Dynamic Versions of Kinetic Monte Carlo

Lattice and Dynamic Versions of Kinetic Monte Carlo 

The KMC method requires that a certain set of reactions be specified. This set includes transformations from reagents to products that correspond to local minima on the PES. Therefore, in the general case, to construct the table of reactions in KMC method, one should determine local minima on the PES and then determine the rate constants of transitions between them. Since PES is modified after each reaction, the process of searching for local minima should be dynamically performed in the course of the KMC run. This implementation of the KMC method is called dynamic KMC, since the set of all possible reactions at a given time is determined dynamically during the run rather than specified before calculations. Therefore, to implement dynamic KMC, it is required to specify an energy functional for the calculation of PES, methods of searching for local minima, and methods for the calculation of rate constants for transitions between local minima. 

As in the MD method, PES for KMC can be derived from first-principles methods or using empirical energy functionals described above. However, the KMC method requires the accurate evaluation of the PES not only near the local minima, but also for transition regions between them. The corresponding empirical potentials are called reactive, since they can be used to calculate parameters of chemical reactions. The development of reactive potentials is quite a difficult problem, since chemical reactions usually include the breaking or formation of new bonds and a reconfiguration of the electronic structure. At present, a few types of reactive empirical potentials can semi-quantitatively reproduce the results of first-principles calculations these are EAM and MEAM potentials for metals and bond-order potentials (Tersoff and Brenner) for covalent semiconductors and organics. 

The search for local minima in the neighborhood of a given local minimum is usually performed by the excitation of the system from this state followed by the relaxation of the system. If the relaxation of the excited system results in a state different from the initial state (and explored earlier), then a new local minimum is found, otherwise the evolution of the excited system is continued. The ways of moving out of the initial state can be different in temperature accelerated dynamics (TAD) by Sorensen and Voter [78], MD is used at high temperatures in the activation-relaxation technique (ART) by Mousseau and Barkema [79] and the local activated Monte Carlo method (LAMC) [80], the system evolves along the direction opposite to the direction of the force in the long-scale kinetic Monte Carlo 

To estimate the activation energy (Efor the given reagents and products, one can use methods for searching of saddle points for given stationary points, such as the nudged elastic band method (NEB) [83], 

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Lattice and Dynamic Versions of Kinetic Monte Carlo. 485... 

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