Predicting Supramolecular Structure from the Statistics of Individual Molecular Events

Abstract

As manipulating the self-assembly of supramolecular and nanoscaleconstructs at the single-molecule level increasingly becomes the norm, new theo-retical scaffolds must be erected to replace the thermodynamic and kinetics basedmodels used to describe traditional bulk phase active syntheses. Like the statisticalmechanics underpinning these latter theories, the framework we propose uses stateprobabilities as its fundamental objects; but, contrary to the Gibbsian paradigm,our theory directly models the transition probabilities between the initial and finalstates of a trajectory, foregoing the need to assume ergodicity. We leverage theseprobabilities in the context of molecular self-assembly to compute the overall likeli-hood that a specified experimental condition leads to a desired structural outcome.We demonstrate the application of this framework to a simple toy model in whichNidentical molecules can assemble into oligomers of different lengths and con-clude with a discussion of how the high computational cost of such a fine-grainedmodel can be overcome through approximation when extending it to larger, morecomplex systems

Publication
MONET

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