[QE-users] Thermodynamics with DFT+U

Thu Oct 29 18:36:31 CET 2020

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 <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
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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>

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