A robust and fast method is presented that provides a simple real-space convergent solution for identifying equilibrium orientations of crystallization H 2 O molecules in ionic crystals, on the basis of zero net torque. The predicted H 2 O orientations constrained by rotational equilibrium are compared with neutron scattering experiments and/or ab initio density functional theory (DFT) calculations. The comparison shows that predicted and observed H 2 O orientations are consistent, demonstrating the reliability of the reported torque method. Moreover, the rotational equilibrium conditions predict an alternative, not previously observed, H 2 O orientation in kernite [Na 2 B 4 O 6 (OH) 2 Á3H 2 O], and this may explain anomalously large displacement parameters that have been reported for this mineral. Complementary DFT computations corroborate that the two orientations are geometrically distinct and energetically near degenerate.research papers

The crystal structure of the U(iv)-phosphate mineral vyacheslavite has been solved from precession electron diffraction tomography (PEDT) data from the natural nano-crystal and further refined using density-functional theory (DFT) calculations.

The crystal structure of lead uranyl-oxide hydroxy-hydrate mineral curite, ideally Pb 3 (H 2 O) 2 [(UO 2 ) 4 O 4 (OH) 3 ] 2 , was studied by means of single-crystal X-ray diffraction and theoretical calculations in order to localize positions of hydrogen atoms in the structure. This study has demonstrated that hydrogen atoms can be localized successfully also in materials for which the conventional approach of structure analysis failed, here due to very high absorption of X-rays by the mineral matrix. The theoretical calculations, based on the Torque method, provide a robust, fast realspace method for determining H 2 O orientations from their rotational equilibrium condition. In line with previous results we found that curite is orthorhombic, with space group Pnma, unit-cell parameters a ¼ 12.5510(10), b ¼ 8.3760(4), c ¼ 13.0107(9)Å, V ¼ 1367.78(16)Å 3 , and two formula units per unit cell. The structure (R 1 ¼ 3.58% for 1374 reflections with I > 3sI) contains uranyl-hydroxo-oxide sheets of the unique topology among uranyl oxide minerals and compounds and an interlayer space with Pb 2+ cations and a single H 2 O molecule, which is coordinated to the Pb-site. Current results show that curite is slightly non-stoichiometric in Pb content ($3.02 Pb per unit cell, Z ¼ 2); the charge-balance mechanism is via (OH) 4 O 2 substitution within the sheets of uranyl polyhedra. Disproving earlier predictions, the current study shows that curite contains only one H 2 O group, with [4]-coordinated oxygen. The hydrogen bonding network maintains the bonding between the sheets in addition to Pb-O bonds;among them, a H-bond is crucial between the OH group on an apical O Uranyl atom of an adjacent sheet that stabilizes the entire structure. The results show that the combination of experimental X-ray data and the Torque method can successfully reveal hydrogen bonding especially for complex crystal structures and materials where X-rays fail to provide unambiguous hydrogen positions.