Symmetrized multipole analysis of coupled orientation-translation distributions

Symmetrized multipole formalism, in diffraction studies of orientationally disordered molecular crystals, is generalized to include coupling between orientations and translations of a rigid body and anharmonicity in the center-of-mass motion. This generalized formalism is intended for use with direct multipole analysis of the observed form factors. In the relationships between the radial multipole coefficients of the dynamic and static density, correlations cause a mixing in the multipole order. In the dynamic form factor the parameters describing the coupling are linear combinations of the multipole expansion coefficients of the corresponding rigid-body distribution. Parameters describing anisotropy are directly the multipole expansion coefficients of the rigid-body center-of-mass distribution. As an example of the formalism, neutron diffraction data from cubic KCN, NaCN, KOD, NaOD and CBr₄ and rhombohedral RbNO₃ are reanalyzed with direct multipole analysis. In these examples the importance of coupling seems to grow with the complexity of the crystal.