  0.24823  0.00000
>         -0.14997  0.00000  0.79097  0.00000 -0.14997
>          0.00000  0.24823  0.00000  0.68074  0.00000
>         -0.18121  0.00000 -0.14997  0.00000  0.75404
>  Density matrix DNDN block, real part.  L= 2
>          0.16036  0.00000  0.05754  0.00000  0.03920
>          0.00000  0.19403  0.00000 -0.08197  0.00000
>          0.05754  0.00000  0.11826  0.00000  0.05754
>          0.00000 -0.08197  0.00000  0.19403  0.00000
>          0.03920  0.00000  0.05754  0.00000  0.16036
>
>
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>
>



-- 
Laurence Marks
Department of Materials Science and Engineering
MSE Rm 2036 Cook Hall
2220 N Campus Drive
Northwestern University
Evanston, IL 60208, USA
Tel: (847) 491-3996 Fax: (847) 491-7820
email: L-marks at northwestern dot edu
Web: www.numis.northwestern.edu
Chair, Commission on Electron Crystallography of IUCR
www.numis.northwestern.edu/
Research is to see what everybody else has seen, and to think what
nobody else has thought
Albert Szent-Gyorgi