Concurrent Coupling of Length Scales in Solid State Systems

A strategic objective of computational materials physics is the accurate description of specific materials on length scales spanning the electronic to the macroscopic. We describe progress towards this goal by reviewing a seamless coupling of quantum to statistical to continuum mechanics, involving two models, implemented via parallel algorithms on supercomputers, for unifying finite elements (FE), molecular dynamics (MD) and semi-empirical tight-binding (TB). The first approach, FE/MD/TB Coupling of Length Scales (FE/MD/TB CLS), consists of a hybrid model in which simulations of the three scales are run concurrently with the minimal coupling that guarantees physical consistency. The second approach, Coarse-Grained Molecular Dynamics (CGMD), introduces an effective model, a scale-dependent generalization of finite elements which passes smoothly into molecular dynamics as the mesh is reduced to atomic spacing. These methodologies are illustrated and validated using the examples of crack propagation in silicon and the dynamics of micro-resonators. We also briefly review a number of other approaches to multiscale modeling.