Kinetic Monte Carlo simulation trajectories

What we gained compared to standard MD simulations, is that the extremely long trajectories required until the system hops to a different basin, have been replaced by a transition described by TST and kinetic Monte Carlo. In this way, one is able to sample many more conformations than with an ordinary MD simulation. 

Gillespie s algorithm numerically reproduces the solution of the chemical master equation, simulating the individual occurrences of reactions. This type of description is called a jump Markov process, a type of stochastic process. A jump Markov process describes a system that has a probability of discontinuously transitioning from one state to another. This type of algorithm is also known as kinetic Monte Carlo. An ensemble of simulation trajectories in state space is required to accurately capture the probabilistic nature of the transient behavior of the system. 

Recent advances have resulted from the development of more powerful experimental methods and because the classical collision dynamics can now be calculated fully using high-speed computers. By applying Monte Carlo techniques to the selection of starting conditions for trajectory calculations, a reaction can be simulated with a sample very much smaller than the number of reactive encounters that must necessarily occur in any kinetic experiment, and models for reaction can therefore be tested. The remainder of this introduction is devoted to a simple explanation of the classical dynamics of collisions, a description of the parameters needed to define them, and the relationship between these and the rate coefficient for a reaction [9]. 

These experiments are important because they are performed on a reaction for which a priori calculations of V(rAB, rBC, rCA) are likely to have their best chance of success as only three electrons are involved. Even here the accurate computation of V, frequently termed the potential-energy hypersurface, is extremely difficult. Porter and Karplus [19] have determined a semiempirical hypersurface, and Karplus, Porter, and Sharma [20] have calculated classical trajectories across it. This type of computer experiment has been mentioned before and will be described in greater detail later. The objective of Karplus et al. was to calculate aR(E) and E0. Collisions were therefore simulated at selected values of E, with other collision parameters selected by Monte Carlo procedures, and the subsequent trajectories were calculated using the classical equations of motion. Above E0, oR was found to rise to a maximum value, of the same order of magnitude as the gas-kinetic cross section, and then gradually to decrease to greater energies. 

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