The new automated iterative Hirshfeld atom refinement method is explained and validated through comparison of structural models of Gly–l-Ala obtained from synchrotron X-ray and neutron diffraction data at 12, 50, 150 and 295 K. Structural parameters involving hydrogen atoms are determined with comparable precision from both experiments and agree mostly to within two combined standard uncertainties.

Single crystals of h8-naphthalene have been examined by both X-ray and neutron diffraction over a range of temperatures from 5 to 295 K. The aim of this case study was to measure the anisotropic displacement parameters (ADPs) of carbons and hydrogens and to interpret them using the model of thermal motion proposed by Bürgi and Capelli (Acta Cryst. 2000, A56, 403). The traditional rigid-body analysis expresses the low-frequency motions in terms of molecular translations and librations only, whereas the Bürgi-Capelli treatment also includes the high-frequency internal modes. We show that a considerable improvement occurs by representing the internal modes by a single second-rank tensor and that a further improvement follows by including a Grüneisen parameter to account for volume thermal expansion. By applying the treatment to multi-temperature diffraction data, there is a considerable reduction in the ratio of number of adjustable parameters/number of independent observations.

No abstract

A quasi-harmonic molecular-mean-®eld model for analyzing anharmonic temperature evolution of anisotropic displacement parameters is described. Anharmonic effects are taken into account through a Gru È neisen-type temperature dependence of effective vibrational frequencies. The method is applied to neutron and X-ray diffraction data of hexamethylenetetramine measured between 15 and 298 K. The resulting Gru È neisen parameters and other characteristics of molecular motion in the solid state agree well with those obtained from independent vibrational data. The analysis also suggests errors in the ADP's due to insuf®cient extinction corrections in the diffraction data.

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.