Electroneutrality in molecular dynamics simulation

You can find a recent, straightforward introduction to proper treatment of periodic charged systems in Ballenegger, Cerda and Arnold’s 2009 paper on charged slabs (Simulations of non-neutral slab systems with long-range electrostatic interactions in two-dimensional periodic boundary conditions | The Journal of Chemical Physics | AIP Publishing ; this paper is cited in the LAMMPS kspace modify documentation). Depending on your level of analysis, the results of such simulations are either mostly right, mostly wrong, or mostly useless.

Charged periodic simulations can be mostly right because you can simply imagine smearing a counter charge density uniformly throughout space. You don’t even need extra calculations because such a space charge exerts no forces. (As renowned physicist Syndrome might say, “when all space is charged … no space is charged.”) It simply amounts to a static added self-energy term for the counter-charge.

But such simulations can be mostly wrong if there is a real counter charge with physically significant behaviour. A simple, intuitive example is lipid bilayer membrane simulations. Suppose you simulate a lipid bilayer with explicit water and ions, but the ions have a net charge. The uniform counter-charge described earlier exists even within the lipid tail volume. This is non-physical – the dielectric constant is much lower in the lipid tail volume, and in a real system all charged and polar molecules will rarely enter that space. So, relative to a realistic simulation, in a charged simulation water molecules and ions will penetrate far too often into the membrane space.

Which is why charged simulations are often useless – if your system volume is so small (relative to the macroscopic system of interest) that you cannot afford to put in the counter-charge, it is almost certainly so small that you will have other significant finite size effects that destroy any realism in the simulation results. My default judgement would be to doubt such a simulation until proven otherwise.

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