[Pw_forum] Ewald and Coulomb

[jiayudai]

Dear Axel and Yun-Peng,

Thanks for your physial translation. Now, i think i can understand the physical figures in this problem. As axel said, the forces can be correct, but the energies are wrong. However, what i want to get is the pressure from positive ions. Thus, i should need the correct energies at first. For the treatment of Coulomb interations, we usually do the summation within a cutoff of a distance if we only use the formation of 1/r. This is an approach but it can solve the problem of divergence. Therefore, i think we can change the ewald formula in DFT using 1/r (with a cutoff). Is it?

Message: 7
Date: Sat, 14 Jan 2012 14:10:17 -0500
From: Axel Kohlmeyer <akohlmey at gmail.com>
Subject: Re: [Pw_forum] Ewald and Coulomb
To: PWSCF Forum <pw_forum at pwscf.org>
Message-ID:
<CADTmJ6H_qwNpHMVSk1EO2UD_N0PQ93Jo9b=UD5+qDoVHe_Gc2A at mail.gmail.com>
Content-Type: text/plain; charset=ISO-8859-1
2012/1/14 jiayudai <daijiayu at nudt.edu.cn>:
> Dear Yun-Peng,
>
> Thanks for your explanation. In fact, what i mean is that how to treat the
> ion-ion interactions with some charges. For example, sometimes we want to
> take out one or more electrons out of the system, thus the tot_charge in the
> system is not zero. In an extreme case, all electrons are ionized and taken
> out, there are only positive ions in the system. In this case, the Ewald
> potential should not be right but the real Coulomb potential should be
> correct. Since Ewald scheme considers the screnning by the electrons. Thus,
> i want to use the exact 1/r potential to represent the Ewald scheme. So, how
> can we reach this goal?
if you want to look at things at this level,
then you have to accept the fact that you
cannot remove electrons from an infinite
system. only from a finite system.
you can still do the calculation with a
periodic system, if you ignore the divergent
term that stems from the total charge of
your unit cell. if you do ewald summation
with conducting boundary conditions, the
forces will not be affected (at least not for
the classical system), but the energy is
- of course - wrong.
either this approach is good enough to you,
or you have to use a real space DFT code
instead, where you don't have to worry about
periodicity by construction (but have some
other issues...).
axel.

>
> Best wishes.
>
> Jiayu
>
>
>
>
>>>>>>>>>>>>>>>>>>>>
> what do you mean by "true Coulomb potential"? Based on density functional
> theory, adding an uniform potential to the system make no difference. In
> fact, the ion-ion interaction energy is an infinite value because of 1/r
> type of Coulomb potential. However, if an uniform charge density which makes
> total charge zero, hence uniform Coulomb potential is added to the system,
> the electrostatic energy as well as potential is finite, at the same time,
> physics keep unchanged.
> best wishes,Yun-Peng
>
> Date: Fri, 13 Jan 2012 21:49:59 +0800
>
>
> From: daijiayu at nudt.edu.cn
> To: pw_forum at pwscf.org
> Subject: [Pw_forum] Ewald and Coulomb
>
>
> Dear users and developers,
>
> Happy new year!
>
>
>
> I have a confusion about the calculations of ion-ion interactions. We know,
> we usually use Ewald scheme to represent the real Coulomb potentials in a
> periodic cell. Generally, it is correct for a neutral system or one electron
> taken out (or into ) system. However, if the system is constructed with
> partially charged ions, that is to say, there are more positive charges than
> negative charges, the Ewald scheme should be not right. Although this system
> is not stable, but there should be some properties deserved to study.
>
> So, how can we calculate the true Coulomb potentials in DFT? That is to say,
> we do not use Ewald, but only use th 1/r type. I know it can be realized in
> classical calculations, but i did not find the path to get it in QE.
>
>
>
> Thanks a lot.
>
>
>
> Jiayu
>
>
>  
The pressure of positive ions confused me for a long time, i think it can be obtained using the 1/r interactions, but i can not make sure. Is there some other physics in it?

Thanks.

Jiayu

Message: 7
Date: Sat, 14 Jan 2012 14:10:17 -0500
From: Axel Kohlmeyer <akohlmey at gmail.com>
Subject: Re: [Pw_forum] Ewald and Coulomb
To: PWSCF Forum <pw_forum at pwscf.org>
Message-ID:
<CADTmJ6H_qwNpHMVSk1EO2UD_N0PQ93Jo9b=UD5+qDoVHe_Gc2A at mail.gmail.com>
Content-Type: text/plain; charset=ISO-8859-1
2012/1/14 jiayudai <daijiayu at nudt.edu.cn>:
> Dear Yun-Peng,
>
> Thanks for your explanation. In fact, what i mean is that how to treat the
> ion-ion interactions with some charges. For example, sometimes we want to
> take out one or more electrons out of the system, thus the tot_charge in the
> system is not zero. In an extreme case, all electrons are ionized and taken
> out, there are only positive ions in the system. In this case, the Ewald
> potential should not be right but the real Coulomb potential should be
> correct. Since Ewald scheme considers the screnning by the electrons. Thus,
> i want to use the exact 1/r potential to represent the Ewald scheme. So, how
> can we reach this goal?
if you want to look at things at this level,
then you have to accept the fact that you
cannot remove electrons from an infinite
system. only from a finite system.
you can still do the calculation with a
periodic system, if you ignore the divergent
term that stems from the total charge of
your unit cell. if you do ewald summation
with conducting boundary conditions, the
forces will not be affected (at least not for
the classical system), but the energy is
- of course - wrong.
either this approach is good enough to you,
or you have to use a real space DFT code
instead, where you don't have to worry about
periodicity by construction (but have some
other issues...).
axel.

>
> Best wishes.
>
> Jiayu
>
>
>
>
>>>>>>>>>>>>>>>>>>>>
> what do you mean by "true Coulomb potential"? Based on density functional
> theory, adding an uniform potential to the system make no difference. In
> fact, the ion-ion interaction energy is an infinite value because of 1/r
> type of Coulomb potential. However, if an uniform charge density which makes
> total charge zero, hence uniform Coulomb potential is added to the system,
> the electrostatic energy as well as potential is finite, at the same time,
> physics keep unchanged.
> best wishes,Yun-Peng
>
> Date: Fri, 13 Jan 2012 21:49:59 +0800
>
>
> From: daijiayu at nudt.edu.cn
> To: pw_forum at pwscf.org
> Subject: [Pw_forum] Ewald and Coulomb
>
>
> Dear users and developers,
>
> Happy new year!
>
>
>
> I have a confusion about the calculations of ion-ion interactions. We know,
> we usually use Ewald scheme to represent the real Coulomb potentials in a
> periodic cell. Generally, it is correct for a neutral system or one electron
> taken out (or into ) system. However, if the system is constructed with
> partially charged ions, that is to say, there are more positive charges than
> negative charges, the Ewald scheme should be not right. Although this system
> is not stable, but there should be some properties deserved to study.
>
> So, how can we calculate the true Coulomb potentials in DFT? That is to say,
> we do not use Ewald, but only use th 1/r type. I know it can be realized in
> classical calculations, but i did not find the path to get it in QE.
>
>
>
> Thanks a lot.
>
>
>
> Jiayu
>
>
>
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