those of the flexibility model, we define a dimensionless ‘match’ coefficient, $m_{\mathbf{k},i}$, as $$\label{mequation}
m_{\mathbf{k},i} = \Omega^2 \sum_j\frac{\mathbf{e}_{\mathbf{k},i}^\mathrm{phonon}\cdot\mathbf{e}_{\mathbf{k},j}^\mathrm{model}}{\Omega^2+\tilde{\omega}^2_{\mathbf{k},j}} \label{eq:m}$$ where $\mathbf{e}_{\mathbf{k},i}^\mathrm{phonon}$ is the eigenvector of the *ab initio* phonon mode $i$ at wave vector $\mathbf{k}$, $\mathbf{e}_{\mathbf{k},j}^\mathrm{model}$ is the eigenvector of a mode $j$ in the flexibility model calculated at the same wave vector $\mathbf{k}$, and $\tilde{\omega}_{\mathbf{k},j}$ is the corresponding angular frequency in the flexibility model. $\Omega$ is a scale factor that avoids division-by-zero errors when $\tilde{\omega}_{\mathbf{k},j}=0$, giving instead a value of $m_{\mathbf{k},i}  = \Omega^2/(\Omega^2+\tilde{\omega}^2_{\mathbf{k},j})=1$ when $\tilde{\omega}^2_{\mathbf{k},j}=0$ (we used a value $\Omega = 1$ THz). This sets the range of $m_{\mathbf{k},i}$ values from 0 to 1. A value of $m_{\mathbf{k},i}$ close to 1 occurs when the *ab initio* phonon $i$ is a close match to a flexibility model mode that leaves the defined ‘rigid’ units undistorted. A value of $m_{\mathbf{k},i}$ close to 0 arises when the *ab initio* phonon $i$ involves significant distortions of the rigid units described in the flexibility model. Therefore $m_{\mathbf{k},i}$ is a measure of the extent to which mode $i$ of wave vector $\mathbf{k}$ in the *ab initio* model matches any modes given in the flexibility model at the same wave vector. Our practical implementation of this 