<p>Fabien knows this better than I do.</p>
<div class="gmail_quote">On Aug 12, 2011 11:24 AM, "David Tompsett" <<a href="mailto:dat36@cam.ac.uk">dat36@cam.ac.uk</a>> wrote:<br type="attribution">> Dear Laurence and Fabian,<br>> <br>> Thanks for you replies. I'd like to make a few comments and ask a few<br>
> questions further:<br>> <br>> 1) The relations that Fabian sent to me indicate that EORB includes both the<br>> interactions and the double counting correction. So Laurence if that is<br>> right then EORB is more than just the double counting term.<br>
> <br>> 2) Interestingly, Novak et al. [Phys. Stat. Sol. (B) 243, 563 (2006)]<br>> indicates that for excact exchange both exchange and correlations for<br>> E^LDA_xc are subtracted off by the double counting term. This seems in<br>
> contradiction to the original PBE0 paper (Perdew et al. J Chem Phys 105,<br>> 9982(1996)) where only exchange is subtracted off.<br>> <br>> 3) Also, it is hard to see difference between the interaction in the two<br>
> methods because they are very similar in form. If I look at equation (2) in<br>> both Shick and Novak they look very similar. Is the difference that HF only<br>> includes direct exchange, while DFT+U includes spin-dependent exchange?<br>
> By looking at Czyzyk and Sawatzky PRB 49,14211 (1994) relations are given in<br>> the appendix between the direct U_mm' and indirect J_mm' interactions and<br>> the Slater integrals. Does HF just ignore J_mm'?<br>
> <br>> The only other place that they are very different is in the double counting<br>> terms. But as you say these can matter a lot.<br>> <br>> Cheers,<br>> David.<br>> <br>> On Fri, Aug 12, 2011 at 2:32 PM, <<a href="mailto:tran@theochem.tuwien.ac.at">tran@theochem.tuwien.ac.at</a>> wrote:<br>
> <br>>> Hello,<br>>><br>>> For LDA+U, :EORB is Eq. (24) of Shick et al.<br>>> [Phys. Rev. B 60, 10763 (1999)], but calculated with a different<br>>> expression.<br>>><br>>> For HF, :EORB is the sum of the last 3 terms of Eq. (12) of<br>
>> Novak et al. [Phys. Stat. Sol. (B) 243, 563 (2006)] (for PBE0,<br>>> 0.25 is included in :EORB).<br>>><br>>> In the HF or PBE0 schemes only exchange is involved. So, this is<br>>> understandable why the ORB package is run twice (once for each spin).<br>
>><br>>> For LDA+U, both exchange and Coulomb interactions are involved, and<br>>> because of Coulomb, there is a mixing of spin up and down. Still, the<br>>> orb package is run twice: once for each value of the sum over sigma<br>
>> [Eq. (2) of Shick et al.]. The dc term is calculated twice, but divided<br>>> by two (Edc/2.d0 in vldau.f).<br>>><br>>> As I said, with PBE0 only exchange is corrected for the selected<br>>> electrons, while both exchange and correlation are corrected with<br>
>> LDA+U. Energetically this will have certainely an influence, but this<br>>> does not automatically mean that the density matrices will be different<br>>> (e.g., both methods could lead to the same electronic configuration)<br>
>><br>>> F. Tran<br>>><br>>> On Fri, 12 Aug 2011, David Tompsett wrote:<br>>><br>>> > Dear All,<br>>> ><br>>> > I am trying to understand the meaning of the :EORB terms that are printed<br>
>> in<br>>> > the scf file. Specifically I am trying to compare results between DFT+U<br>>> and<br>>> > on-site PBE0.<br>>> ><br>>> > For the relevant ion in PBE0 I obtain:<br>
>> > :EORB: 0.78998998<br>>> > :EORB: 0.00187235<br>>> ><br>>> > For DFT+U=5.5 J=1.2 (a U value comparable to that from PBE0)<br>>> > :EORB: 3.50441505<br>>> > :EORB: -2.13956456<br>
>> ><br>>> > Firstly, why are there separate values for each spin? I though they had<br>>> spin<br>>> > off-diagonal Hund's contributions and so there should be just one value?<br>>> ><br>
>> > Secondly, why are the values from PBE0 so different to those from DFT+U.<br>>> The<br>>> > F^0 Slater integral was 24 eV which is 6eV if we multiply by 25%.<br>>> Therefore<br>>> > I don't understand why things are so different since the density matrix<br>
>> is<br>>> > similar in both cases (see below). Is it because we are yet to subtract<br>>> off<br>>> > double counting corrections etc?<br>>> ><br>>> > Thanks,<br>>> > David.<br>
>> ><br>>> > For PBE0:<br>>> > Density matrix UPUP block, real part. L= 2<br>>> > 0.72230 0.00000 -0.16986 0.00000 -0.20538<br>>> > 0.00000 0.64110 0.00000 0.27822 0.00000<br>
>> > -0.16986 0.00000 0.76498 0.00000 -0.16986<br>>> > 0.00000 0.27822 0.00000 0.64110 0.00000<br>>> > -0.20538 0.00000 -0.16986 0.00000 0.72230<br>>> > Density matrix DNDN block, real part. L= 2<br>
>> > 0.16036 0.00000 0.05754 0.00000 0.03920<br>>> > 0.00000 0.19403 0.00000 -0.08197 0.00000<br>>> > 0.05754 0.00000 0.11826 0.00000 0.05754<br>>> > 0.00000 -0.08197 0.00000 0.19403 0.00000<br>
>> > 0.03920 0.00000 0.05754 0.00000 0.16036<br>>> ><br>>> > For DFT+U:<br>>> > Density matrix UPUP block, real part. L= 2<br>>> > 0.75404 0.00000 -0.14997 0.00000 -0.18121<br>
>> > 0.00000 0.68074 0.00000 0.24823 0.00000<br>>> > -0.14997 0.00000 0.79097 0.00000 -0.14997<br>>> > 0.00000 0.24823 0.00000 0.68074 0.00000<br>>> > -0.18121 0.00000 -0.14997 0.00000 0.75404<br>
>> > Density matrix DNDN block, real part. L= 2<br>>> > 0.16036 0.00000 0.05754 0.00000 0.03920<br>>> > 0.00000 0.19403 0.00000 -0.08197 0.00000<br>>> > 0.05754 0.00000 0.11826 0.00000 0.05754<br>
>> > 0.00000 -0.08197 0.00000 0.19403 0.00000<br>>> > 0.03920 0.00000 0.05754 0.00000 0.16036<br>>> ><br>>> _______________________________________________<br>>> Wien mailing list<br>
>> <a href="mailto:Wien@zeus.theochem.tuwien.ac.at">Wien@zeus.theochem.tuwien.ac.at</a><br>>> <a href="http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien">http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien</a><br>
>><br></div>