Atomistic Simulation Methods

Abstract

From the time they were pioneered several decades ago, atomistic computer simulation methods such as molecular dynamics (MD) and Monte Carlo (MC) have led to great strides in the description of materials. The limitation of atomistic methods to simulating systems containing a small number of particles is a pathological problem in spite of continuous progress in pushing the limit toward systems of ever increasing sizes. System size is an especially critical issue when one desires a high degree of accuracy in modeling the interatomic forces between the atoms constituting the system with first-principle atomistic simulation approaches. While small system size is an issue for atomistic simulations of bulk materials, the possibility of simulating small systems provides fresh opportunities for scientific advances in the field of nanomaterials. In contrast to modeling bulk materials, atomistic computer simulations could greatly speed up the development of materials at the nanoscale. Nanomaterials exhibit sizes intermediate between those of isolated atoms, molecules, and bulk materials with dimensions scaling from several to hundreds of nanometers. Such systems are ideal for computational studies using MD or MC methods, because these simulations can be done at the realistic size limit, imparting them with predictive capabilities. Therefore, nanomaterials offer a fertile ground for contributions from atomistic computer simulations. There is already extensive literature on atomistic computer simulations of nanoscale systems; it is not our intention to present an exhaustive review of such studies. A few illustrative examples include: MD simulations of carbon nanotubes, fullerenes, nanoclusters of polymers, and a plethora of nanostructures: nanorod, nanoindentation, nanomesa, and nanowire. Self-assembly is regarded as an extremely powerful approach in the construction of nanoscale structures. Reviews on MC simulation studies of self-assembling processes in aqueous media have appeared in the literature recently. MD and MC have also been extensively employed to simulate the formation of self-assembled monolayers on solid substrates. MD and MC methods find their origin in classical statistical mechanics. Provided a model for the interactions between the atomic constituents of some system (for instance, in the form of interatomic or intermolecular potentials that describe the energy of the system as a function of its microscopic degrees of freedom) exists, one can sample deterministically (MD) or stochastically (MC) the microscopic states of the system. The microscopic degrees of freedom usually consist of the set of positions and momenta of the particles. The original intent of MD and MC is, once equilibrium is achieved, to use the concepts of temporal averaging (MD) or statistical averaging (MC) over the sampled microscopic states to calculate the properties of a macroscopic system. This calculation necessitates that the system studied satisfies two hypotheses; namely, the long-time limit and the thermodynamic limit.