[QE-users] Thermodynamics with DFT+U

[EDUARDO ARIEL MENENDEZ PROUPIN]

Hello!
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.

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:

  1.  Two phases of a material
  2.  Two antiferromagnetic configurations
  3.  Crystal with a transition metal impurity vs clean crystal and impurity in bulk metal.

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, https://doi.org/10.1016/j.isci.2023.106033).

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.

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.
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.

Best regards,

Eduardo A. Menéndez Proupin
Departamento de Física Aplicada I
Universidad de Sevilla
Teléfono: +34 9554 20231
https://personal.us.es/emenendez/
https://personal.us.es/emenendez/docencia/
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