I made these plots a few years ago for a class on quantum chemical simulation at MIT; I still find them interesting to look at sometimes. These plots were produced from a molecular dynamics simulation with magnesium chloride in an explicit water solvent using various water models such as TIP3P/TIP4P and SPCFW.
You will notice that the quantities plotted below have wildly fluctuating raw data due to the small number of explicit solvent molecules present in the simulation. How is this useful? The point here is that the averages of these quantities stabilize and reach equilibrium by the end of the simulation. Molecular dynamics simulations frequently makes use of the
ergodic hypothesis in this way.
Each plot includes the raw data, a smoothed version of the raw data, and a cumulative average. For experimentalists, it is usually only the average at the end of simulation that is important as this is assumed to be the equilibrium value of the measured quantity.
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| Water density (no solute) over time in the SPCFW model. |
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| Water temperature (no solute) over time in the SPCFW model. |
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| Water temperature (no solute) over time in the SPCFW model. |
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| Radial probability distribution of water molecules around magnesium and chloride ions in solution. Note the secondary water shell of magnesium. |
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| Distance between magnesium ion and both accompanying chloride ions over time in solution. |
