A computational framework for studying normal mode dynamics

In solids and molecules, atoms vibrate about their respective equilibrium positions, and this thermal motion can be understood as a superposition of the structure’s normal modes, which are collective movements of atoms vibrating at certain frequencies. These vibrational modes play important roles in a variety of material properties and physical phenomena such as chemical reactions, mass/ion diffusivity, phase transitions, thermal conductivity, electrical conductivity, and any property which is affected by atomic motion. It is therefore important to study the dynamics and energy transfer processes of normal modes in a variety of systems, so that we may better understand or engineer a wide variety of phenomena.

Here I introduce a computational framework for studying vibrational modes in any general system by calculating various mode properties such as anharmonic coupling constants. With this information, we may simulate time-dependent energy transfer processes among vibrational modes, and study their heat transfer in any general system of atoms. I show example calculations and simulations to elucidate the physical mechanisms of heat transfer in crystalline, amorphous, and alloy materials, along with mechanisms of interfacial heat transfer. This framework is packaged into an open-source program called ModeCode which uses the LAMMPS C++ library to generally calculate vibrational modes in any system modeled by any potential in LAMMPS. ModeCode is massively parallel to support the scalable calculation of vibrational modes in systems with ~100,000+ atoms, allowing us to computationally study vibrational modes in realistic systems of interest.