[QE-users] Thermodynamics with DFT+U

Thu Oct 29 17:29:14 CET 2020

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>

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