Extracting Information from Simulations

A necessary (but not sufficient) requirement for producing a representative sampling is that the system is in equilibrium. The starting configuration may be generated by completely random positions (and velocities for MD), but is more often taken either from a previous simulation or by placing the particles at or near the lattice points of a suitable crystal. The system is then equilibrated by running perhaps 104-105 MC or MD steps, followed by perhaps 105-107 production steps.Various quantities, such as the average potential energy or correlation functions, can be monitored to validate whether equilibrium has been achieved.

The averaging in eq. (14.1) should be over configurations that are uncorrelated, and this is not the case for nearby points in an MD trajectory or sequence of MC steps. The whole set of points should therefore be divided into blocks with a length that is sufficiently long to make equivalent points in two neighbouring blocks uncorrelated, but preferably also with a length that is sufficiently short so that no information is lost. Flyvbjerg and Pedersen have shown how to determine the optimum block length by a sequence of statistical analyses.47 For the original data set the mean and variance are calculated according to eq. (14.32).

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