Preface

Kinetic Monte Carlo (kMC) simulations form still a quite new area of research. Figure 1 shows the number of publications (articles or reviews) with “kinetic Monte Carlo” in the title or abstract according to the abstract and citation database Scopus. There are two things to note. On the one hand it is not a very extensive area of research yet. A very diligent researcher can still keep track of all publications that appear. On the other hand, the number of publications is rapidly growing. Figure 1 shows that there were no publications before 1993 that used the term kMC. This does not mean that there have been no kMC simulations before that year. There have been some but the term was not used yet. In fact, there are still people, who do what we will call kMC simulations here, but who do not use the term. One mundane reason for that is probably that they use an algorithm that they regard as one of many possible algorithms for doing Monte Carlo (MC) simulations. Why give it a special name? Another reason may be historical. Instead of kMC, people have used and still use the term dynamic MC. This is a term introduced by D.T. Gillespie for his algorithms that use MC to solve macroscopic rate equations. These algorithms are often almost identical to the ones we will describe in Chap. 3, and it seems reasonable to use the same term even when the algorithms are used for different problems. There has been a tendency to be more strict in the terminology however. For example, the term Stochastic Simulation Algorithm is now often used when using MC for rate equations. There are even people that restrict the term kMC to one particular algorithm, the Variable Step Size Method in our terminology (see Sect. 3.2), even though all other algorithms in Chap. 3 give exactly the same results. But the term kMC has also been used for rate equations. So the situation concerning terminology is still fluent. So what do we mean when we use the term kMC? There are always two aspects to kMC as we will discuss it here. We will regard a system as a set of minima of a potential-energy surface (PES). The evolution of a system in real time will then be regarded as hops from one minimum to a neighboring one. These are the elementary events of kMC. The second aspect concerns the algorithms. The hops in kMC will be seen to be stochastic processes and the algorithms use random numbers to determine at which times the hops occur and to which neighboring minimum they go. This is