While carrying out constant volume simulations, I've observed that sometimes when the gaseous molecules come closer from their initial spacing, an empty space is created in the box. As I should imagine the system in PBC:

  • does that mean that there are pockets of material and gaps of vacuum throughout my system in a zoomed out bigger picture?
  • How does this affect the calculation of results on averaging for a continuous system?
  • Should anything be done to prevent such occurrences?
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    $\begingroup$ Are you simulating a system that is at least partly a gas? $\endgroup$
    – wzkchem5
    Jul 16, 2021 at 21:13
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    $\begingroup$ Yes. For example, if I freeze the positions of a nucleus kind of ice in one part of the box and leave gaseous molecules around it, the gas eventually builds around the nucleus and leaves the extra space as a large vacuum in the box. $\endgroup$ Jul 17, 2021 at 13:13
  • 2
    $\begingroup$ This is completely natural, as long as the gas condensed to a density that is consistent with a liquid or a solid. As your simulation is constant volume, the extra space won't collapse. $\endgroup$
    – wzkchem5
    Jul 17, 2021 at 13:21
  • $\begingroup$ @wzkchem5 are you able to turn that into an answer? Our unanswered queue got a bit big lately and I'm trying to trim it down a bit! $\endgroup$ Jul 31, 2021 at 0:33
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    $\begingroup$ @wzkchem5 I agree that your comment can probably be extended to an answer. $\endgroup$
    – Tyberius
    Aug 24, 2021 at 15:46

1 Answer 1


Following Nike and Tyberius's suggestions, I rewrite my comment into an answer.

Firstly, it is obvious that when the volume of the simulation box is sufficiently large, then a significant fraction of the box must be gaseous. Secondly, note that the simulation box has a finite size, so that when the equilibrium pressure of the gas is sufficiently low, it may well be that there is not even a single gaseous molecule during the whole simulation, and all molecules cluster together as a solid, a liquid, or a mixture of solid and liquid.

But even if this happens, it does not mean that the real material is a very porous, uniform mixture of small particles/droplets and vacuum. The reason why in your simulation the material behaves as such, is that you have employed the PBC. When the PBC is active, any particle that is much smaller than the size of the box cannot meet and merge with its periodic image (otherwise the PBC is violated), so that once all molecules in a box forms a single cluster, the condensing process stops there. While in reality, there is no such thing as the PBC, and the particles/droplets are free to find each other and merge, until you end up with macroscopic rain drops or snowflakes. Unfortunately, in calculations you must either only consider a microscopic number of molecules, or use the PBC, due to computational cost considerations, which means that you have to live with such artifacts of the simulation.


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