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Published October 1998 | Published
Journal Article Open

Correlation of Internal Torsional Motion with Overall Molecular Motion in Crystals


The simple one-parameter Dunitz-White model for internal torsional motion accompanying overall molecular motion in crystals ignores the correlations between this torsion and the overall translation and libration. These correlations are explicitly considered here, in quadratic approximation (based on the linear approximation for displacements). For each attached rigid group (ARG) undergoing a torsional libration, there are, in addition to the mean-square libration amplitude, six correlations to be considered, three with the overall molecular libration and three with the overall translation. Because it is impossible from the observed quadratic mean displacements to distinguish the torsional motion from the overall molecular libration parallel to the torsional axis, the present analysis emphasizes the overall libration parallel to the torsional axis, which we term Λ. In the general case there are only six determinable parameters for each ARG. If the torsional axis of the ARG lies on a molecular symmetry element, the number of parameters is reduced to three or fewer. Examples of analyses with these correlations included, and without them, are compared.

Additional Information

© 1998 International Union of Crystallography. (Received 23 December 1997; accepted 23 February 1998) We have benefitted from many discussions with Hans-Beat Bürgi, who provided the proofs in Appendix B, and with Jack Dunitz and Emily Maverick, and from the helpful suggestions of Uri Shmueli and several referees.

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