[Wien] Meaning of EORB

[Laurence Marks]

Fabien knows this better than I do.
On Aug 12, 2011 11:24 AM, "David Tompsett" <dat36 at cam.ac.uk> wrote:
> 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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