The thermal-motion bond-length correction for diatomic and triatomic molecules

The bond-length correction which is needed to correct for the effects of thermal motion is derived for diatomic and triatomic molecules. We treat the molecules as rigid-body oscillators and assume that the correlation tensor S is symmetric when the origin of the librations is at the centre of gravity. For diatomic molecules consisting of atoms of different masses and for linear triatomic molecules a simple solution is obtained. For diatomic molecules consisting of equal atoms and for angular triatomic molecules one can determine the correction only by introducing an unknown lattice-dynamical parameter. The value of this parameter can be assessed to a certain extent and can be determined from the vibration tensors of the atoms of asymmetric diatomic and linear triatomic molecules. Thus one obtains an experimental distribution of the lattice-dynamical parameter which is also likely to hold for symmetric diatomic and angular triatomic molecules. The corrections are calculated for 11 water molecules for which very accurate structural data are available.