# Re: question on the charged system

From: Mark Abraham (Mark.Abraham_at_anu.edu.au)
Date: Wed May 17 2006 - 19:57:08 CDT

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.

> 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

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