Crystallographic analysis of the thermal motion of the inclusion complex of cyclomaltoheptaose (beta-cyclodextrin) with hexamethylenetetramine.

The crystal structure of the inclusion complex of cyclomaltoheptaose (beta-cyclodextrin) with hexamethylenetetramine was determined at temperatures of 123, 173, 223, and 293 K. The rigid-body motion of the host and guest molecules was evaluated by means of the TLS method that represents the molecular motion in terms of translation, libration, and screw motion. In increasing the temperature from 123 to 293 K, the amplitude of the rigid body vibration of the host molecule was increased from 1.0 to 1.3 degrees in the rotational motion and from 0.16 to 0.17 A in the translational motion. The cyclomaltoheptaose molecule has the flexibility in seven alpha-(1-->4)-linkages, and each glucose unit was in the rotational vibration around an axis through two glycosidic oxygen atoms. As a result, the rigid-body parameters of cyclomaltoheptaose were considered to be overestimated because of including the contribution from the local motion of glucose units. In contrast, for the guest molecule having no structural flexibility, the TLS analysis demonstrated that the atomic thermal vibration was mostly derived from the rigid body motion. The rotational amplitude of hexamethylenetetramine was changed from 5.2 to 6.6 degrees in increasing the temperature from 123 to 293 K, while the change of the translational amplitude was from 0.20 to 0.23 A. The translational motion of the guest molecule was hindered by the inside wall of the host cavity. The molecular motion was characterized by the rotational vibration around the axis through two nitrogen atoms that were involved in the hydrogen-bond formation.