Uncertainty quantification of Kinetic Monte Carlo models constructed on-the-fly using molecular dynamics
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Research Letter
Uncertainty quantification of Kinetic Monte Carlo models constructed on-the-fly using molecular dynamics Abhijit Chatterjee, Department of Chemical Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India Address all correspondence to Abhijit Chatterjee at [email protected] (Received 23 January 2018; accepted 30 April 2018)
Abstract Kinetic Monte Carlo (KMC) models of complex materials and biomolecules are increasingly being constructed using molecular dynamics (MD). A KMC model contains a catalog of states and kinetic pathways, which enables study of the dynamics. The completeness of the catalog is crucial to the model accuracy and is linked to the quality of the MD data used for model construction. Therefore, quantifying the uncertainty due to missing states and pathways is important. A review on computational procedures available for on-the-fly KMC model construction using MD, uncertainty measurement, and algorithms for guiding further MD sampling in an accelerated manner is presented.
Introduction Kinetic Monte Carlo (KMC) is often the method of choice while studying the long-time dynamical evolution of molecular- and meso-scale materials and biomolecular systems.[1–5] To generate dynamical trajectories of the system, a KMC model requires a catalog of metastable states, i.e., longlived configurations of the system, and the kinetic pathways that specify how fast the system can interconvert between the states. In KMC, pathways are defined in terms of the starting and end states and their associated rate constants. The continuous time trajectories generated using a KMC model are available as “discrete” state-to-state transitions. Achieving dimensionality reduction from the large number of atomic degrees of freedom to a significantly smaller “network” of states constitutes a major advantage of the KMC method. However, the same property also introduces a challenge since the catalog of states and pathways is generally not known at the outset for most complex materials and biomolecules.[6] For instance, configurations visited during the unfolding of a protein from its folded state might be unknown but these states are required as an input in the KMC model to accurately describe the dynamical unfolding process.[7,8] To address this issue, KMC models can be constructed using molecular dynamics (MD).[2,5,9] In MD, one solves the Newton’s equations of motion to generate dynamical trajectories.[10] The input provided to an MD calculation includes the initial atomic positions and velocities, the MD time-step (typically in femtoseconds) and an interatomic potential or a force field for the system. MD is computationally more expensive than KMC. One can have best of both worlds by learning about the discrete states and kinetic pathways of the system by postprocessing several independent MD trajectories to generate a
concise KMC model.[11,12] States and pathways sampled in the MD trajectory are incorporated into the KMC model. Alternatively, we can direct our efforts toward parts of the configurat
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