Coloring variants of the Re3B type

The Re3B type, space group Cmcm, has boron-centered trigonal prisms as central building units and is one of the basic structure types with numerous binary and ternary representatives. The coloring of different atoms on the two crystallographically independent rhenium sites leads to a manifold of compounds with different bonding peculiarities that are rather isopointal than isotypic with the prototype. Typical compounds are the S-phase precipitate MgCuAl2, the silicide ScPt2Si or the iodide Th0.5Pb0.5I3 (PuBr3 type). Differences in size or composition might force symmetry reductions. This is discussed for YZn3 (space group Pnma) and the different coloring variants ScRhSi2 and TaNi2P which show different twists of the trigonal prisms. Striking singular representatives with lower symmetry structures are BaThBr6 (Pmma) and NbCo2B (P21/c) which allow different ordering/distortion patterns for the prisms. All these crystal chemical details are discussed on the basis of group subgroup schemes (Bärnighausen trees).

Symmetry relations in wurtzite nitrides and oxide nitrides and the curious case of Pmc21

Binary III–V nitrides such as AlN, GaN and InN in the wurtzite-type structure have long been considered as potent semiconducting materials because of their optoelectronic properties, amongst others. With rising concerns over the utilization of scarce elements, a replacement of the trivalent cations by others in ternary and multinary nitrides has led to the development of different variants of nitrides and oxide nitrides crystallizing in lower-symmetry variants of wurtzite. This work presents the symmetry relationships between these structural types specific to nitrides and oxide nitrides and updates some prior work on this matter. The non-existence of compounds crystallizing in Pmc21, formally the highest subgroup of the wurtzite type fulfilling Pauling's rules for 1:1:2 stoichiometries, has been puzzling scientists for a while; a rationalization is given, from a crystallographic basis, of why this space group is unlikely to be adopted.

Porphyrinoids with Vinylene Bridges

Porphyrinoids containing vinylene bridges, such as triphyrin(2.1.1), porphycene, porphyrin(2.1.2.1), and hexaphyrin(2.1.2.1.2.1), are a relatively new family of porphyrinoids. Vinylene bridges give porphyrinoids a lower symmetry and a flexibility of the framework and they permit cis/trans-isomerization reactions; these factors confer unique properties to these substances, such as coordination to metal ions and aromaticity switching. In this account, the synthesis, crystal structures, and properties of new porphyrinoids containing vinylene bridges are summarized.1 Introduction2 Triphyrin(2.1.1)3 Porphycene4 Porphyrin(2.1.2.1)5 Hexaphyrin(2.1.2.1.2.1)6 Conclusion

The Fedorov–Groth law revisited: complexity analysis using mineralogical data

The Fedorov–Groth law points out that, on average, chemical simplicity corresponds to higher symmetry, and chemically complex compounds usually have lower symmetry than chemically simple compounds. Using mineralogical data, it is demonstrated that the Fedorov–Groth law is valid and statistically meaningful, when chemical complexity is expressed as the amount of Shannon chemical information per atom and the degree of symmetry as the order of the point group of a mineral.

Optimizing the refinement of merohedrally twinned P61 HIV-1 protease–inhibitor cocrystal structures

Twinning is a crystal-growth anomaly in which protein monomers exist in different orientations but are related in a specific way, causing diffraction reflections to overlap. Twinning imposes additional symmetry on the data, often leading to the assignment of a higher symmetry space group. Specifically, in merohedral twinning, reflections from each monomer overlap and require a twin law to model unique structural data from overlapping reflections. Neglecting twinning in the crystallographic analysis of quasi-rotationally symmetric homo-oligomeric protein structures can mask the degree of structural non-identity between monomers. In particular, any deviations from perfect symmetry will be lost if higher than appropriate symmetry is applied during crystallographic analysis. Such cases warrant choosing between the highest symmetry space group possible or determining whether the monomers have distinguishable structural asymmetries and thus require a lower symmetry space group and a twin law. Using hexagonal cocrystals of HIV-1 protease, a C 2-symmetric homodimer whose symmetry is broken by bound ligand, it is shown that both assigning a lower symmetry space group and applying a twin law during refinement are critical to achieving a structural model that more accurately fits the electron density. By re-analyzing three recently published HIV-1 protease structures, improvements in nearly every crystallographic metric are demonstrated. Most importantly, a procedure is demonstrated where the inhibitor can be reliably modeled in a single orientation. This protocol may be applicable to many other homo-oligomers in the PDB.

The stabilities and geometries of Re-encapsulated Sin(n=16, 20, 24, 28, 32, 36, and 40) clusters: A computational investigation

Geometry optimization of the mixed SinRe (n=12, 16, 20, 24, 28, 32, 36, and 40) cages with doublet, quartet, and sextet spin configurations is carried out systematically at the UHF/LanL2DZ level. Equilibrium structures, total energies, and stabilities of Re@Sin cages are presented and discussed. The calculated results show that all Re@Sin cages of highest symmetry undergo slight distortion into much more stable structures of lower symmetry. The Re atom in the Re@Sin (n=12, 16, 20, 24, 28, 32, 36, and 40) cages deviates from the cage center site of Sin fullerenes. Charge-transfer between Re and Si atoms makes a contribution to the stability of the Sin fullerenes; In addition, the relative stability is discussed, the most stable geometry is assigned.

Raman and single-crystal X-ray diffraction evidence of pressure-induced phase transitions in a perovskite-like framework of [(C3H7)4N] [Mn(N(CN)2)3]

The [TPrA][Mn(dca)3] perovskite shows highly anisotropic compression and the presence of three pressure-induced phase transitions near 0.4, 3 and 5 GPa into lower symmetry phases.