[Pw_forum] difference between DFT+U+J and rotational invariant DFT+U of lda_u_kind =1

Jia Chen jiachenchem at gmail.com
Wed Mar 19 04:31:51 CET 2014

```Dear Prof. Matteo Cococcioni,

Thank you very much for explanation, it helps me a lot. According to the
document of pw input file, rotational invariant DFT+U is implemented in pw
now, with lda_u_type=1. I think my input files are correct, when I use
rotational invariant DFT+U and DFT+U+J you developed.

I hope you can understand that my hesitation to put data I don't understand
on a public place. I can describe my problem. It seems to be related to the
question why U_eff=U-J is valid. I have two spin states of a
transition-metal ion. As you know, U favours high-spin state, and
conventional wisdom tells us J should favours high-spin too. It is easy to
understand why in simplified DFT+U, J does the opposite, since it is just a
reduction of  U. I expected, by fully rotational invariant DFT+U, J favours
high-spin energetically. But, in my calculations, rotational invariant
DFT+U behaves just like the its' simplified version. Only the DFT+U+J
method shows the right trend.

If DFT+U+J is just a simple version of rotational invariant DFT+U, I still
don't know why rotational invariant DFT+U fails for this particular
problem. I also don't think U_eff=U-J has too much physics ground, but, in
calculations, it seems to be true...  Any comment on this topic is very
welcome.

Bests
Jia

On Tue, Mar 18, 2014 at 5:39 AM, Matteo Cococcioni <matteo at umn.edu> wrote:

>
> Dear Jia,
>
> when we did the work you cite (the PRB paper on CuO) we understood we
> needed to have explicit magnetic interactions in the +U functional, but we
> tried to understand if there were simpler ways to add it than using the
> otationally invariant implementation of DFT+U. On the other hand the
> simpler version of it by Dudarev et al (PRB 98) was too simple as it
> reduces the role of J to a mere reduction of the effective U (that is,
> U_eff = U-J). To be honest, this latter point I have never fully
> understood: one gets the simpler version of the +U correction by setting J
> = 0 in the fully rotational one, so I don't see how one could end up with
> an effective U that is U-J. Anyway, what we tried to do was to re-analyze
> the approximation the simpler version is based on (in the limit where U_eff
> does actually result to be equal to U-J) and to check whether or not other
> terms of the same order were arising. And it seems to us that an extra one
>
> I will try to clarify specific questions of yours below.
>
>
> On Tue, Mar 18, 2014 at 3:07 AM, Jia Chen <jiachenchem at gmail.com> wrote:
>
>> Dear all,
>>
>> I am working on molecule with localized d electrons and two different
>> spin states, especially correlation due to Hund's coupling J at this
>> moment. I tried the DFT+U+J method (PRB 84, 115108, 2011) implemented in
>> Quantum Espresso, and found out the J dependence is quite different from
>> the rotational invariant DFT+U (PRB 52 R5467, 1995).
>>
>
>
> first of all: make sure you are using Hubbard_J0 (lda_plus_u_kind = 0).
> the Hubbard_J relates to the non-collinear implementation and I'm not sure
> what it does in case of nspin = 2. Although I didn't participate to this
> implementation, I believe that it might reduce to the fully rotational
> implementation, but I'm not sure and other people can confirm.
>
>
>
>> I am surprised by the results, because rotational invariant DFT+U has
>> full coulomb interaction parametrized by Slater integrals, Hund's coupling
>> J show up in anisotropic and spin polarized interactions. As a model, it
>> covers both Hund's first and second rule. Theoretically, I don't know
>> what's missing in this method.
>>
>>
>
> see above and below.
>
>
>
>> Apparently, developers of DFT+U+J know how to go beyond rotational
>> invariant DFT+U. I read the paper, but still don't understand the idea
>> behind it. I would like to ask two questions:
>> 1. What is not right in rotational invariant DFT+U, as a Hartree-Fock
>> level theory regarding J?
>>
>
>
> the fact that it is Hartree-Fock level of theory. In fact, as we wrote in
> the paper, the extra term we added is beyond HF in the sense that it cannot
> be captured supposing that the many-body wave function consists of a single
> Slater determinant.
>
>
>
>> 2. How DFT+U+J improves rotational invariant DFT+U, just in general?
>>
>
>
> we didn't compare the two. but if you end up doing please report the
> results on this forum.
>
> Hope this helps. best,
>
> Matteo
>
>
>
>>
>>
>> Cheers
>> --
>> Jia Chen
>> Postdoc, Columbia University
>>
>>
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>
>
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--
Jia Chen
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