[QE-users] Can an increase in the basis-set increase the total energy of a system?

[Giovanni Cantele]

Hi,

users writing on this forum are usually requested to sign their post with
name and affiliation.

This being said, what you find can be perfectly logic.

You have to distinguish between ecutrho and ecutwfc.

The total energy is expected to have a "variational" behavior  with respect
to ecutwfc, because ecutwfc controls the size of the plane wave basis set:
the larger ecutwfc, the larger the basis set, the smaller the total energy.
At which values of ecutwfc should one stop? This can be controlled by
looking at the convergence of calculated properties (e.g. forces of energy
differences or phonon frequencies, and so on, depending on what you're
interested in).

A different logic must be applied to ecutrho. Indeed, ecutrho controls the
representation of the part of the charge density that is not expected to
change significantly during the scf cycle and that is added to the total
charge density at the end of each scf cycle. For norm-conserving
pseudopotential ecuttho=4*ecutwfc exactly reproduces the charge density,
whereas for pseudopotentials that are not norm conserving you need more
plane waves to represent the charge density localized on the atomic cores.
As such, you fix ecutrho = 6, 8, 12, .... times ecutwfc (see also here:
https://www.quantum-espresso.org/Doc/INPUT_PW.html#idm301). So, saying that
you find a minimum total energy with respect to ecutrho is strictly
speaking "wrong", because this parameter does not control the size of the
basis set but only the accuracy with which you represent the charge
density. So, the purpose is that of finding a value of ecutrho at which you
reach a satisfactory convergence, not the minimum energy. The total energy,
as a function of ecutrho, can either increase or decrease, because it is a
matter of numerical accuracy (good versus band representation of the charge
density), not of basis set size.

Giovanni

-- 

Giovanni Cantele, PhD
CNR-SPIN
c/o Dipartimento di Fisica
Universita' di Napoli "Federico II"
Complesso Universitario M. S. Angelo - Ed. 6
Via Cintia, I-80126, Napoli, Italy
e-mail: giovanni.cantele at spin.cnr.it <giovanni.cantele at spin.cnr.it>
Phone: +39 081 676910
Skype contact: giocan74

ResearcherID: http://www.researcherid.com/rid/A-1951-2009
Web page: https://sites.google.com/view/giovanni-cantele/home


Il giorno mar 21 feb 2023 alle ore 10:56 NM SALMA <
rose-marron2008 at hotmail.fr> ha scritto:

> Hello,
>
> I was doing the convergence testing of CuI material.
> For a fixed Ecutwfc value, when I increase the Ecutrho the total energy of
> the system increase. I was expecting the inverse.
> For example for Ecutwfc=90 Ry and Ecutrho= 180 Ry the total energy=
> -2368.11704109 Ry
> and for Ecutwfc=90 Ry and Ecutrho=450 Ry the total energy= -2368.11613851
> Ry.
> Is that logic? I thought that an increase in the basis-set minimize the
> system energy.
>
> I also remarked in the pseudopotential file  that :
>   For Cu : - Suggested minimum cutoff for wavefunctions:  45. Ry
>                 - Suggested minimum cutoff for charge density: 236. Ry
>
>   For I  :     - Suggested minimum cutoff for wavefunctions:  24. Ry
>                  - Suggested minimum cutoff for charge density: 109. Ry
>
> So how it can be that the suggested minimum cutoff for charge density of
> Cu is 236 Ry, while I found that the system have a minimum total energy for
> Ecutrho=180 Ry
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