Ab Initio-Based Stochastic Simulations of Kinetic Processes on Surfaces

Introduction

Integrated computational simulations have been experiencing booming developments in the last decade. The concept is originated from the requirements of understanding innovative properties of materials with artificial structures and guiding synthesis of high-performance materials at nano-scale. Contemporary computational materials science demands detailed information of electronic structures with high accuracy and the ability to describe dynamical processes of phenomena covering large spatial and temporal scale, such as material fatigue, heterogeneous catalysis, and crystal growth, etc. Although traditional quantum physics/chemistry methods and phenomenological models have been developed very maturely at both ends of the concept of integrated computational simulations, it is only within the recent ten years that researchers start bridging them together and apply the integrated methods to materials engineering (Reuter2003, Rojal2007). In prevailing studies, stochastic methods (mainly Monte Carlo methods) are employed to mimic the complex nature of kinetics, i.e. multiple evolution options from the current state. Key dynamical parameters are then determined by atomistic simulations, e.g., density functional theory (DFT) or molecular dynamics. Piana et al. employed molecular dynamics to obtain 40 key kinetic parameters and performed simulations on urea crystal growth in two different solutes. (Piana2005). Honkala et al. used ab initio calculations to determine reliable parameters even including local chemical environments to calculate the productivity of ammonia synthesis catalyzed by nanoparticle of Ru (Honkala2005). Their calculated turn over frequencies are in good agreement with measured ones. Ab initio-based stochastic simulations also have been applied to study mechanical failure of materials (Fu2004), self organization (Mo2005, Negulyaev2008, Ziegler2008), thin film deposition (Huang1998), and electrochemical processes in solid oxide fuel cells (Pornprasertsuk2007, Wang2010), etc. Computational simulations are able to present detailed insight of phenomena or study effects of various factors which are very difficult or even impossible to be obtained by experiments. For example, Zhu et al. performed systematic kinetic Monte Carlo simulations to study effects of external stress on the growth of quantum dots on substrates (Zhu2007).

However, due to the diversity of the properties of materials, processes, and purposes of simulations, corresponding models are very different from one to another. General requirements of models are: (1) the model should be able to describe critical steps of kinetics, i.e., the rate determining steps of chemical reactions or atomic piling ups during quantum dot growths, etc., and (2) the model should contain reasonable number of parameters which can be handled by ab initio calculations. Different models and/or algorithms have been developed to meet different simulation goals and interested systems. For instance, Voter developed “hyperdynamics” to expedite the system evolution (Voter1997). Henkelman and Jónsson developed on-the-fly dynamical simulation method so that the simulator is able to automatically determine and update the migration list during simulations (Henkelman2001). Parallel algorithms of kinetic Monte Carlo methods have also been developed by several groups (Shim2005, Martínez2011). These developments essentially strengthen the powers of this hierarchical multi-scale approach. In this chapter, we introduce basic theory and several key algorithms of ab initio-based stochastic methods. Two examples are presented in order to illustrate the general processes of these stochastic methods, including generating models, incorporating ab initio data into models, analyzing outputs, etc. Both examples describe the morphological evolution and chemical/physical kinetic processes on surfaces since surface has become a very important medium in modern science and technology.