On the Accuracy Of Some Common Molecular Dynamics Algorithms

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Abstract
Attention is drawn to the fact that some of the algorithms used in the simulation of molecular dynamics are less accurate than is commonly believed. In particular, we show that many of the "Verlet-equivalent" integration schemes are not equivalent to the Verlet algorithm, and consequently are not necessarily third order schemes which exhibit exact time-reversal symmetry. Of this class of algorithms, only Beeman's technique is found to generate the optimal positions and velocities for a third order technique. It is also pointed out that the method of constraints introduces errors of O(tau(3)) in to the calculated position, and hence limits the accuracy of simulations that employ this method to second order.