Crystal Structure of HAsUO6 4H2O

The crystal structure of HAsUO₆ 4H₂O was solved at 295 K by X-ray analysis. Reasons for structural changes due to temperature variation are analyzed.     

The isotypic hydrogen phosphate and arsenate dihydrates M2HXO4·2H2O (M = Rb,Cs; X = P,As)

The four isotypic alkaline metal monohydrogen arsenate(V) and phosphate(V) dihydrates M₂HXO₄·2H₂O (M = Rb, Cs; X = P, As) [namely dicaesium monohydrogen arsenate(V) dihydrate, Cs₂HAsO₄·2H₂O, dicaesium monohydrogen phosphate(V) dihydrate, Cs₂HPO₄·2H₂O, dirubidium monohydrogen arsenate(V) dihydrate, Rb₂HAsO₄·2H₂O, and dirubidium monohydrogen phosphate(V) dihydrate, Rb₂HPO₄·2H₂O] were synthesized by reaction of an aqueous H₃XO₄ solution with one equivalent of aqueous M₂CO₃. Their crystal structures are made up of undulating chains extending along [001] of tetrahedral [XO₃(OH)]⁻ anions connected via strong O—H...O hydrogen bonds. These chains are in turn connected into a three‐dimensional network via medium‐strength hydrogen bonding involving the water molecules. Two crystallographically different M⁺ cations are located in channels running along [001] or in the free space of the [XO₃(OH)]⁻ chains, respectively. They are coordinated by eight and twelve O atoms forming irregular polyhedra. The structures possess pseudosymmetry. Due to the ordering of the protons in the [XO₃(OH)]⁻ chains in the actual structures, the symmetry is reduced from C2/c to P2₁/c. Nevertheless, the deviation from C2/c symmetry is minute.     

Prevalence and Significance of Approximate Symmetry in Organic Pc Structures

A survey has been made of the well determined (R≤0.050) organic crystal structures that have only a single glide plane (e. g., are in space group Pc) and that have more than one crystallographically independent formula unit (Z′>1); the goal was to discover what fraction have additional approximate symmetry. Of the 377 unique structures examined 8 % should almost certainly been refined in a higher-symmetry unit cell; 86 % of the remaining 347 have approximate symmetry that is periodic in at least one dimension. While these percentages are similar to those found for P1 structures (C. P. Brock, Acta Crystallogr., Sect. B 2022 , 78, 576–588), the types of approximate symmetry differ because 89 % of the P1, Z′>1 structures were composed of enantiopure material. The 347 reliable Pc structures include 118 that are slightly distorted or mimicked Cc and P2₁/c structures, 15 of which were reported as having been determined at room temperature. The distortions in another 72 are so large that the approximate symmetry must be seen as periodic in two dimensions only. These results suggest that symmetry lowering may accompany transformation of a crystal nucleus to a macroscopic crystal.     

Synthesis and crystal structures of two structurally related kryptoracemates

Kryptoracemates are racemic compounds (pairs of enantiomers) that crystallize in Sohnke space groups (space groups that contain neither inversion centres nor mirror or glide planes nor rotoinversion axes). Thus, the two symmetry‐independent molecules cannot be transformed into one another by any symmetry element present in the crystal structure. Usually, the conformation of the two enantiomers is rather similar if not identical. Sometimes, the two enantiomers are related by a pseudosymmetry element, which is often a pseudocentre of inversion, because inversion symmetry is thought to be favourable for crystal packing. We obtained crystals of two kryptoracemates of two very similar compounds differing in just one residue, namely rac‐N‐[(1S ,2R ,3S )‐2‐methyl‐3‐(5‐methylfuran‐2‐yl)‐1‐phenyl‐3‐(pivalamido)propyl]benzamide, C₂₇H₃₂N₂O₃, (I), and rac‐N‐[(1S ,2S ,3R )‐2‐methyl‐3‐(5‐methylfuran‐2‐yl)‐1‐phenyl‐3‐(propionamido)propyl]benzamide dichloromethane hemisolvate, C₂₅H₂₈N₂O₃·0.5CH₂Cl₂, (II). The crystals of both compounds contain both enantiomers of these chiral molecules. However, since the space groups [P 2₁2₁2₁ for (I) and P 1 for (II)] contain neither inversion centres nor mirror or glide planes nor rotoinversion axes, there are both enantiomers in the asymmetric unit, which is a rather uncommon phenomenon. In addition, it is remarkable that (II) contains two pairs of enantiomers in the asymmetric unit. In the crystal, molecules are connected by intermolecular N—H…O hydrogen bonds to form chains or layered structures.     

Triple-Decker Complexes. 14. [1] A Model for Refinement of the End-for-End Disordered Cationic Triple-Decker Complex [Cp*Ru(μ-η5:η5-C4Me4P)FeCp*]+

The solid-state structure of the triple-decker salt [Cp*Fe(-⁵:⁵-C₄Me₄P)RuCp*] · CF₃SO₃ shows orientational disorder for the pseudosymmetric cations. A chemically related compound was used to define a restrained structure model. Comparison of different refinement strategies proves that this restrained model is superior to an unrestrained treatment.     

