<div dir="ltr"><div><div><div>Dear Prof. Matteo Cococcioni,<br><br></div>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, <a name="144d81dff213d4b0_id3119661"></a>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. <br>
<br></div>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. <br>
<br></div><div>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.<br>
</div><div><div><br></div><div>Bests<br></div><div>Jia<br></div></div></div><div class="gmail_extra"><br><br><div class="gmail_quote">On Tue, Mar 18, 2014 at 5:39 AM, Matteo Cococcioni <span dir="ltr"><<a href="mailto:matteo@umn.edu" target="_blank">matteo@umn.edu</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><br><div class="gmail_extra">Dear Jia,<br><br></div><div class="gmail_extra">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.<br>
<br></div><div class="gmail_extra">I will try to clarify specific questions of yours below.<br></div><div class="gmail_extra"><br><br><div class="gmail_quote"><div class="">On Tue, Mar 18, 2014 at 3:07 AM, Jia Chen <span dir="ltr"><<a href="mailto:jiachenchem@gmail.com" target="_blank">jiachenchem@gmail.com</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div><div><div><div><div><div>Dear all,<br><br></div>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). <br>
</div></div></div></div></div></div></blockquote><div><br><br></div></div><div>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.<br>
</div><div class=""><div> <br><br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div><div><div><div><div>
<br>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.<br>
<br></div></div></div></div></div></div></blockquote><div><br></div></div><div><br>see above and below.<br></div><div class=""><div><br> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div dir="ltr"><div><div><div><div><div></div>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:<br>
</div>1. What is not right in rotational invariant DFT+U, as a Hartree-Fock level theory regarding J?<br></div></div></div></div></blockquote><div><br><br></div></div><div>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.<br>
</div><div class=""><div><br> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div><div><div>
</div>2. How DFT+U+J improves rotational invariant DFT+U, just in general?<br></div></div></div></blockquote><div><br><br></div></div><div>we didn't compare the two. but if you end up doing please report the results on this forum.<br>
<br></div><div>Hope this helps. best,<br><br></div><div>Matteo<br></div><div><br> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div class=""><div dir="ltr"><div>
<div><br></div>
Appreciate your help!<br><br></div>Cheers<span><font color="#888888"><br><div><div><div><div><div><div><div><div>-- <br><div dir="ltr">Jia Chen<br></div><div>Postdoc, Columbia University<br>
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