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Hello!</div>
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I have read this thread, which is from three years ago, and I would like to know if there is any update, consensus, or a study about this issue. </div>
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The topic of the thread was how to compare the energies of two systems when there is at least one element subject to Hubbard correction, in the case that the Hubbard parameters are computed self-consistently via the HP code, and have different values in the
two systems compared. Should we choose one average value, or use the computed value for each system? The two systems may be either:</div>
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">Two phases of a material</span></li><li style="font-family: Arial, Helvetica, sans-serif; font-size: 12pt; list-style-type: "b) "; color: rgb(0, 0, 0);">
<span style="font-family: Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">Two antiferromagnetic configurations</span></li><li style="font-family: Arial, Helvetica, sans-serif; font-size: 12pt; list-style-type: "c) "; color: rgb(0, 0, 0);">
<span style="font-family: Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">Crystal with a transition metal impurity vs clean crystal and impurity in bulk metal.<br>
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<div class="elementToProof"><span style="font-family: Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">I may have a case of type (b), with certain energy order when using the self-consistent U values for each AFM configuration, and the opposite
order when the same U is used for both configurations. The same U was computed for one configuration, I am waiting for the queue to finish calculations with the other U, but this is published (Naveas et al,
<a href="https://doi.org/10.1016/j.isci.2023.106033" id="LPlnk822446">https://doi.org/10.1016/j.isci.2023.106033</a>).</span></div>
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<div class="elementToProof"><span style="font-family: Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">Concerning the advantage of self consistency, let me rise the example LiCoO2 that comes with the HP code. The example produces U for Co
and also for O, as well as V(Co-O). U(O-2p)=8.0439 eV. Is this parameter useful? As the example is not converged w.r.t. to k-points and cutoffs the number may change, but U(O-2p) is still there. I read PRB101, 064305 (2020) by Floris et al, and it seems that
U(O-2p) is discarded. I am curious why, but I couldn't find a discussion. Maybe there is another article. My point here is that using self consistent parameters for some elements and shells, and discarding others is just a partial self-consistency.</span></div>
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<div class="elementToProof"><span style="font-family: Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">A related question is whether the forces and energies are consistent with variable U and V. That is, Let us move the Fe impurity atom
inside a crystal, and recompute the U and V for each position. Force is the gradient of energy obtained in the Hellman-Feynman way, I guess with constant U,V.</span></div>
<div class="elementToProof"><span style="font-family: Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">Pressure is the negative of the derivative of the energy with respect to volume, which implies a variation of U and V. I guess the stress
is computed with constant U, V. I think that self-consistency could be implemented, but first we must be sure that comparing energies with variable, self-consistent parameters is correct.</span></div>
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<div class="elementToProof"><span style="font-family: Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">Best regards,</span></div>
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Eduardo A. Menéndez Proupin</div>
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Departamento de Física Aplicada I</div>
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Universidad de Sevilla</div>
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Teléfono: +34 9554 20231</div>
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<a href="https://personal.us.es/emenendez/">https://personal.us.es/emenendez/</a></div>
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<a href="https://personal.us.es/emenendez/docencia/">https://personal.us.es/emenendez/docencia/</a><br>
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