Re: question on the charged system

From: Hyonseok Hwang (
Date: Wed May 17 2006 - 22:25:04 CDT

Dear Mark,

Thanks a lot for your reply. I should have mentioned the reference in
my previous email. The reference is

T. Darden, D. Pearlman, L. G. Pedersen, JCP v109, p10921 (98).

The eq. (2.16) in the paper explains about the self energy and the
uniform neutralizing plasma. If you look at the equation, you will find
that the equation is independent of the atomic positions.

I found out another nice paper regarding the Ewald sum and charged
system. Actually, it is not a published paper. so please google it. You
will find it easily.

The title of paper is "Plain Ewald and PME" written by Thierry Matthey.
(posted the date is June 25, 2005)

This paper explains why the uniform neutralizing plasma is needed in the
charged system.

After reading those two papers, my feeling is like this. When we use
Ewald sum or PME in a charged system, for example, in NAMD, we
"implicitly" use the uniform neutralizing plasma method to avoid the
divergence of the Ewald sum and to neutralize the system. So the
dynamics is correct, but the energy is not correct by some constant. The
constant is given in Eq. (5) in Matthey's paper.

Consequently, when we do some simulations on a charged system with PME
without putting any neutralizing counterions, I think that we implicitly
opt to the "uniform neutralizing plasma method". So the system is still
neutralized by the neutralizing plasma and the dynamics is correct, but
the energy is incorrect by some amount.

This is just my thought. If there is something wrong, please correct me


Mark Abraham wrote:
> Sterling Paramore wrote:
>> My 2 cents:
>> I've never heard of this neutralizing plasma.
> It's a physical interpretation of what happens in the "trick" where the
> conditionally-convergent Ewald sum is partitioned into two functions
> that converge rapidly in either real or reciprocal space. See (among
> others) Deserno & Holm, J Chem Phys 109:7678. The four early PME papers
> I checked just now require neutrality for their derivations, but none
> state that neutrality is prerequisite for application of the methods.
>> However, if your system is charged and the Ewald sum does not
>> converge then you do not have well defined energy. Without a well
>> defined energy, you cannot have a well defined thermodynamic state or
>> phase space distribution function. Since the whole point of molecular
>> dynamics is to sample the distribution function, even if the dynamics
>> are "right," they are without meaning if the energy diverges.
> I disagree. If the energy as evaluated is not being used in determining
> the dynamics step - as is normal in MD where the integration of the
> forces is what happens - then the value might as well be zero. You are
> sampling the correct phase space through the forces being correct. The
> dynamics being "right" is normally all you need, although an accurate
> energy evaluation is nice as a check that things are going as planned.
> Obviously an MC simulation would be a different affair.
> You can take a single particle in a harmonic oscillator, give it a
> position and velocity and integrate the forces to watch the time
> evolution. You never need to compute the energy to generate the
> dynamics. The fact that the total energy is a simple function of the
> position and momentum is irrelevant until one comes to want to check
> that the integration is good enough.
> Certainly for many systems you won't want a highly charged state because
> it is unphysical.
> Does anyone know whether astrophysicists use the Ewald sum for their
> gravitational simulations - if every particle has positive mass than it
> is equivalent to an all-positively-charged electrostatic simulation?
> They certainly use multipole methods...
>>> Dear NAMD users,
>>> I have a general question on the charged system. Although this is not
>>> directly associated with the NAMD , I hope you will let me ask this.
>>> Some people claim that the Ewald sum is meaningful only for a neutral
>>> system. They say that in a case of a charged system, we should
>>> neutralize the system to avoid the divergence in the Ewald sum. And
>>> in order to neutralize the system, people use the "uniform background
>>> neutralizing plasma" method with Ewald sum or particle mesh Ewald
>>> (PME) for charged systems. But, when I look at the equation for the
>>> uniform neutralizing plasma, it is just a constant (I mean,
>>> independent of the positions of particles) added to the Ewald sum
>>> equation.
> Can you provide a reference for this please?
> In fact, since what we need in the simulation, is not the
>>> energy, but force, I don't think that the uniform neutralizing plasma
>>> DOES NOT affect the dynamics AT ALL. Consequently, unless we are
>>> interested in the properties associated with the energy of the
>>> system, I don't think we have to include the neutralizing plasma term
>>> in the Ewald sum. I mean that we don't have to neutralize the system
>>> if we are interested in properties such as the structure of the system.
>>> As a result, if there is something wrong with my argument, please
>>> correct me.
>>> Thanks a lot.
>>> -Hyon
> Mark

Hyonseok Hwang
Postdoctoral Fellow
Department of Chemistry
Northwestern University
2145 Sheridan Rd.
Evanston, IL 60208-3113 USA

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