where N q is the number of points used to sample the Brillouin zone (i.e. 1000 for all systems considered here). Due to numerical issues, a small number of modes for some materials exhibited unphysical imaginary frequencies. These frequencies were set to 0 in all subsequent analyses to reflect the flatness of the potential energy surface along their respective eigenvectors. The displacement of an atom κ in Cartesian direction α ∈ {x, y, z} at lattice position l associated with excitation of mode ν at point q is 70