Cospectral polymers: Differentiation via semiflexibility

We consider polymer structures which are known in the mathematical literature as "cospectral." Their graphs have (in spite of the different architectures) exactly the same Laplacian spectra. Now, these spectra determine in Gaussian (Rouse-type) approaches many static as well as dynamical polymer characteristics. Hence, in such approaches for cospectral graphs many mesoscopic quantities are predicted to be indistinguishable. Here we show that the introduction of semiflexibility into the generalized Gaussian structure scheme leads to different spectra and hence to distinct macroscopic patterns. Moreover, particular semiflexible situations allow us to distinguish well between cospectral structures. We confirm our theoretical results through Monte Carlo simulations.     

Cadmium(II) thio‐ and selenocyanate complexes of 3,3′‐bis(1,2,4‐triazol‐4‐yl)‐1,1′‐biadamantane,a ligand designed with an `extended nanodiamond' aliphatic platform

In the structures of the Cd^II pseudohalide coordination polymer poly[[diaquabis[μ₂‐3,3′‐bis(1,2,4‐triazol‐4‐yl)‐1,1′‐biadamantane‐κ²N¹:N^1′]cadmium(II)] dithiocyanate dihydrate], {[Cd(C₂₄H₃₂N₆)₂(H₂O)₂](NCS)₂·2H₂O}_n, (I), and the isomorphous selenocyanate analogue, {[Cd(C₂₄H₃₂N₆)₂(H₂O)₂](NCSe)₂·2H₂O}_n, (II), the Cd^II cations occupy inversion centres and have octahedral CdN₄O₂ environments, completed by four N atoms of the organic ligands [Cd—N = 2.316 (2) and 2.361 (2) Å for (I), and 2.313 (3) and 2.372 (3) Å for (II)] and two trans‐coordinated aqua ligands [Cd—O = 2.3189 (15) Å for (I) and 2.323 (2) Å for (II)]. In each compound, the ligand displays a bidentate N¹:N^1′‐bridging mode, connecting the metal centres at a distance of 14.66 Å into two‐dimensional nets of (4,4)‐topology, while the uncoordinated thio(seleno)cyanate anions reside inside the net cavities. Hydrogen bonding between the water molecules, anions and 1,2,4‐triazole N atoms supports the tight packing, with an interlayer distance of 6.09 Å.     

Spectroscopic and electronic structure studies of a dimethyl sulfoxide reductase catalytic intermediate: implications for electron- and atom-transfer reactivity

The electronic structure of a genuine paramagnetic des-oxo Mo(V) catalytic intermediate in the reaction of dimethyl sulfoxide reductase (DMSOR) with (CH(3))(3)NO has been probed by electron paramagnetic resonance (EPR), electronic absorption, and magnetic circular dichroism (MCD) spectroscopies. EPR spectroscopy reveals rhombic g- and A-tensors that indicate a low-symmetry geometry for this intermediate and a singly occupied molecular orbital that is dominantly metal centered. The excited-state spectroscopic data were interpreted in the context of electronic structure calculations, and this has resulted in a full assignment of the observed MCD and electronic absorption bands, a detailed understanding of the metal-ligand bonding scheme, and an evaluation of the Mo(V) coordination geometry and Mo(V)-S(dithiolene) covalency as it pertains to the stability of the intermediate and electron-transfer regeneration. Finally, the relationship between des-oxo Mo(V) and des-oxo Mo(IV) geometric and electronic structures is discussed relative to the reaction coordinate in members of the DMSOR enzyme family.     

Semitransitive subsemigroups of the singular part of the finite symmetric inverse semigroup

We prove that the minimal cardinality of a semitransitive subsemigroup in the singular part $\mathcal{I}_{n}\setminus \mathcal{S}_{n}$ of the symmetric inverse semigroup $\mathcal{I}_{n}$ is 2n?p+1, where p is the greatest proper divisor of n, and classify all semitransitive subsemigroups of this minimal cardinality.     

