For toluene, due to its relatively small size, MC and NCMC result in relatively similar acceptance profiles as a function of the amount of rotation (Figure (a) and (b)), except perhaps that NCMC yields improved acceptance of intermediate amounts of rotation between 0 and 180 degrees. However, for 3iodotoluene (Figure (b) and (c)), standard MC results in virtually no acceptance of moves larger than 20 degrees ((5 ± 2) ⇥ 10 5 %), whereas NCMC retains good acceptance of such moves (0.68 ± 0.07 %). (For the MC case on the 3-iodotoluene system, we performed a total of ten trials of 2,000,000 MC attempts and in each trial, typically saw at most one or two accepted moves consisting of significant rotations.) Accounting for the 6500 relaxation steps used in NCMC, MC would have a (3 ± 1) ⇥ 10 1 % acceptance of significant rotations indicating that NCMC is still approximately twice as efficient than MC in this case. This is further supported by SI Figure , where we examine how effective MC versus NCMC moves are at sampling new binding modes not represented in the MD trajectory providing the starting points for our move attempts. For MC, only very few moves outside the starting region are accepted, whereas NCMC is quite effective at sampling new binding modes. Additionally, MC gives the apparently false impression that the initial set of binding modes is by far the most favorable (because it is so difficult to find a combination of ligand orientation and protein conformation which can allow a rotational move to be accepted with no relaxation), whereas NCMC suggests that there are alternate binding modes that may be considerably more favorable.