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Re: [ESPResSo-users] P3M epsilon

From: Axel Arnold
Subject: Re: [ESPResSo-users] P3M epsilon
Date: Mon, 7 Nov 2011 16:46:30 +0100
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Just some background to understand Stefan's tips:

The Bjerrum length contains the epsilon_0  epsilon_r of the assumed medium 
surrounding the particles. The epsilon that you can set is the _relative_  
dielectric constant of the medium that surrounds your particles while doing 
the summation in ascending shells of replicas. That is, we assume that while 
doing the periodic summation, your large, but still finite set of replicas is 
surrounded by another medium of dielectric constant epsilon_0  epsilon_r 
epsilon.  In the limit, this is really just the relative dielectric constant 
at infinity, but unfortunately, the system remembers this polarization, which 
is just an artifact of periodic bc.

Regarding the question of metallic or non-metallic bc: for systems with free 
ions, the question is clear - you need to use metallic bc to avoid unphysical 
polarization. For dipolar liquids, even if simulated by explicit, but bound 
charges, you have more freedom. Some properties converge faster if the 
dielectric constant at infinity matches the dielectric constant of your 
simulation box. However, that is something you typically don't know a 
priori... Leaving things at metallic is therefore mostly a good idea.

Many regards,

On Monday 07 November 2011 09:45:39 Stefan Kesselheim wrote:
> Dear Farnoosh,
> On 11/07/2011 09:16 AM, Farnoosh Farahpoor wrote:
> > Dear Espresso developers
> > 
> > I have a question about P3M method. When we use the "inter" command
> > with coulomb interaction we should set the Bjerrum length. This
> > quantity contains all of the information about electrostatic strength
> > in a medium with a specified temperature.
> > But there is another option in P3M method, "epsilon" (The dielectric
> > constant of the surrounding medium). Why and when we should set this
> > parameter? What does it mean that it "Defaults to metallic."?
> > When I am simulating a polyelectrolyte in water in the room
> > temperature shall I set it to the reduced magnitude of permittivity of
> > water?
> This parameter is typical for coulomb interactions in 3D-periodic
> systems: When taking the limit of infinitely many replicas of the box in
> all directions the results of the sum depends on the boundary conditions
> "behind" the replicas. In other words: the limit of infinitely many
> replicas does not remove dependence on the dielectric permittivity
> outside of the considered system.
> The dielectric properties outside of the system create a harmonic
> potential for the total dipole moment of the system proportional to
> 1/epsilon_{\infinity}. This means if epsilon_{\infinity}<\infinity the
> total dipole moment of the system will stay finite all the time and in
> thermal equilibrium be gaussian distributed, while it performs an
> unbounded random walk in case of metallic (infinity) boundary conditions.
> We spend quite some time getting a good idea of what the physical
> meaning of this parameter is, but we did not find a very good
> interpretation. It is an artifact of the fact that all real systems are
> large, but finite, and infinite systems create mathematical difficulties
> with the 1/r coulomb potential. My personal opinion is that only
> metallic boundary conditions correspond to "proper" physics, because
> then the equations of motion don't  change when a particle is at the
> same folded position but in different replicas.
> I know Kai Grass used metallic boundary conditions when simulating the
> electrophoretic mobility of a polyelectrolyte.
> Maybe someone else has a better answer to that question...
> Cheers and good luck,
> Stefan
> > Thank you in advance for your concern
> > With best regards
> > Farnoush

JP Dr. Axel Arnold
ICP, Universit├Ąt Stuttgart
Pfaffenwaldring 27
70569 Stuttgart, Germany
Email: address@hidden
Tel: +49 711 685 67609

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