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

[Matteo Cococcioni]

Dear Jia,

see below.

On Wed, Mar 19, 2014 at 4:31 AM, Jia Chen <jiachenchem at gmail.com> wrote:

> 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.
>
>
our DFT+U+J is the one you get with hubbard_u_kind = 0 and Hubbard_J0 =/= 0.


> 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.
>


As I wrote yesterday in my email DFT+U+J0 is NOT a simpler version of the
rotational invariant DFT+U. if you simplify the rotational invariant DFT+U
you obtain the dudarev DFT+U, possibly with U_eff = U-J.

best,

Matteo



>
> 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
>> needed to be added.
>>
>> 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
>>
>>
>>
>>>
>>> Appreciate your help!
>>>
>>> Cheers
>>> --
>>> Jia Chen
>>> Postdoc, Columbia University
>>>
>>>
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>>>
>>
>>
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>
>
>
> --
> Jia Chen
>
>
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