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Coulomb-Energies and MMM2D

From: Fabian Glatzel
Subject: Coulomb-Energies and MMM2D
Date: Tue, 26 Nov 2019 15:32:43 +0100

Dear espressomd developers,

I'm still heaving some issues with the Coulomb energy using ELC with the pot_diff parameter as well as using MMM2D with pot_diff.
The used system is a 2d plate capacitor (periodic boundary conditions along x&y) with charged hard spheres (Weeks-Chandler-Andersen) and with an external potential of 1V.
I simulated this system using three different setups:
1) ELC and the pot_diff argument
2) MMM2D and the pot_diff argument
3) ELC and a linear electric potential (corresponding to a constant surface charge density at the electrodes and hence neglecting the effect of image charges)

First, the density profile obtained with MMM2D shows some nonphysical behavior. For example, the density profile of the negative ions near the right electrode miss the typical rise that the positive ions near the left electrode show (see ). Of course, the ions are identical up to their charge.
Concerning the Coulomb energy, I cannot make any sense from the numbers i get via MMM2D or ELC with pot_diff. However, they are more or less consistent with each other. From what I see I would guess that there is possibly a sign error. But maybe I should first explain where this impression comes from:
As stated above I also simulated the system using ELC without the pot_diff argument but using a linear electric potential instead. The density profiles obtained via this method fit the ones from ELC with ext_pot parameter quite good. However, the energy contributions using ELC and the linear electric potential are:
coulomb: ~ +10650
external_fields: ~ -23000

Using ELC with ext_pot i get:
coulomb: ~ +14400

I guess this explains part of my confusion. Further, if the change in the coulomb energy during charging is monitored another unexpected behavior can be seen using the pot_diff argument. A smaller Coulomb energy is obtained at pot_diff=0V than at pot_diff=1V. However, if the decrease in Coulomb energy due to the external charge (implicitly handled via pot_diff) was not bigger than the increase of the Coulomb energy  due to the ion-ion contributions in the system, the system should not change its density profile at all.

I wrote a little example script to show these effects. To keep it as simple as possible it contains some hard coded numbers etc... Via the index in line 8 the used method can be chosen (ELC, MMM2D or ELC + External Field). In line 10 it can be set if the density profile is written to a file. The other stuff should be self-explanatory.
The example script can be downloaded via:

I look forward to hearing from you.
Also, let me thank you in advance since i know it can consume quite a bit of time...

Best wishes,


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