Kinetic Monte Carlo

The kinetic Monte Carlo (KMC) method is a Monte Carlo method computer simulation intended to simulate the time evolution of some processes occurring in nature. Typically these are processes that occur with known transition rates among states. It is important to understand that these rates are inputs to the KMC algorithm, the method itself cannot predict them.

The KMC method is essentially the same as the dynamic Monte Carlo method and the Gillespie algorithm.

One possible classification of KMC algorithms is as rejection-KMC (rKMC) and rejection-free-KMC (rfKMC).

A rfKMC algorithm for simulating the time evolution of a system, where some processes can occur with known rates r, can be written for instance as follows:

(Note: because the average value of $\ln(1/u^{\prime })$ $\ln(1/u^{\prime })$ is equal to unity, the same average time scale can be obtained by instead using $\Delta t=Q_{k}^{-1}$ $\Delta t=Q_{k}^{-1}$ in step 9. In this case, however, the delay associated with transition i will not be drawn from the Poisson distribution described by the rate $Q_{k}$ $Q_{k}$ , but will instead be the mean of that distribution.)

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