Importance of correlated motions on the low barrier rotational potentials of crystalline molecular gyroscopes

The energetic and structural changes taking place upon rotation of the central phenylene of 1,4-bis(3,3,3-triphenylpropynyl)benzene in the solid state were computed using molecular mechanics calculations. Pseudopolymorphic crystals of a benzene clathrate (1A) and a desolvated form (1B) were analyzed with models that account for varying degrees of freedom within the corresponding lattices. The calculated rotational barriers in a rigid lattice approximation, 78 kcal/mol for 1A and 72 kcal/mol for 1B, are about 5 times greater than those previously measured by variable-temperature 13C CPMAS NMR and quadrupolar echo 2H NMR line-shape analysis: 12.8 kcal/mol for 1A and 14.6 kcal/mol for 1B. The potential energy barriers calculated with a model that restricts whole body rotation and translational motions but allows for internal rotations give results that are near the experimental free-energy barriers. The calculated barriers for 1A and 1B are 15.5 and 16.2 kcal/mol, respectively. The differences between the rigid and partially relaxed models are attributed to the effect of correlated motions of the lattice and the rotating group, which are evident from the structural analysis of the atomic position data as a function of the dihedral angle of the rotator. The displacements of neighboring molecules near the rotary transition states for 1A and 1B can be as large as 2.7 and 1.1 A, respectively. The displacement and oscillation (C2) of interpenetrating phenyl rings from neighboring rotors proximal to the event are significant for both 1A and 1B. In addition, 6-fold (C6) benzene rotations in clathrate 1A were found to be directly correlated to the rotation of the phenylene rotator.