The term "kinetic Monte Carlo" (KMC) refers to a general class of simulation methods that use random numbers to model transient processes or phenomena (i.e. those with time-varying features). When based on the foundation of first-principles laws and statistical mechanics, these methods become powerful tools able to deliver deep understanding and predictive capability. This tutorial consists of a series of video lectures discussing the fundamental concepts of statistical mechanics underpinning KMC, as well as some algorithmic aspects pertaining to the graph-theoretical KMC and Zacros.
While setting up a simulation in Zacros is not difficult, it is important to have an understanding of the theory underpinning statistical mechanics and kinetic Monte Carlo (KMC). This series of lectures, which were first developed for the Thomas Young Centre Materials Modelling Course, provide an introduction to the relevant concepts.
Part 1 - Overview of Fundamental Principles in Statistical Mechanics
This lecture starts with a reminder of basic concepts and key equations of classical thermodynamics, and subsequently introduces the general and powerful framework of statistical mechanics. We discuss the concepts of microstates, Hamiltonian, as well as averaging towards macroscopically observable quantities. We finally explain what ensembles are, and introduce three commonly used ones: the microcanonical, the canonical and the grand-canonical ensembles.
Lecture slides in pdf format (opens in a new window).
Part 2 - From Partition Functions to Thermodynamic Observables
In this lecture, we apply the statistical-mechanical framework to obtain thermodynamic expressions for observables of systems such as monoatomic and diatomic ideal gases, as well as adsorbates on the edge of a catalytic nanoparticle in the absence versus in the presence of lateral interactions. We discuss in detail the mathematical techniques used in these investigations and the physical meaning of the results obtained.
Lecture slides in pdf format (opens in a new window).
Part 3 - Kinetic Monte Carlo Simulations of Surface Reactions
The last lecture of this series concerns the simulation of surface reactions with on-lattice kinetic Monte Carlo. After a brief motivation, we discuss the fundamendals of transition state theory for the estimation of kinetic constants of elementary reaction events. We then discuss the KMC method for simulating entire reaction pathways on catalytic surfaces, and move on to more advanced topics specific to the graph-theoretical KMC implementation, which Zacros incoroporates.
Lecture slides in pdf format (opens in a new window).