Monte Carlo methodologies for enhanced configurational sampling of dense systems: motion of a spherical solute in a polymer melt as a model problem

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Abstract
A number of traditional and novel Monte Carlo (MC) methodologies for configurational sampling in condensed phases are studied. The stochastic motion of a spherical solute molecule in a melt of short polyethylene chains is used as a model problem to assess the efficiency of the MC algorithms. Traditional MC methods, such as Metropolis MC and force-bias MC with or without preferential sampling, are inefficient in imparting significant mobility to the guest in the dense many-chain system. Two novel MC algorithms, based on local-Hessian information, are introduced here for the first time. Multidimensional force- or anti-force-bias along local eigenvector directions, and Metropolis MC with eigenvalue-scaling are found surprisingly inefficient for the problem at hand. Significant mobilities are achieved only with a new energy-biased MC method, which ignores the existing barriers and performs a coarse-grained random walk over local energy minima. As well as evaluating the various MC algorithms, this work also addresses questions pertinent to the model problem examined here, namely (i) if polymer segment mobility is necessary to obtain significant MC mobility of the solute, and (ii) what is the onset of solute stochastic diffusion in these systems.