Folding temperature, potential energy surfaces

The extension of Gillespie s algorithm to spatially distributed systems is straightforward. A lattice is used to represent binding sites of adsorbates, which correspond to local minima of the potential energy surface. The discrete nature of KMC coupled with possible separation of time scales of various processes could render KMC inefficient. The work of Bortz et al. on the n-fold or continuous time MC CTMC) method can lead to computational speedup of the KMC method, which, however, has been underutilized most probably because of its difficult implementation. This method classifies all atoms in a finite number of classes according to their transition probability. Probabilities are computed a priori and each event is successful, in contrast to the Metropolis method (and other null event algorithms) whose fraction of unsuccessful (null) events increases drastically at low temperatures and for stiff problems. In conjunction with efficient search within a class and dynamic variation of atom coordi-nates, " the CPU time can be practically independent of lattice size. After each event, the time is incremented by a continuous amount. 

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