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I have seen that depending on the simulation approach, different number of water molecules are employed for studying liquid water properties.

32 in early DFT calculations
The electronic structure of liquid water within density-functional theory The Journal of Chemical Physics 123, 014501 (2005); https://doi.org/10.1063/1.1940612

216 in early classical molecular dynamic simulations

Molecular Dynamics Study of Liquid Water The Journal of Chemical Physics 55, 3336 (1971); https://doi.org/10.1063/1.1676585

256 I'm not sure if this number of water molecules is just for computational reasons $2^8$= 256

So I'm wondering, What is the reasoning behind them?,

Edit: In other words, If I want to obtain the ambient density of the system and I don't know anything about it (number of molecules or the size of the simulation box, assuming cubic), what should I do?

As a starting point, the only thing I know is that the size of the simulation box should be chosen considering a number density that corresponds to the experimental density of the system.

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closed as unclear what you're asking by Mithoron, Jon Custer, M.A.R., Todd Minehardt, Nilay Ghosh Apr 13 '18 at 4:39

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ Different simulation methods require different amounts of computational horsepower. You simulate as many particles as you can afford to... $\endgroup$ – Jon Custer Apr 12 '18 at 19:58
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Generally speaking, you use as many molecules in a simulation as you possibly can. There are a couple of caveats. For instance, if you wish to do a simulation using an expensive method (relative to a classical potential) like DFT, you will need to use fewer molecules. This has the obvious drawback that when you use periodic boundary conditions, each molecule will interact with its own reflections much more than we would like (which is not at all). Nowadays, we can certainly do simulations with more than 32 water molecules using DFT.

Also, there is no reason to just keep using larger and larger numbers because it is known that interactions between molecules in the liquid die off reasonably quickly with distance, so at some point you stop gaining anything by adding more molecules. All of the long range effects can be handled by using periodic boundary conditions, which works very well if each molecule is far enough from its own image that a molecule does not have short-range interactions with itself.

Another consideration is that the number of molecules you use depends a lot on what property you are interested in studying. Conventional wisdom about the number of molecules needed is usually associated with the number of molecules that give converged average energies. If you are interested in something like diffusion coefficients, however, you may need quite a few more molecules before convergence is achieved. I have read that up to 512, or even 768, can be needed to get good diffusion coefficients around room temperature for water.

It is true that sometimes a specific number of molecules is chosen to match a specific density you want to do simulations at. This, however, isn't usually too big of a deal as you can always change your box size to match the density you are trying to achieve.

There is no physical reason that people choose powers of 2 for the number of molecules other than that computational scientists tend to use powers of 2. The number 216 is probably used because some seminal paper used this number and got good results, so people tend to just stick with the trend.

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