Dear Yuriii: Treating U as a response property may not be sufficient. Response properties are not bound neither from above nor from below, and a particular (valid!) value of U may still correspond to unphysical values of energy due to the approximate nature of DFT+U. The situation is somewhat similar to using self-consistent vs HF densities in DFT to get the total energies (see K.Burke works on that).
But in general, the study of this interesting question seems to be a real scientific challenge. -- Ilya Ryabinkin, Senior Research Fellow, OTI Lumionics Inc Toronto, Canada. On Thu, Oct 29, 2020 at 1:37 PM Timrov Iurii <[email protected]> wrote: > Dear Giuseppe, > > > Thank you for your comment! > > > > In principle you are right, but if you try to compute, e.g., formation > > heats or formation energy of defects by using different U values (I > > did it long time ago in the case of TiO2 related studies for metallic > > Ti, for TiO2, for Ti2O3) you fall sometimes very far from experimental > > references, farther then using non corrected GGA. > > > Ok, I see. So you used semiempirical U and things got worse, right? It > would be interesting to see what happens if ab initio U is used for each > structure. > > > > I've used semiempirically averaged values in a lot of studies > (including the > > correction of O- and N-related bands in oxides and nitrides) and > > things are a bit semiempirical, obviously, but still quite improved > > with respect to GGA. As long as you motivate what you are doing, I do > > not see particular harm in semiempirical U corrections! > > > Ok. Of course, one is free to choose whether to use a semiempirical or ab > initio U. But I see the following issues when using semiempirical U: > > - choice of the Hubbard manifold. U depends a lot on the Hubbard manifold > (atomic, ortho-atomic, Wannier functions, etc.). Different codes use > different Hubbard manifolds. So if one takes U from some paper where it was > determined semiempirically (e.g. using VASP) and use it in QE (with a > different manifold) the results can be totally different > > - choice of the pseudopotential (see Appendix in J. Chem. Phys. 129, > 134314 (2008)). From this reference you can see that the pseudopotentials > generated in different oxidation states require different U. It is easy to > compute U for a given pseudo, but how to determine it semiempirically (try > to reproduce some experimental quantity? and what to do if there is no > experimental data for the material under investigation?) > > - choice the exchange-correlation functional: PW91, PBE, PBEsol, ... - > each time the U correction is not exactly the same. For each functional U > must be tuned by hand if done semiempirically. > > So for a given computational setup (Hubbard manifold, pseudos, functional, > etc.) I would simply compute U from first principles (luckily we have now > theories and codes to do that, which was not the case in the past). And > when one wants to do a high-throughput study for thousands of materials, > fitting U for each system to the experimental data would kill the whole > idea of high-throughput. Just my thoughts. > > > Thanks! > > > Greetings, > > Iurii > > > -- > Dr. Iurii TIMROV > Postdoctoral Researcher > STI - IMX - THEOS and NCCR - MARVEL > Swiss Federal Institute of Technology Lausanne (EPFL) > CH-1015 Lausanne, Switzerland > +41 21 69 34 881 > http://people.epfl.ch/265334 > ------------------------------ > *From:* users <[email protected]> on behalf of > Giuseppe Mattioli <[email protected]> > *Sent:* Thursday, October 29, 2020 5:58:39 PM > *To:* Quantum ESPRESSO users Forum > *Subject:* Re: [QE-users] Thermodynamics with DFT+U > > > Dear Iurii > In principle you are right, but if you try to compute, e.g., formation > heats or formation energy of defects by using different U values (I > did it long time ago in the case of TiO2 related studies for metallic > Ti, for TiO2, for Ti2O3) you fall sometimes very far from experimental > references, farther then using non corrected GGA. I've used > semiempirically averaged values in a lot of studies (including the > correction of O- and N-related bands in oxides and nitrides) and > things are a bit semiempirical, obviously, but still quite improved > with respect to GGA. As long as you motivate what you are doing, I do > not see particular harm in semiempirical U corrections! > Best > Giuseppe > > Quoting Timrov Iurii <[email protected]>: > > > Dear Malte, > > > > > > This is not an easy question. Let me express my opinion. > > > > > >> I read many times in papers that I should not compare total energies of > >> DFT+U calculations with different U values. > > > > > > Can you give some references please? > > > > > > Well the problem is that in literature often people still use > > empirical values of U. In this case, I agree that the comparison of > > energies will depend strongly on U which one chooses based on some > > arguments. But if one computes U from first principles, then U is a > > response property of each system (and the response is different in > > each system, hence different U) then it makes sense to me to compare > > energies (but I am not aware of any theoretical proof that it is > > allowed to do so). > > > > > > For example, in LiCoO2 the computed value of U for Co-3d is 6.91 eV, > > while U for Co-3d in CoO is 4.55 eV (both using 'atomic' orbitals > > and some pseudos on top of PBEsol - see PRB 101, 064305 (2020)). So > > in both cases we consider Co-3d states, but the value of U is very > > different. This is so because Co-3d states require different > > corrections when they are in different chemical environments (these > > Co-3d states hybridize differently with ligands in different > > compounds). If you use an average value of 5.73 eV for both systems, > > then this value is not a response property of any of these systems > > (I do not know what it is in this case). > > > > > > One can also see DFT+U as DFT with a Hubbard functional: the U > > correction is different for different systems (why should it be the > > same?). It's like hybrids: people tune the value of alpha in PBE0 > > for each system (alpha is related to the inverse of the dielectric > > constant), and alpha is different for different systems (because the > > dielectric constant is different). So here is the same, U is > > different for different systems: different systems need different > > amount of the corrections to restore the piece-wise linearity of the > > energy (PRB 71, 035105 (2005)) and alleviate self-interactions. > > > > > > The comparison of energies with different ab initio U values was > > done in these papers: PRB 99, 094102 (2019); PRR 2, 023313 (2020); > > PRM 3, 033801 (2019). > > > > > >> What should I do in case of complex hull calculations of a phase > diagram? > > > > > > I would compute U for each phase and compare energies. > > > > > >> With QE it is now possible to calculate the U values for each > >> composition by the hp.x code. Can I > > compare the resulting total energies with each other safely? > > > > > > Well there is no general consensus on this issue, in part because > > still many people use empirical U. I think that if U is computed ab > > initio (i.e. it is really a response property of each material) then > > it makes sense to compare energies with different U values (U > > computed for each system). But people are still investigating this > > issue. > > > > > > I will be happy to hear other opinions, and to hear > > corrections/remarks if something what I said is misleading. > > > > > > Greetings, > > > > Iurii > > > > > > -- > > Dr. Iurii TIMROV > > Postdoctoral Researcher > > STI - IMX - THEOS and NCCR - MARVEL > > Swiss Federal Institute of Technology Lausanne (EPFL) > > CH-1015 Lausanne, Switzerland > > +41 21 69 34 881 > > http://people.epfl.ch/265334 > > ________________________________ > > From: users <[email protected]> on behalf of > > Giuseppe Mattioli <[email protected]> > > Sent: Thursday, October 29, 2020 3:52:48 PM > > To: Quantum ESPRESSO users Forum > > Subject: Re: [QE-users] Thermodynamics with DFT+U > > > > > > Dear Malte > > I suppose that, as a trivial rule of thumb, if U values are not so > > different then you can use some average value for all systems. > > HTH > > Giuseppe > > > > Quoting Malte Sachs <[email protected]>: > > > >> Dear all, > >> > >> I read many times in papers that I should not compare total energies > >> of DFT+U calculations with different U values. What should I do in > >> case of complex hull calculations of a phase diagram? With QE it is > >> now possible to calculate the U values for each composition by the > >> hp.x code. Can I compare the resulting total energies with each > >> other safely? > >> > >> Best regards, > >> Malte > >> > >> -- > >> Malte Sachs > >> Anorganische Chemie, Fluorchemie > >> Philipps-Universität Marburg > >> Hans-Meerwein-Straße 4 > >> 35032 Marburg (Paketpost: 35043 Marburg) > >> Tel.: +49 (0)6421 28 - 25 68 0 > >> http://www.uni-marburg.de/fb15/ag-kraus/ > > > > > > > > GIUSEPPE MATTIOLI > > CNR - ISTITUTO DI STRUTTURA DELLA MATERIA > > Via Salaria Km 29,300 - C.P. 10 > > I-00015 - Monterotondo Scalo (RM) > > Mob (*preferred*) +39 373 7305625 > > Tel + 39 06 90672342 - Fax +39 06 90672316 > > E-mail: <[email protected]> > > > > _______________________________________________ > > Quantum ESPRESSO is supported by MaX > > (www.max-centre.eu<http://www.max-centre.eu>) > > users mailing list [email protected] > > https://lists.quantum-espresso.org/mailman/listinfo/users > > > > GIUSEPPE MATTIOLI > CNR - ISTITUTO DI STRUTTURA DELLA MATERIA > Via Salaria Km 29,300 - C.P. 10 > I-00015 - Monterotondo Scalo (RM) > Mob (*preferred*) +39 373 7305625 > Tel + 39 06 90672342 - Fax +39 06 90672316 > E-mail: <[email protected]> > > _______________________________________________ > Quantum ESPRESSO is supported by MaX (www.max-centre.eu) > users mailing list [email protected] > https://lists.quantum-espresso.org/mailman/listinfo/users > _______________________________________________ > Quantum ESPRESSO is supported by MaX (www.max-centre.eu) > users mailing list [email protected] > https://lists.quantum-espresso.org/mailman/listinfo/users
_______________________________________________ Quantum ESPRESSO is supported by MaX (www.max-centre.eu) users mailing list [email protected] https://lists.quantum-espresso.org/mailman/listinfo/users
