Here, we provide details of our NCMC move proposals for ligand binding mode sampling. We combine thermodynamic perturbation of the ligand (alchemically changing its interactions with the protein) with uniform random rotation around the ligand center of mass (COM). Specifically, we scale over a series of n NCMC steps until the ligand no longer interacts with the protein (removing its steric and electrostatic interactions). scales the interactions between the ligand and the rest of the system; to elaborate further, controls the strength of interactions between the ligand and its environment, with = 1 corresponding to the fully interacting state, and = 0 corresponding to the non-interacting state (as discussed in 2.5. The ligand is then randomly rotated to a new orientation in the binding site around its center of mass. Then its interactions are turned back on by scaling over a series of another n NCMC steps, as conceptually shown in Figure . Finally, we use the analogue of the Metropolis-Hastings acceptance criteria that satisfies Eq. 4 to accept or reject the resulting move.