Applications of the King and Lipscomb expression for the X-ray scattering of a hindered rotor

The King and Lipscomb expression for the scattering of groups undergoing hindered rotation against a cosine potential function about an axis has been modified and incorporated into a routine full-matrix structure-factor and least-squares program. The model has been evaluated in several cases and has been found to be an excellent representation for π-bonded C_nH_n groups in organometallic compounds in that the hindered rotor representation, with only nine variables, is frequently competitive with individual atom models. The parameters of the model concerned with thermal motion have been related to the more conventional parameters to enable the deduction of good starting values for the hindered-rotor refinement. The parameter that in the formal model is associated with the height of the barrier potential function is shown to be a shape parameter that is related more properly with the root-mean-square libration about the axis. Bond lengths derived from the model are corrected for this dominant libration.