[Pw_forum] Ewald and Coulomb

[Peter Wang]

Let’s consider positive point charges q in one dimensional lattice, that is, at x=a*j, j=-infinity,...,-2,-1,0,1,2,...,+infinity. In order to calculate the electrostatic energy due to Coulomb interaction between the charge at x=0 and all the other charges, one should calculate the summation: 1/a * sum_j q^2/j. However, the summation is not converged and is positive infinite. In summary, electrostatic interaction energy for charged system is infinite and one needs some other technique to calculate it.

Yun-Peng

From: jiayudai 
Sent: Saturday, January 14, 2012 10:17 PM
To: pw_forum at pwscf.org 
Subject: Re: [Pw_forum] Ewald and Coulomb

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?

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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