Diffusion Monte Carlo extended systems

Investigation of the motion of adsorbed molecules, which give mechanisms and rates of re-orientation and diffusion, require alternative approaches. For systems that contain highly mobile species. Molecular Dynamics (MD) techniques are widely used. However, for many adsorbates the timescales of motion are much longer than can feasibly be simulated, so that MD is only relevant either for small molecules or at high temperatures. In order to simulate slower diffusion, the process must be considered in terms of rare events with significant activations. The activated processes are then usefully treated by transition state theory, and the associated processes treated over extended timescales and volumes by, for example, Kinetic Monte Carlo (KMQ techniques. 

Finally, an entirely different approach to simulating gelation is the Dynamic Monte Carlo (DMC) method, in which chemical reactions are modeled by stochastic integration of phenomenological kinetic rate laws [23]. This has been used successfully to understand the onset of gel formation, first-shell substitution effects, and the influence of cyclization in silicon alkoxide systems [24—26]. However, this approach has not so far been extended to include the instantaneous positions and diffusion of each oUgomer, which would be necessary in order for the calculation to generate an actual model of an aerogel that could be used in subsequent simulations. 

In contrast to Monte Carlo simulations, the molecular dynamics method simulates the motions of molecules however, this can only be extended up to very short time-scales because the time step per cycle is so small. Thus, the method cannot be used to model collective motions, which are important in diffusion and hydrodynamic flows, for example. For this it is necessary to turn to more coarse-grained models, where molecular details are ignored. Here the properties of collections of molecules are simulated, or the fluid structure is simulated at an even larger length-scale where the system behaves as a continuum. Some of these methods are now discussed. 

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