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I am trying to build a solid-liquid interface to be simulate using molecular dynamics. Since, I would be using ab initio molecular dynamics (cpmd or cp2k), I need the minimum cell dimensions. Please suggest some ways to fix the cell dimensions.

The issues that I am concerned about are given in for example in the science paper (http://science.sciencemag.org/content/303/5658/658.full). It is said that there should be a minimum size of the system (specially in the direction perpendicular to the slab) to attain trustworthy results. I am not able to find how and why? For example, if I take 3-10 layers of atoms for making the surface how to determine which one would yield the trustworthy results?

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First, when it comes to periodic boundary conditions, you should make sure that your system does not interact with itself through the boundaries. A way to check it is to see if the electron density is low in vacuum (in case your system has some void separating surfaces).

Energies should also be checked to be converged with respect to cutoff energies, $k$ point selection, etc.. This means that you have attained the "maximum performance" you could; e.g. a well-converged result means that improving parameters do not significantly changes results.

Furthermore, convergence with respect to slab thickness is also important: as you increase slab thickness, the properties of the inner layer should approach the properties of the bulk. How fast this happens depends on your system.

A good reference for all this is this one.

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