Brownian dynamics simulations: Statistical error of correlation functions

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Abstract
Exact expressions for the statistical errors arising from the replacement of the ensemble average by a finite time average in diffusive Brownian dynamics simulations are derived for the displacement correlation function and the orientational correlation function. The results are illustrated by analyzing Brownian dynamics simulations of some oligomeric molecules. These include flexible and rigid dimers and models for the α helix. Flexibility is found to have a significant effect on rotational diffusion.