Dynamics of molecules in crystals from multi-temperature anisotropic displacement parameters. I. theory.

A new model for analysing the temperature evolution of anisotropic displacement parameters (ADP's) is presented. It allows for a separation of temperature-dependent from temperature-independent contributions to ADP's and provides a fairly detailed description of the temperature-dependent large-amplitude molecular motions in crystals in terms of correlated atomic displacements and associated effective vibrational frequencies. It can detect disorder in the crystal structure, systematic error in the diffraction data and the effects of non-spherical electron-density distributions on ADP's in X-ray data. The analysis requires diffraction data measured at multiple temperatures.