Algorithm¶

KMCLib implements the VSSM or n-fold way algorithm [Ref.1] for performing lattice KMC simulations. The algorithm in its most simple form starts with an initial configuration on a lattice and a description of all possible elementary processes in the system with their corresponding reaction rates.

• The processes are matched with the local geometry at each lattice site and for each process the list of sites where it is available (i.e. where it is possible to perform the process) is stored.
• The total possible rate for each process is calculated and a process to perform is chosen with probability proportional to its relative total rate.
• A site to perform the chosen process at is selected at random from the list of sites where the chosen process is available.
• Time is propagated by drawing the length of the next time step randomly from an exponentially decreasing time distribution with the exponent given by the total possible rate in the system.

We have also made modifications to the algorithm to include the possibility to run simulations with custom rates that are calculated on-the-fly during the simulation. This important feature adds enormous flexibility compared to only using fixed rate processes.

The two different ways to determine the process rates (at simulation start-up or during the simulation) can easily be combined. Some of the processes can get their rates updated during the simulation while other rates are given from the start of the simulation. The rate update framework is very flexible and allows the user to define the desired behavior via Python code. It is e.g. possible to couple the update of the process rates to global or local geometrical parameters, such that a temperature or pressure gradient can affect the local rates of diffusion processes differently at different sites, or that the process rates are being modified at sites in the vicinity of certain atom types or geometrical features that may arise during the simulation.

The Usage examples demonstrate how to use the custom rate modifications, and the algorithm is described in full detail in [Ref.8] where we also show timings and scaling behavior of KMCLib. Remember that you can always look at the source code directly to investigate the implementation.