[QE-users] Thermodynamics with DFT+U

Fri Oct 30 12:21:23 CET 2020

Dear Iurii, dear Giuseppe,

thank you for the interesting discussion. My "knowledge" comes from 
papers using empirical U values. I see that my question is  still 
related to an ongoing debate. However, your arguments and references 
helped my for my discussion. Thanks a lot,

best regards,
Malte

Am 29.10.20 um 18:36 schrieb Timrov Iurii:
>
> 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. Soyou 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 - THEOSand 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 <users-bounces at lists.quantum-espresso.org> on behalf of 
> Giuseppe Mattioli <giuseppe.mattioli at ism.cnr.it>
> *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 <iurii.timrov at epfl.ch>:
>
> > 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 <users-bounces at lists.quantum-espresso.org> on behalf of
> > Giuseppe Mattioli <giuseppe.mattioli at ism.cnr.it>
> > 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 <malte.sachs at chemie.uni-marburg.de>:
> >
> >> 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: <giuseppe.mattioli at ism.cnr.it>
> >
> > _______________________________________________
> > Quantum ESPRESSO is supported by MaX
> > (www.max-centre.eu<http://www.max-centre.eu 
> <http://www.max-centre.eu<http://www.max-centre.eu>>)
> > users mailing list users at lists.quantum-espresso.org
> > 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: <giuseppe.mattioli at ism.cnr.it>
>
> _______________________________________________
> Quantum ESPRESSO is supported by MaX (www.max-centre.eu 
> <http://www.max-centre.eu>)
> users mailing list users at lists.quantum-espresso.org
> https://lists.quantum-espresso.org/mailman/listinfo/users
>
> _______________________________________________
> Quantum ESPRESSO is supported by MaX (www.max-centre.eu)
> users mailing list users at lists.quantum-espresso.org
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-- 
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/

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