<br />
Dear Axel and Yun-Peng,<br />
<br />
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?<br />
<span _fck_bookmark="1" style="display: none"> </span>
<p>
<span _fck_bookmark="1" style="display: none">Message: 7<br />
Date: Sat, 14 Jan 2012 14:10:17 -0500<br />
From: Axel Kohlmeyer <<a href="mailto:akohlmey@gmai">akohlmey@gmai</a>l.com><br />
Subject: Re: [Pw_forum] Ewald and Coulomb<br />
To: PWSCF Forum <pw_<a href="mailto:forum@pwscf.o">forum@pwscf.o</a>rg><br />
Message-ID:<br />
<CADTmJ6H_qwNpHMVSk1EO2UD_N0PQ93Jo9b=UD5+qDoVHe_<a href="mailto:Gc2A@mail.gma">Gc2A@mail.gma</a>il.com><br />
Content-Type: text/plain; charset=ISO-8859-1</span></p>
<p>
<span _fck_bookmark="1" style="display: none">2012/1/14 jiayudai <<a href="mailto:daijiayu@nudt">daijiayu@nudt</a>.edu.cn>:<br />
> Dear Yun-Peng,<br />
><br />
> Thanks for your explanation. In fact, what i mean is that how to treat the<br />
> ion-ion interactions with some charges. For example, sometimes we want to<br />
> take out one or more electrons out of the system, thus the tot_charge in the<br />
> system is not zero. In an extreme case, all electrons are ionized and taken<br />
> out, there are only positive ions in the system. In this case, the Ewald<br />
> potential should not be right but the real Coulomb potential should be<br />
> correct. Since Ewald scheme considers the screnning by the electrons. Thus,<br />
> i want to use the exact 1/r potential to represent the Ewald scheme. So, how<br />
> can we reach this goal?</span></p>
<p>
<span _fck_bookmark="1" style="display: none">if you want to look at things at this level,<br />
then you have to accept the fact that you<br />
cannot remove electrons from an infinite<br />
system. only from a finite system.</span></p>
<p>
<span _fck_bookmark="1" style="display: none">you can still do the calculation with a<br />
periodic system, if you ignore the divergent<br />
term that stems from the total charge of<br />
your unit cell. if you do ewald summation<br />
with conducting boundary conditions, the<br />
forces will not be affected (at least not for<br />
the classical system), but the energy is<br />
- of course - wrong.</span></p>
<p>
<span _fck_bookmark="1" style="display: none">either this approach is good enough to you,<br />
or you have to use a real space DFT code<br />
instead, where you don't have to worry about<br />
periodicity by construction (but have some<br />
other issues...).</span></p>
<p>
<span _fck_bookmark="1" style="display: none">axel.</span></p>
<p>
<br />
<span _fck_bookmark="1" style="display: none">><br />
> Best wishes.<br />
><br />
> Jiayu<br />
><br />
><br />
><br />
><br />
>>>>>>>>>>>>>>>>>>>><br />
> what do you mean by "true Coulomb potential"? Based on density functional<br />
> theory, adding an uniform potential to the system make no difference. In<br />
> fact, the ion-ion interaction energy is an infinite value because of 1/r<br />
> type of Coulomb potential. However, if an uniform charge density which makes<br />
> total charge zero, hence uniform Coulomb potential is added to the system,<br />
> the electrostatic energy as well as potential is finite, at the same time,<br />
> physics keep unchanged.<br />
> best wishes,Yun-Peng<br />
><br />
> Date: Fri, 13 Jan 2012 21:49:59 +0800<br />
><br />
><br />
> From: <a href="mailto:daijiayu@nudt">daijiayu@nudt</a>.edu.cn<br />
> To: pw_<a href="mailto:forum@pwscf.o">forum@pwscf.o</a>rg<br />
> Subject: [Pw_forum] Ewald and Coulomb<br />
><br />
><br />
> Dear users and developers,<br />
><br />
> Happy new year!<br />
><br />
><br />
><br />
> I have a confusion about the calculations of ion-ion interactions. We know,<br />
> we usually use Ewald scheme to represent the real Coulomb potentials in a<br />
> periodic cell. Generally, it is correct for a neutral system or one electron<br />
> taken out (or into ) system. However, if the system is constructed with<br />
> partially charged ions, that is to say, there are more positive charges than<br />
> negative charges, the Ewald scheme should be not right. Although this system<br />
> is not stable, but there should be some properties deserved to study.<br />
><br />
> So, how can we calculate the true Coulomb potentials in DFT? That is to say,<br />
> we do not use Ewald, but only use th 1/r type. I know it can be realized in<br />
> classical calculations, but i did not find the path to get it in QE.<br />
><br />
><br />
><br />
> Thanks a lot.<br />
><br />
><br />
><br />
> Jiayu<br />
><br />
><br />
></span></p>
<span _fck_bookmark="1" style="display: none"> </span>
<p>
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?<br />
<br />
Thanks.<br />
<br />
Jiayu<br />
<br />
Message: 7<br />
Date: Sat, 14 Jan 2012 14:10:17 -0500<br />
From: Axel Kohlmeyer <<a href="mailto:akohlmey@gmai">akohlmey@gmai</a>l.com><br />
Subject: Re: [Pw_forum] Ewald and Coulomb<br />
To: PWSCF Forum <pw_<a href="mailto:forum@pwscf.o">forum@pwscf.o</a>rg><br />
Message-ID:<br />
<CADTmJ6H_qwNpHMVSk1EO2UD_N0PQ93Jo9b=UD5+qDoVHe_<a href="mailto:Gc2A@mail.gma">Gc2A@mail.gma</a>il.com><br />
Content-Type: text/plain; charset=ISO-8859-1</p>
<p>
2012/1/14 jiayudai <<a href="mailto:daijiayu@nudt">daijiayu@nudt</a>.edu.cn>:<br />
> Dear Yun-Peng,<br />
><br />
> Thanks for your explanation. In fact, what i mean is that how to treat the<br />
> ion-ion interactions with some charges. For example, sometimes we want to<br />
> take out one or more electrons out of the system, thus the tot_charge in the<br />
> system is not zero. In an extreme case, all electrons are ionized and taken<br />
> out, there are only positive ions in the system. In this case, the Ewald<br />
> potential should not be right but the real Coulomb potential should be<br />
> correct. Since Ewald scheme considers the screnning by the electrons. Thus,<br />
> i want to use the exact 1/r potential to represent the Ewald scheme. So, how<br />
> can we reach this goal?</p>
<p>
if you want to look at things at this level,<br />
then you have to accept the fact that you<br />
cannot remove electrons from an infinite<br />
system. only from a finite system.</p>
<p>
you can still do the calculation with a<br />
periodic system, if you ignore the divergent<br />
term that stems from the total charge of<br />
your unit cell. if you do ewald summation<br />
with conducting boundary conditions, the<br />
forces will not be affected (at least not for<br />
the classical system), but the energy is<br />
- of course - wrong.</p>
<p>
either this approach is good enough to you,<br />
or you have to use a real space DFT code<br />
instead, where you don't have to worry about<br />
periodicity by construction (but have some<br />
other issues...).</p>
<p>
axel.</p>
<p>
<br />
><br />
> Best wishes.<br />
&g