Improving the Efficiency of Configurational-Bias Monte Carlo: Extension of the Jacobian-Gaussian Scheme to Interior Sections of Cyclic and Polymeric Molecules

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The Jacobian-Gaussian method, which has recently been developed for generating bending angle trials, is extended to the conformational sampling of inner segments of a long chain or cyclic molecule where regular configurational-bias Monte Carlo was found to be very inefficient or simply incapable (i.e., for the cyclic case). For these molecules, a new conformational move would be required where one interior section is relocated while the rest of the molecule, before and after this section, is fixed. Techniques have been developed to extend the regular configurational-bias Monte Carlo to such a fixed-end points case by introducing a biasing probability function. Each trial is weighted by this function to ensure the closure of the molecule by selecting appropriate growth direction. However, the acceptance rate might be reduced significantly due to the incongruity of this weight and the energy weight. In addition, the last steps of closing the molecule include several bending and torsional energies that are coupled to each other. Thus, generating a trial that is acceptable for all energetic terms becomes a difficult problem. The Jacobian-Gaussian method can overcome these two problems with the following two principles: First, basic geometrical constraints must be fulfilled to guarantee molecular closure, which avoids the need of the biasing probability function. Second, the growth variables are transformed into those used explicitly in expressing the various intramolecular energies between fixed points to allow for the trials to be generated directly according to the Boltzmann distributions of these energetic terms, which improves the acceptance rates dramatically. This method has been examined on the growth of inner segments of linear and cyclic alkanes, which proves its higher efficiency over that of traditional methods.

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Journal of chemical theory and computation

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