Principal axes for clusters in crystals investigated by the tensor of inertia: a case study with BH4in Mg(BH4)2

Abstract

Knowledge of how chemically predefined clusters of atoms are arranged in a crystal and how they can reorientate under external excitations is of great importance for structure determination and a description of structural transformations. In general, the probability of cluster reorientation depends on the activation energy and thus on the symmetry of the cluster and its environment. In addition to the many experimental methods available for studying molecular reorientations in a crystal, there is also a theoretical method, known for many years, that can be used to describe the reorientation processes, namely the determination of the principal axes of the cluster's tensor of inertia (TI). By such calculations, insight may be gained into the effective shape of the cluster and the orientations of the distinct reorientation axes. In the present work, such a methodology has been applied to an analysis of borohydride, BH4, clusters in several structures proposed by theoretical calculations as well as experimental studies of magnesium borohydride, Mg(BH4)2. The calculation of orientations for the TI principal axes as well as pseudo-twofold axes of the cluster revealed a strong correlation between these orientations and the Mg—B—Mg angle for the two Mg neighbours of the cluster. The exceptions from that well defined dependence are observed for the principal TI axes in situations when the cluster deformations are small and the symmetry is close to spherical, when the orientations of the principal axes are prone to fluctuations.