Metropolis Monte Carlo technique applications

The best-known physically robust method for calculating the conformational properties of polymer chains is Rory s rotational isomeric state (RIS) theory. RIS has been applied to many polymers over several decades. See Honeycutt [12] for a concise recent review. However, there are technical difficulties preventing the routine and easy application of RIS in a reliable manner to polymers with complex repeat unit structures, and especially to polymers containing rings along the chain backbone. As techniques for the atomistic simulation of polymers have evolved, the calculation of conformational properties by atomistic simulations has become an attractive and increasingly feasible alternative. The RIS Metropolis Monte Carlo method of Honeycutt [13] (see Bicerano et al [14,15] for some applications) enables the direct estimation of Coo, lp and Rg via atomistic simulations. It also calculates a value for [r ] indirectly, as a "derived" property, in terms of the properties which it estimates directly. These calculated values are useful as semi-quantitative predictors of the actual [rj] of a polymer, subject to the limitation that they only take the effects of intrinsic chain stiffness into account but neglect the possible (and often relatively secondary) effects of the polymer-solvent interactions. 

Results that have been obtained using conventional Monte Carlo techniques have played a central role in the very great advances made recently in the theory of fluids. Some of these results are discussed elsewhere in this volume. What seems astonishing from the methodological standpoint is that the application of the technique has changed scarcely at all since its original introduction to statistical mechanics by Metropolis et al This remark is meant partly as a tribute to the brilliance of that early work. 

Molecular dynamics (MD) methods are nearly as old as the Metropolis Monte Carlo method. The first applications of MD techniques for molecular simulation were made to simple fluids. Simulations for complex liquids such as water followed, and the first MD simulation of a biomacromolecule was performed over 10 years ago. Since then, the MD technique has been used extensively in the study of biomolecules, and the increased utility of this technique parallels closely the development of computer resources. 

Monte Carlo search methods are stochastic techniques based on the use of random numbers and probability statistics to sample conformational space. The name Monte Carlo was originally coined by Metropolis and Ulam [4] during the Manhattan Project of World War II because of the similarity of this simulation technique to games of chance. Today a variety of Monte Carlo (MC) simulation methods are routinely used in diverse fields such as atmospheric studies, nuclear physics, traffic flow, and, of course, biochemistry and biophysics. In this section we focus on the application of the Monte Carlo method for... 

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