ΔH primary exp(-βΔG primary ) + ΔH secondary exp(-βΔG secondary ) exp(-βΔG primary ) + exp(-βΔG secondary ) z observables for other cyclodextrin-guest calculations, with deviations within statistical uncertainty . Equilibration consisted of 50,000 steps of energy minimization, 100 ps of heating from 0 to 300 K, and then 2000 ps of additional NPT simulation. AMBER's Langevin thermostat with a collision rate of 1 ps -1 , the Monte Carlo barostat, a nonbonded cutoff of 9 Å and default PME parameters, were used for the NPT simulations. An isotropic analytic correction to the Lennard-Jones interactions is applied beyond the cutoff distance . Production NPT simulations were run for a minimum of 2.5 ns and maximum of 50 ns per window, except for the windows used to calculate the enthalpy, which were each simulated for 1 μs. In the GAFF v1.7 and GAFF v2.1 simulations, the exact length of each window's simulation was determined by the uncertainty in the work done in each λ window. In particular, for restraint energy in window , we define the instantaneous SEM of as σ(λ i ), and each window (except for the windows used to calculate ΔH) was simulated until the value of , defined as fell below a threshold of 0.02 kcal/mol during the attach phase and 0.1 kcal/mol during the pull phase.