Transferable Hirshfeld atom model for rapid evaluation of aspherical atomic form factors.

Form factors based on aspherical models of atomic electron density have brought great improvement in the accuracies of hydrogen atom parameters derived from X-ray crystal structure refinement. Today, two main groups of such models are available, the banks of transferable atomic densities parametrized using the Hansen-Coppens multipole model which allows for rapid evaluation of atomic form factors and Hirshfeld atom refinement (HAR)-related methods which are usually more accurate but also slower. In this work, a model that combines the ideas utilized in the two approaches is tested. It uses atomic electron densities based on Hirshfeld partitions of electron densities, which are precalculated and stored in a databank. This model was also applied during the refinement of the structures of five small molecules. A comparison of the resulting hydrogen atom parameters with those derived from neutron diffraction data indicates that they are more accurate than those obtained with the Hansen-Coppens based databank, and only slightly less accurate than those obtained with a version of HAR that neglects the crystal environment. The advantage of using HAR becomes more noticeable when the effects of the environment are included. To speed up calculations, atomic densities were represented by multipole expansion with spherical harmonics up to l = 7, which used numerical radial functions (a different approach to that applied in the Hansen-Coppens model). Calculations of atomic form factors for the small protein crambin (at 0.73 Šresolution) took only 68 s using 12 CPU cores.

Atomic and electronic structures of an extremely fragile liquid.

The structure of high-temperature liquids is an important topic for understanding the fragility of liquids. Here we report the structure of a high-temperature non-glass-forming oxide liquid, ZrO2, at an atomistic and electronic level. The Bhatia-Thornton number-number structure factor of ZrO2 does not show a first sharp diffraction peak. The atomic structure comprises ZrO5, ZrO6 and ZrO7 polyhedra with a significant contribution of edge sharing of oxygen in addition to corner sharing. The variety of large oxygen coordination and polyhedral connections with short Zr-O bond lifetimes, induced by the relatively large ionic radius of zirconium, disturbs the evolution of intermediate-range ordering, which leads to a reduced electronic band gap and increased delocalization in the ionic Zr-O bonding. The details of the chemical bonding explain the extremely low viscosity of the liquid and the absence of a first sharp diffraction peak, and indicate that liquid ZrO2 is an extremely fragile liquid.