Interdisciplinary Applied Mathematics

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2. Errors in Fluctuations: Errors in the estimate of fluctuation averages of the type (SA?) may be estimated simply on the assumption that the process A(t) obeys Gaussian statistics. The resulting formula is (Allen and Tildesley, 1994)


a20((SA20)run) = 2t’A(SA20 )20/tmn, where a slightly different correlation time appears:


t’a = 2 J dt(SA(t)SA)20/(SA20f.


0


For an exponentially decaying correlation function, t’a = tA is the usual correlation time.

16.1.5 Practical Guidelines


In this section we outline some of the issues that are faced in setting up and running an MD simulation. If one is using an MD package or an in-house program, it is necessary to choose the various parameters properly. This section discusses how to make a prudent choice of the important parameters and how various choices affect the accuracy and the speed of the simulation.


1.    Size    of the    Time Step.    We would    like to    use    as large a time    step    as


possible so that we can explore more of the phase space of the system. However, since we truncate the Taylor’s series expansions, the time step needs to be small enough so that the expansions can provide a reliable estimate of the atomic positions and velocities at the end of the time step. For typical time-marching algorithms with a time accuracy of order three, one uses a time step that is a fraction of the period of the highest-frequency motion in the system. A good way of checking whether the time step is small enough is to run an equilibrium simulation without temperature coupling. If the fluctuation in the total energy is less than 0.5% of the total energy of the system, the time step is typically acceptable. For a typical simulation of water transport, where the O—H bond length is fixed, a time step size of 1.0 to 2.0 fs is commonly used.

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