Dioxomolybdenum(VI) and dioxotungsten(VI) complexes supported by an amido ligand

Stepwise addition of one equivalent of n-butyllithium and trimethylsilyl chloride to 2-tert-butylmercaptoaniline affords the new ligand 1-(Me3SiNH)-2-(t-BuS)C6H4 (LH), that reacts with one equivalent of butyllithium to its lithium salt LLi. Dioxodichloromolybdenum [MoO2Cl2] and dioxodichlorotungsten dimethoxyethane [WO2Cl2(dme)] react in tetrahydrofuran solution at low temperature with two equivalents LLi to monomeric dioxomolybdenum(VI) [MoO2L2] (1) and dioxotungsten(VI) complex [WO2L2] (2) employing two bidentate amido thioether ligands. The crystallographic determination of the molecular structures of 1 and 2 show evidence for M...S contacts. The reaction of [MoO2Cl2] with LLi in tetrahydrofuran solution at room temperature leads next to 1 to two compounds where silyl group migration from nitrogen to oxygen atoms occurs forming [Mo(=NL')2(OSiMe)2] (3) and [Mo(=NL')2(OSiMe3)L] (4, L' = N-2-t-BuSC6H4) as determined by NMR spectroscopy. Compound 4 was isolated in low yield and its molecular structure determined by X-ray crystallography. Higher yields of a bisimido complex can be obtained by the direct reaction of one equivalent of LLi with [Mo(NAr)2Cl2(dme)] (Ar = 2,6-Me2C6H4) forming [Mo(NAr)2LCl] (5).     

Presentation for the Partial Dual Symmetric Inverse Monoid

We give a monoid presentation in terms of generators and define relations for the partial analogue of the finite dual symmetric inverse monoid.     

A dihydroxidotetracopper(II) framework supported by 4,4′‐(adamantane‐1,3‐diyl)bis(1,2,4‐triazole) and benzene‐1,3,5‐tricarboxylate bridges

The new bifunctional ligand 4,4′‐(adamantane‐1,3‐diyl)bis(1,2,4‐triazole) (tr₂ad) and benzene‐1,3,5‐tricarboxylate sustain complementary coordination bridging for the three‐dimensional framework of poly[[bis[μ₃‐4,4′‐(adamantane‐1,3‐diyl)bis(1,2,4‐triazole)‐κ³N¹:N²:N^1′]bis(μ₄‐benzene‐1,3,5‐tricarboxylato‐κ⁴O¹:O^1′:O³:O⁵)di‐μ₃‐hydroxido‐κ⁶O:O:O‐tetracopper(II)] dihydrate], {[Cu₄(C₉H₃O₆)₂(OH)₂(C₁₄H₁₈N₆)₂]·2H₂O}_n. The net node is a centrosymmetric (μ₃‐OH)₂Cu₄ cluster [Cu—O = 1.9525 (14)–2.0770 (15) Å and Cu...Cu = 3.0536 (5) Å] involving two independent copper ions in tetragonal pyramidal CuO₄N and trigonal bipyramidal CuO₃N₂ environments. One carboxylate group of the anion is bridging and the other two are monodentate, leading to the connection of three hydroxide clusters and the generation of neutral coordination layers separated by 9.3583 (5) Å. The interlayer linkage is effected by μ₃‐tr₂ad ligands, with one triazole group N¹:N²‐bridging and the second monodentate [Cu—N = 1.9893 (19), 2.010 (2) and 2.411 (2) Å]. In total, the hydroxide clusters are linked to six close neighbors within the carboxylate layer and to four neighbors via tr₂ad bridges. Hydrogen bonding of solvent water molecules to noncoordinated triazole N atoms and carboxylate groups provides two additional links for the net, which adopts a 12‐connected topology corresponding to hexagonal closest packing. The study also introduces a new type of bis(triazole) ligand, which may find wider applications for supramolecular synthesis.     

A refinement of Stone duality to skew Boolean algebras

We establish two theorems that refine the classical Stone duality between generalized Boolean algebras and locally compact Boolean spaces. In the first theorem, we prove that the category of left-handed skew Boolean algebras whose morphisms are proper skew Boolean algebra homomorphisms is equivalent to the category of étale spaces over locally compact Boolean spaces whose morphisms are étale space cohomomorphisms over continuous proper maps. In the second theorem, we prove that the category of left-handed skew Boolean -algebras whose morphisms are proper skew Boolean -algebra homomorphisms is equivalent to the category of étale spaces with compact clopen equalizers over locally compact Boolean spaces whose morphisms are injective étale space cohomomorphisms over continuous proper maps.     

Front Cover: In Celebration of the International Year of the Periodic Table 2019 (Chem. Eur. J. 1/2019)

The cover of this issue is directly from the Editorial Team at Chemistry – A European Journal . The image depicts a journal vision for an international Chemistree Journalis , a rare and unique species of elemental value, designed in celebration of the International Year of the Periodic Table. Find out more information in the Editorial by H. Ross 10.1002/chem.201806058 .