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

Matteo Cococcioni matteo at umn.edu
Tue Mar 18 10:39:10 CET 2014

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,


> Appreciate your help!
> Cheers
> --
> Jia Chen
> Postdoc, Columbia University
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