The thermal-motion correction for bond angles

Expressions for the thermal-motion correction of bond angles are derived by determining the mean angle. Thus the joint distribution of the three relevant nuclei is used in the harmonic approximation of the nuclear vibrations. To calculate the correction in practice, the coupling tensors among the three relevant atoms must be known, these being a characteristic feature of the joint distribution. Since the coupling tensors cannot be measured, they must be determined from simple models of motion or from the interatomic force constants. The model of rigid-body motions can be applied in many cases, and for this model it is shown that the angle correction can be calculated from the corrected bond lengths. Approximate expressions for upper and lower bounds of the angle correction are derived.