Abstract

The transformation laws for the weighting and covariance matrices of the components of the atomic vibration tensors are derived. It is shown that the use of unit-weight matrices in the least-squares determination of the rigid-body vibration tensors TLS from the atomic vibration components leads to incompatible results when the TLS parameters are refined in different Cartesian coordinate systems. Numerical results for some molecules showed that the differences in the obtained components of TLS usually lie within the range of two standard deviations. If the covariances of the atomic vibration components are taken into account in some simple form the incompatibilities vanish.