A computational framework for modeling and simulating vibrational mode dynamics

Atomic vibrations influence a variety of phenomena in solids and molecules, ranging from thermal transport to chemical reactions. These vibrations can be decomposed into normal modes, often known as phonons, which are collective motions of atoms vibrating at certain frequencies; this provides a rigorous basis for understanding atomic motion and its effects on material phenomena, since phonons can be detected and excited experimentally. Unfortunately, traditional theories such as the phonon gas model do not allow for the general study of vibrational modes since they only apply to ideal crystals where modes have a wave-like characteristic. Traditional computational methods based on molecular dynamics (MD) simulations allow for the study of phonons in more general systems with disorder, where the modes are less wave-like, but traditional methods do not simulate mode interactions and energy transfer between modes. Here we present, for the first time, a theory and massively parallel open-source software for modeling vibrational modes and simulating their interactions, or energy transfers, in large systems (>10 3 atoms) using MD. This is achieved by rewriting the atomic equations of motion in mode coordinates, from which analytical expressions for anharmonic mode coupling constants arise. Hamiltonian mechanics then provides a simple expression for calculating power transfer between modes. As a simple application of this theory, we perform MD simulations of phonon-interface scattering in a silicon–germanium superlattice and show the various pathways of energy transfer that occur. We also highlight that while many interaction pathways exist, only a tiny fraction of these pathways transfer significant amounts of energy, which is surprising. The approach allows for the prediction and simulation of mode/phonon interactions, thus unveiling the real-time dynamics of phonon behavior and energy transport.