Phonon absorbing boundary conditions for molecular dynamics

With the goal of minimizing the domain size for molecular dynamics (MD) simulations, we develop a new class of absorbing boundary conditions (ABCs) that mimic the phonon absorption properties of an unbounded exterior. The proposed MD-ABCs are extensions of perfectly matched discrete layers (PMDLs), originally developed as an absorbing boundary condition for continuous wave propagation problems. Called MD-PMDL, this extension carefully targets the absorption of phonons, the high frequency waves, whose propagation properties are completely different from continuous waves. This paper presents the derivation of MD-PMDL for general lattice systems, followed by explicit application to one-dimensional and two-dimensional square lattice systems. The accuracy of MD-PMDL for phonon absorption is proven by analyzing reflection coefficients, and demonstrated through numerical experiments. Unlike existing MD-ABCs, MD-PMDL is local in both space and time and thus more efficient. Based on their favorable properties, it is concluded that MD-PMDL could provide a more effective alternative to existing MD-ABCs.