[QE-users] [EXT] Total energy of charged slabs

Tue Aug 17 05:00:48 CEST 2021

I here post the following 'again' because my mailer failed to leave
the delivered mark on the message.

---
One of the ways to handle charged system in DFT calculation is
to use the ESM method.

M. Otani and O. Sugino, "First-principles calculations of charged
surfaces and interfaces: A plane-wave nonrepeated slab approach," PRB
73, 115407 (2006).

It has been implemented in the QE; see the files in the directory:
 qe-6.8/PW/examples/ESM_example

> Besides, another related question is how we define the zero energy in
> QE?

Energy zero is defined arbitrarily in any DFT calculations. I usually
estimate the energy standard (rather than the energy zero) to be the
potential energy of vacuum in the slab system.

You can estimate it by plotting the x-y averaged potential energies
along the z-direction. This function is also implemented in the ESM
calculation (check the *.esm file in the working directory of QE).

---
best regards
kazume NISHIDATE
敬具 西館数芽

nisidate at iwate-u.ac.jp
kazume.nishidate at gmail.com

2021年8月17日(火) 8:52 Andreussi, Oliviero <Oliviero.Andreussi at unt.edu>:

> Hi Zhenyao,
>
> I am writing to give some remarks on simulating negatively charged slabs,
> as I am afraid that the correct answer requires to know what the package
> “sxdefectalign2d” does exactly (which I don’t).
>
> A charged slab that is infinitely periodic along x and y must have an
> infinite energy. It is not just a matter of interactions with periodic
> replicas, even if you remove the periodicity along z, this is not enough to
> make your energy finite. If you correct for PBC on the perpendicular
> direction, the energy should still be a function of the cell size, as a
> uniformly charged slab generates a constant field in space, so the
> electrostatic energy of the system is proportional to the cell volume. If
> the charged defect is only in the unit cell, but the periodic cells along x
> and y have no charged defects, than the energy is finite, but I am not sure
> if this is what “sxdefectalign2d” does, as it seems to me kind of tricky to
> implement.
>
> If what you wanted to study is an infinitely periodic charged slab (say
> because it is connected to a potential difference), in order for the energy
> to be finite and well defined you need to have some compensating charge
> somewhere. If you are modeling the interface of a material in an
> electrochemical cell, one possibility is to include a model for ionic
> diffuse layer in the space above/below your slab. This can be done with
> Environ (www.quantum-environ.org), which is a library for modeling
> continuum embeddings coupled with QE.
>
> Standard DFT (e.g. PBE) suffers from self-interaction errors, among other
> approximations. As a result, in negative systems you may have that the
> extra electron in an anion is not bound, i.e. it’s orbital energy is
> greater than zero. Thus, the stable configuration for the extra electron
> would be delocalized over the entire cell. If your simulation cell is
> small, the free electron states may be slightly higher in energy than your
> band energy and the extra electron could still converge, with a positive
> band energy. This is what happens in quantum chemistry codes when you use
> DFT to simulate anions: having localized basis sets force the extra
> electron to stay on the atoms, instead of wandering around as a free
> electron.
>
> I don’t know if this helps, but I would suggest to be particularly careful
> with charged slabs.
>
> Best,
>
> Oliviero Andreussi
> --
> Assistant Professor
> Department of Physics
> University of North Texas
> Email: oliviero.andreussi at unt.edu <oliviero.andreussi at unt.edu>
> Phone: +1-(940)-369-5316
> Skype: olivieroandreussi
> Web: https://www.materialab.org
>
> On Aug 16, 2021, at 4:30 PM, Zhenyao Fang <zhenyaof at sas.upenn.edu> wrote:
>
> Dear pwscf users,
>
> I am performing some calculations on negatively charged slabs (with one
> additional electron), and I’m mainly focusing on the energy difference
> between charged system and neutral system. With ions fixed, I found that
> the charged system has a higher energy than the neutral system, instead of
> being lower.
>
> The energy difference dE = E(q=-1) - E(q=0) is around 3.944 eV. The LUMO
> position of the neutral slab is 3.462 eV, and the vacuum level for the
> neutral slab is 7.654 eV. Besides, by inspecting the charge difference
> plots, the additional charge is localized inside the slab. I understand
> that there could be problems about jellium background, so I used the
> package “sxdefectalign2d” to correct the interactions due to periodic
> images, and the total energy of the charged slab remains the same as the
> size of vacuum increases.
>
> I’m quite confused by the fact that the total energy would increase with
> one more electron. Since the additional charge is mainly inside the slab,
> it should lower the energy and be stabilised inside the slab. Therefore, I
> was wondering how I can reconcile these controversies. Besides, another
> related question is how we define the zero energy in QE? In other words,
> does LUMO larger or smaller than zero possibly imply the stability of the
> system?
>
> I am looking forward to your replies. Thanks in advance.
>
> Best,
> Zhenyao Fang
>
>
>
>
>
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