Characterising and Controlling Rare Event Dynamics

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Theory and simulation are cornerstones of molecular science, guiding, informing, and interpreting experiments. Some simulations are performed to test the practicality of costly laboratory work, while other calculations may provide information that is not accessible experimentally. Applications cover a diverse range of activities, from drug design in the pharmaceutical industry, through surface catalysis, to predicting the behaviour of soft matter in materials such as liquid crystals, which are used in display technology.For computer simulations to be useful we must achieve some level of confidence in the predictions that are made. Achieving useful accuracy depends on both a sufficiently faithful representation of the interatomic or intermolecular interactions, and on whether the calculated quantities reflect the conditions of the experiment in a statistically meaningful way. Our proposal addresses the latter issue, namely how to sample events of interest that rarely occur on the accessible time scale of simulations. Calculating a meaningful average for some property of interest is impossible for many problems of great contemporary importance using conventional methods. Examples include chemical reactions and changes of structure or phase that correspond to a large barrier on the potential or free energy surface. Conventional simulations of such systems will spend all or most of the available computer time waiting for the barrier to be crossed, and may miss the key transition entirely. More sophisticated simulation techniques are therefore needed, which sample the events of interest directly.Various complementary approaches have been suggested to address this rare events problem and extend computer simulations to larger systems and longer time scales. We propose to combine two of the most successful methods, one that is based on geometry optimisation, and the other on explicit dynamics, to produce a hybrid methodology that is efficient enough to treat mesoscopic problems. The geometry optimisation approach can treat events that are arbitrarily slow, because the barriers in question are calculated directly. Rate constants can then be evaluated using well known tools from unimolecular rate theory, which involves a series of approximations. By combining the pathways determined by geometry optimisation with explicit dynamics we aim to produce much more accurate rate constants and extend the domain accessible to simulation to treat far more complex systems.Two important applications will be considered. First we will analyse the pathways for nucleation in a wide variety of bulk systems, including models that form glasses, liquid crystals, and granular material. Our most ambitious objective is to use this knowledge to gain kinetic control of nucleation. The ability to predict the outcome of nucleation, and change conditions accordingly, would be immediately useful to pharmaceutical companies and to the manufacture of materials based upon glasses or liquid crystals. The ability to describe and predict the ageing properties of glassy materials will immediately find a number of important applications.The second application we would consider involves the design of a molecular motor from mesoscopic building blocks. Here we would seek to determine general design principles that govern the efficiency of converting chemical energy into available work. Hence we would guide experiments in the choice of molecular components to produce an efficient motor, including characteristics of the intermolecular interaction governed by shape, charge, etc.