Dynamically spanning the length scales from the quantum to the continuum

A challenging paradigm in computational sciences is the coupling of the continuum, the atomistic, and the quantum descriptions of matter for a unified dynamic treatment of a single physical problem. We described the recent achievement of such a goal. We have spanned the length scales in a concerted simulation comprising the finite-element method, classical molecular dynamics, quantum tight-binding dynamics and seamless bridges between these different physical descriptions. We illustrate and validate the methodology for rapid crack propagation in silicon.