FIG. 2.

Different strategies for improving the energy difference (ΔU) distribution overlap between L and H levels of theory, which is critical to the convergence of free energy simulations that rely on sampling at either one end-state or both end-states.^32,33,36,40 (a) The two end-states have a gap in the ΔU distribution. (b) One can modify the low-level method (L → L′) to improve the ΔU distribution based on, for example, force-matching^45,55 or a neural network.⁵¹ (c) One can modify the distribution of the same low level method (P_L → $P_L^{\prime }$), with, for example, Tsallis sampling,⁵⁸ to improve the ΔU distribution. (d) One can introduce an intermediate level of method (or distribution) P_M to bridge the distributions at the L and H levels. The staged protocol described here falls into this category.