where U is the total potential energy, θ is the force field parameter, and ⟨⟩ bound and ⟨⟩ free indicate ensemble averages of the host-guest system without any restraining potentials included in the bound and unbound (i.e., free) states, respectively. These two states correspond to the first and last windows of the attach-pull-release (APR) calculations (see Method 2.2 for details). The restraining potentials in the bound and free states do not alter the internal coordinates of the host-guest molecules and, thus, do not contribute to the total potential energy. The restraining potentials in the free state keep the host and guest molecules far apart; thus, we simulate the free host and free guest in the same system. This approach reduces the number of simulations from four to two, as was originally defined by Yin et al. In practice, the gradient ∂U/∂θ is estimated using the central difference method by re-evaluating the potential energy U with a perturbed θ