The threshold algorithm does not involve local optimization of structures in principle. However, we require a method to identify whether a perturbation has led to a new energy basin. For this, perturbed structures are locally energy minimized if the perturbation is accepted (ie. the unminimized energy was under the current lid energy). The minimized structures are compared to each other to identify where trajectories meet. Energy minimization is performed for every accepted perturbed structure because lattice energy landscapes are known to often contain many local minima around observed structures, so every perturbation was assumed to potentially lead to a new local energy basin. Two minima are considered to be connected at a given lid energy if the trajectories that start at or visit these minima are found to sample a common local minimum. Thus, the identification of identical structures (corresponding to the same local minimum) is an essential process to obtain the disconnectivity graph. We use a two-step strategy: 1) a fast initial screen for duplicates is performed by comparison of simulated X-ray diffraction patterns, followed by 2) checking of duplicates using the COMPACK algorithm, which compares interatomic distances and angles within a cluster of 30 molecules taken from the compared crystal structures (see full details in the ESI).