Einstein crystal), ensure that phase space is not too dissimilar to that of the final state of interest, and to converge exponentially weighted averages. However, while free energy methods generally focus on a single path from initial to final state (or a bidirectional path), using FUQ, once the functional derivative is calculated for a given low-fidelity model, the corrections can be made with respect to any other high-fidelity model as long as minimum conditions are satisfied. If the low-fidelity simulation does not explore the regions of phase space relevant for the high-fidelity potential at the conditions of interest the results will be poor; this is most striking when switching potentials results in a structural phase transition. This phase space overlap should be checked as demonstrated here to ensure meaningful results as with free energy methods. Additionally, the functional derivative correction can only be used with a functional discrepancy such that its effect can be described to first order. We also note that the perturbative approach used here is applicable only to input functions that appear linearly in the Hamiltonian so the perturbation can be separated additively. This is not a general limitation of FUQ but of the specific approach used 