A simple graphical method to pinpoint local pseudosymmetries in Z′ > 1 cases

An intuitive method is presented for detecting pseudosymmetries in Z′ > 1 cases as a complement to well‐proven strategies already available in the literature. It is based in the simple idea that the mid‐points between equivalent atoms in symmetrically related molecules are disposed according to simple well‐known patterns, which are easily recognizable by optical inspection. A number of Z′ = 4 cases in the literature are analyzed, which allows some of the potentialities of the method to be revealed.     

Polymorphism of NaVO2F2: a P21/c superstructure with pseudosymmetry of P21/m in the subcell

The ADDSYM routine in the program PLATON [Spek (2015). Acta Cryst. C 71 , 9–18] has helped researchers to avoid structures of (metal–)organic compounds being reported in an unnecessarily low symmetry space group. However, determination of the correct space group may get more complicated in cases of pseudosymmetric inorganic compounds. One example is NaVO₂F₂, which was reported [Crosnier‐Lopez et al. (1994). Eur. J. Solid State Inorg. Chem. 31 , 957–965] in the acentric space group P2₁ based on properties but flagged by ADDSYM as (pseudo)centrosymmetric P2₁/m within default distance tolerances. Herein a systematic investigation reveals that NaVO₂F₂ exists in at least four polymorphs: P2₁, (I), P2₁/m, (II), P2₁/c, (III), and one or more low‐temperature ones. The new centrosymmetric modification, (III), with the space group P2₁/c has a similar atomic packing geometry to phase (I), except for having a doubled c axis. The double‐cell of phase (III) arises from atomic shifts from the glide plane c at (x, , z). With increasing temperature, the number of observed reflections decreases. The odd l reflections gradually become weaker and, correspondingly, all atoms shift towards the glide plane, resulting in a gradual second‐order transformation of (III) into high‐temperature phase (II) (P2₁/m) at below 493 K. At least one first‐order enantiotropic phase transition was observed below 139 K from both the single‐crystal X‐ray diffraction and the differential scanning calorimetry analyses. Periodic first‐principles calculations within density functional theory show that both P2₁/c superstructure (III) and P2₁ substructure (I) are more stable than P2₁/m structure (II), and that P2₁/c superstructure (III) is more stable that P2₁ substructure (I).     

ON PSEUDOSYMMETRY TYPE HYPERSURFACES OF SEMI-EUCLIDEAN SPACES Ⅰ

In this paper the authors investigate hypersurfaces M of a semi-Euclidean space Esn+1, n ≥ 4, satisfying (aC +βR). H ＝ LkQ(g, Hk), k ＝ 1,2,3. Using obtained results they show additional curvature properties of investigated hypersurfaces.     

On the capability of revealing the pseudosymmetry of the chalcopyrite‐type crystal structure

The tetragonal crystal‐structure type of chalcopyrites (chemical formula A^IB^IIIC^VI₂) is a superstructure of sphalerite type. The c /a ratio differs generally from the ideal value 2, i.e., the crystal structure is pseudocubically distorted. For CuInSe₂ and CuGaSe₂ thin films, simulations demonstrate that it is theoretically possible to reveal the tetragonality in electron backscatter‐diffraction (EBSD) patterns for CuGaSe₂, whereas it may not be possible for CuInSe₂. EBSD experiments on CuGaSe₂ thin films using the ”Advanced Fit” band‐detection method show that it is possible to extract accurate misorientation‐angle distributions from the CuGaSe₂ thin film. Pole figures revealing the texture of the CuGaSe₂ thin film are shown, which agree well with X‐ray texture measurements from the same layer. (© 2008 WILEY ‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Crystal structure and pseudosymmetry analysis of the triclinic prodrug cloxazolam (Z′ = 4)

The prodrug cloxazolam [systematic name: 13‐chloro‐2‐(2‐chlorophenyl)‐3‐oxa‐6,9‐diazatricyclo[8.4.0.0^2,6]tetradeca‐1(10),11,13‐trien‐8‐one], C₁₇H₁₄Cl₂N₂O₂, crystallizes in the triclinic space group P, with four chemically identical independent molecules in the asymmetric unit. However, in order to facilitate the analysis of the striking pseudosymmetry relating the four independent molecules, the structure has been analysed and reported in the nonconventional centred B space‐group setting. Pseudosymmetry is an eminently local property, valid only in the realm of the unit‐cell boundary and not propagating to the whole crystal structure. It has been analyzed using the MP procedure described in the preceding article [Baggio (2019). Acta Cryst. C 75 , 837–850]. The molecules consist of a rigid core made up of three rings (five‐, six‐ and seven‐membered) and an extra six‐membered ring joined to the latter group by a single C—C bond, together with a clamping intramolecular C—H…O interaction preventing free rotation and providing additional rigidity. The four molecules in the asymmetric unit pair into dimers with almost exact twofold pseudosymmetry, further linked into (001) slabs as the building bricks of the structure. Interpenetration of slabs finally leads to a three‐dimensional structure of unusual compactness for an organic structure, with a Kitaigorodskii packing index of ca 0.71.