[Wien] Meaning of EORB

[David Tompsett]

Dear Laurence and Fabian,

Thanks for you replies. I'd like to make a few comments and ask a few
questions further:

1) The relations that Fabian sent to me indicate that EORB includes both the
interactions and the double counting correction. So Laurence if that is
right then EORB is more than just the double counting term.

2) Interestingly, Novak et al. [Phys. Stat. Sol. (B) 243, 563 (2006)]
indicates that for excact exchange both exchange and correlations for
E^LDA_xc are subtracted off by the double counting term. This seems in
contradiction to the original PBE0 paper (Perdew et al. J Chem Phys 105,
9982(1996)) where only exchange is subtracted off.

3) Also, it is hard to see difference between the interaction in the two
methods because they are very similar in form. If I look at equation (2) in
both Shick and Novak they look very similar. Is the difference that HF only
includes direct exchange, while DFT+U includes spin-dependent exchange?
By looking at Czyzyk and Sawatzky PRB 49,14211 (1994) relations are given in
the appendix between the direct U_mm' and indirect J_mm' interactions and
the Slater integrals. Does HF just ignore J_mm'?

The only other place that they are very different is in the double counting
terms. But as you say these can matter a lot.

Cheers,
David.

On Fri, Aug 12, 2011 at 2:32 PM, <tran at theochem.tuwien.ac.at> wrote:

> 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
> >
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