[Wien] Meaning of EORB

[tran at theochem.tuwien.ac.at]

Hello,

For LDA+U, :EORB is Eq. (24) of Shick et al.
[Phys. Rev. B 60, 10763 (1999)], but calculated with a different
expression.

For HF, :EORB is the sum of the last 3 terms of Eq. (12) of
Novak et al. [Phys. Stat. Sol. (B) 243, 563 (2006)] (for PBE0,
0.25 is included in :EORB).

In the HF or PBE0 schemes only exchange is involved. So, this is
understandable why the ORB package is run twice (once for each spin).

For LDA+U, both exchange and Coulomb interactions are involved, and
because of Coulomb, there is a mixing of spin up and down. Still, the
orb package is run twice: once for each value of the sum over sigma
[Eq. (2) of Shick et al.]. The dc term is calculated twice, but divided
by two (Edc/2.d0 in vldau.f).

As I said, with PBE0 only exchange is corrected for the selected 
electrons, while both exchange and correlation are corrected with
LDA+U. Energetically this will have certainely an influence, but this
does not automatically mean that the density matrices will be different
(e.g., both methods could lead to the same electronic configuration)

F. Tran

On Fri, 12 Aug 2011, David Tompsett wrote:

> 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
>