Abstract: Movements in molecular machines are usually diverse and coupled, but some of them are often implicit and hard to be observed in experiments. In the present work, the two-or three-dimensional free-energy landscapes characterizing the coupled shuttling and other movements of a series of pH-triggered rotaxanes composed of a crown ether and an H-shaped axle with distinct number of phenyl rings(n=1-3) have been explored. The results show that although the calculated free-energy barriers against shuttling in the rotaxanes(n=2 and 3) change slightly, the movements coupled with the shuttling vary significantly with the axle length. At high pH, the shuttling in the rotaxane of n=2 is coupled with the isomerization of the wheel, while the shuttling in the one of n=3 is accompanied by both the isomerization and the rotation of the macrocycle. In addition, the crown ether underwent greater conformational change during shuttling at low pH compared to that at high pH. These results indicate that disentangling the coupled movements is important to reveal the underlying molecular mechanism of the shuttling.

Key words: Rotaxane, Molecular machine, Molecular movement, Free-energy landscape