Ultimately, the difference in performance between MD/NCMC and the benchmark MD and MD/MC approaches is fairly simple to understand. Conventional MD cannot cross kinetic barriers any faster than their inherent timescales, so, since timescales for interconversion between the slowest binding modes here are around 100ns (Section 3.1), convergence in conventional MD will necessarily take many times longer than 100ns. The MD/MC approach here couples conventional MD with occasional random ligand rotational moves which are accepted or rejected via conventional Monte Carlo, but because the binding site is relatively densely packed-even though it is not solvent exposed-the vast majority of these are rejected for toluene (giving an acceptance rates of 0.091±0.004%). Thus, this approach performs almost equivalently to standard MD. Our NCMC approach implemented in BLUES converges much more rapidly because ligand rotational move proposals can relax before being accepted or rejected, thus dramatically enhancing the acceptance rate to approximately 11%. These acceptance rates are reflected in the transitions between states, (Figure ), which show that MD/NCMC produced 497 transitions. This is more than twice as many transitions than the other methods employed; during the same number of iterations MD produced 242 transitions and MD/MC produced 230 transitions. Also, MD/NCMC produced high transition counts from any given binding mode to any other binding mode, while the other methods primarily produced transitions from a given binding mode to a subset of all the binding modes. Specifically, the other methods had the most transitions between in-plane binding modes (A1-B1 or A2-B2 transitions, Figure (a) and (b)) which are relatively fast to interconvert in normal dynamics, where BLUES had significant numbers of transitions between all binding modes, even the out-of-plane flip, which has a characteristic timescale of roughly 100 ns for conventional MD (Section 3.1). For example, the A1 to A2 transition occurred only twice in standard MD, and once in MD/MC, but 48 times in BLUES. This is also clearly apparent from Figure (left panels), where the MD and MD/MC approaches have few transitions between the top pair of states and the bottom pair of states, but BLUES has a very large number.