Ba 2In 2O 4(OH) 2: Proton sites, disorder and vibrational properties

Abstract

The structure of Ba 2In 2O 4(OH) 2 is analysed by the explicit full optimization of a large number of possible proton arrangements using periodic density functional theory. It is shown that the experimental assignments in which protons appear to be located at high symmetry positions with unphysical bond lengths do not correspond to minima on the potential energy hypersurface. The apparent sites are averages of a number of possible proton locations involving a set of possible local structural environments in which the internuclear separations are more realistic. Such problems with structural refinements are common where profile refinement programs place the atoms at the average position due to dynamic and/or static disorder. Thus while the calculations support a previous neutron diffraction analysis of the structure in that the average structure contains two different proton sites, they also reveal substantial information about the local environments of the protons. In all optimizations, the protons moved from the average positions suggested in the neutron diffraction study with calculated O–H and OH⋯O distances consistent with those observed in other oxides. The energies of different proton distributions vary significantly so the protons are not randomly distributed. We also present an analysis of the vibrational properties of the O–H bonds. Since the strength of the hydrogen bonds is closely related to the local structural environments of the protons, a range of vibrational frequencies is obtained providing a prediction of the vibrational spectra. In O–H⋯O linkages, O–H stretching modes soften with increasing H⋯O hydrogen bond strength, while the in-plane and out-of-plane bending or libration modes stiffen. Together, our results show how modern theoretical methods can provide a clearer understanding of the structure and dynamics of a complex inorganic material.