[QE-users] Momentum matrix element on PBE+U

Fri May 15 11:25:23 CEST 2020

Sorry for multiple typos in my last email, which are due to autocorrection on my Mac. I meant "norm-conserving" pseudopotentils in numerous places in my last email.

Regards,

Iurii

________________________________
From: users <users-bounces at lists.quantum-espresso.org> on behalf of Timrov Iurii <iurii.timrov at epfl.ch>
Sent: Friday, May 15, 2020 11:13:19 AM
To: Quantum ESPRESSO users Forum
Subject: Re: [QE-users] Momentum matrix element on PBE+U

> Did you mean [J. Chem. Phys. 120, 9935 (2004)] by Toby and Dal Corso?

The correct reference (without mistakes) is this: J. Tóbik<https://aip.scitation.org/author/T%C3%B3bik%2C+Jaroslav> and A. Dal Corso<https://aip.scitation.org/author/Dal+Corso%2C+Andrea>, J. Chem. Phys. 120, 9934 (2004).

See Eq. (7) in this paper, which is for the ultra-soft pseudos. For norm-concerning pseudos, see Eq. (14) in S. Baroni and R. Resta, Phys. Rev. B 33, 7017 (1986).

> I could not find an expression for the momentum matrix element in that reference, I think that reference is only about the extra term involving the ultrasoft pseudopotential?

Let me try to explain for the corn-conserving case, which is simpler. The routine "compute_ppsi" has p - i [x, V_{nl}], where p is the momentum and V_{nl} is the nonlocal part of the pseudopotential. See the right-hand side of Eq. (15) in Phys. Rev. B 33, 7017 (1986). See also Eqs. (8) and (9) in

A. Marini, G. Onida, and R. Del Sole, Phys. Rev. B 64, 195125 (2001).

So actually the code computes not only the matrix element of the momentum p, but also it contains an extra contribution due to the non-local part of the pseudopotential. In the DFT+U case, there is yet another term given by Eq. (53) in Phys. Rev. B 101, 064305 (2020).

Finally, some related discussion about this (how to compute an electron velocity using these "tricks") is given in Sec. 6.1.3(a) of my PhD thesis: https://pastel.archives-ouvertes.fr/pastel-00823758/

HTH

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 L Y <xifntx at gmail.com>
Sent: Thursday, May 14, 2020 9:15:47 PM
To: Quantum ESPRESSO users Forum
Subject: Re: [QE-users] Momentum matrix element on PBE+U

Dear Lurii,

Thank you for the quick response!
Did you mean [J. Chem. Phys. 120, 9935 (2004)] by Toby and Dal Corso? I could not find an expression for the momentum matrix element in that reference, I think that reference is only about the extra term involving the ultrasoft pseudopotential?
I ask because I have calculated the momentum matrix elements between valence and conduction bands along symmetry lines in MgO. Everything seems OK, except the fact that there is a noticeable discontinuity of the matrix element at the Gamma point. I did extensive debugging, but could find anything wrong (the band energies are fine and continuous without discontinuity). I suspect I need to do something special for the momentum matrix element, but I cannot figure out the expression.

Best regards,
Lun Yue
Louisiana State University

Den tor. 14. maj 2020 kl. 11.55 skrev Timrov Iurii <iurii.timrov at epfl.ch<mailto:iurii.timrov at epfl.ch>>:

Dear Lun Yue,

The reference is written in the header of that routine.

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<mailto:users-bounces at lists.quantum-espresso.org>> on behalf of lot fun <xifntx at gmail.com<mailto:xifntx at gmail.com>>
Sent: Thursday, May 14, 2020 6:45:16 PM
To: Quantum ESPRESSO users Forum
Subject: Re: [QE-users] Momentum matrix element on PBE+U

Dear Lurii,

I was wondering whether you have any reference on how the momentum matrix element is implemented in QE?
Obviously the PP/src/compute_ppsi.f90 routine is crucial, but I dunno which formula is used there. A reference to a paper would be greatly appreciated!

Best regards,
Lun Yue
Louisiana State University

Den ons. 13. maj 2020 kl. 03.06 skrev Timrov Iurii <iurii.timrov at epfl.ch<mailto:iurii.timrov at epfl.ch>>:

> I encounter this error: 'Error in routine write_p_avg (1): write_p_avg not working with LDA+U'.

The LDA+U does not work in this case because there is a missing term, see Eq. (53) in PRB 101, 064305 (2020).

> Is there a way to circumvent this on Quantum Espresso?

I do not know any apart from adding the missing term.

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<mailto:users-bounces at lists.quantum-espresso.org>> on behalf of Shivesh Sivakumar <shiveshsivakumar at gmail.com<mailto:shiveshsivakumar at gmail.com>>
Sent: Wednesday, May 13, 2020 8:14:25 AM
To: Quantum ESPRESSO users Forum
Subject: [QE-users] Momentum matrix element on PBE+U

Hello users,

Sorry for the repost, but I think my question went unnoticed.
Is there a way to calculate the momentum matrix element in PBE+U on QE? I encounter this error: 'Error in routine write_p_avg (1): write_p_avg not working with LDA+U'. Is there a way to circumvent this on Quantum Espresso?

Best,
Shivesh Sivakumar
University of Washington
Seattle-WA, 98105

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