Evaluating Electron-Transfer Reactivity of Complexes of Actinides in +2 and +3 Oxidation States by using EPR Spectroscopy

The possibility that the relative reactivity of complexes of actinide metals in the +2 and +3 oxidation states could be investigated by examining reactions between An^III and An^II species of Th and U with rare-earth metal reagents that provide EPR confirmation of electron transfer reactivity has been explored. Neither Cp’’₃Th^III nor Cp’’₃U^III will reduce Cp’’₃La^III or Cp’₃Y^III (Cp’=C₅H₄SiMe₃, Cp’’=C₅H₃(SiMe₃)₂). However, both [K(2.2.2-cryptand)][Cp’’₃Th^II] and [K(2.2.2-cryptand)][Cp’’₃U^II] reduce Cp’’₃La^III and Cp’₃Y^III to form [Cp’’₃La^II]¹⁻ and [Cp’₃Y^II]¹⁻, respectively, which were identified by EPR spectroscopy. The reverse reactions also occur which indicates that the reduction potentials are similar. [Cp’’₃La^II]¹⁻ reduces Cp’₃Y^III and the reverse Y^II/La^III combination also occurs. In both cases, the reactions generate EPR spectra indicative of multiple species in the mixtures of La^II and Y^II, which is consistent with ligand exchange and demonstrates that numerous heteroleptic complexes of these Ln^II ions exist.     

Phase‐transformation‐induced twinning of an iron(III) calix[4]pyrrolidine complex

The title compound, tetrachlorido‐1κCl;2κ³Cl‐(2,2,7,7,12,12,17,17‐octamethyl‐21,22,23,24‐tetraazapentacyclo[16.2.1.1^3,6.1^8,11.1^13,16]tetracosane‐1κ⁴N,N′,N′′,N′′′)‐μ₂‐oxido‐diiron(III), [Fe₂Cl₄O(C₂₈H₅₂N₄)], undergoes a slow phase transformation at ca 173 K from monoclinic space group P2₁/n, denoted form (I), to the maximal non‐isomorphic subgroup, triclinic space group P, denoted form (II), which is accompanied by nonmerohedral twinning [twin fractions of 0.693 (4) and 0.307 (4)]. The transformation was found to be reversible, as on raising the temperature the crystal reverted to monoclinic form (I). In the asymmetric unit of form (I), Z′ = 1, while in form (II), Z′ = 2, with a very small reduction (ca 1.8%) in the unit‐cell volume. The two independent molecules (A and B) in form (II) are related by a pseudo‐twofold screw axis along the b axis. The molecular overlay of molecule A on molecule B has an r.m.s. deviation of 0.353 Å, with the largest distance between two equivalent atoms being 1.202 Å. The reaction of calix[4]pyrrolidine, the fully reduced form of meso‐octamethylporphyrinogen, with FeCl₃ gave a red–brown solid that was recrystallized from ethanol in air, resulting in the formation of the title compound. In both forms, (I) and (II), the Fe^III atoms are coordinated to the macrocyclic ligand and have distorted octahedral FeN₄OCl coordination spheres. These Fe^III atoms lie out of the mean plane of the four N atoms, displaced towards the O atom of the [OFeCl₃] unit by 0.2265 (5) Å in form (I), and by 0.2210 (14) and 0.2089 (14) Å, respectively, in the two independent molecules (A and B) of form (II). The geometry of the [OFeCl₃] units are similar, with each Fe^III atom having a tetrahedral coordination sphere. The NH H atoms are directed below the planes of the macrocycles and are hydrogen bonded to the coordinated Cl⁻ ions. There are also intramolecular C—H...Cl hydrogen bonds present in both (I) and (II). In form (I), there are no significant intermolecular interactions present. In form (II), the individual molecules are arranged in alternate layers parallel to the ac plane. The B molecules are linked by a C—H...Cl hydrogen bond, forming chains along [100].     

A counterexample to the reconstruction of <Emphasis Type="Italic">ω</Emphasis>-categorical structures from their endomorphism monoid

We present an example of two countable ω-categorical structures, one of which has a finite relational language, whose endomorphism monoids are isomorphic as abstract monoids, but not as topological monoids—in other words, no isomorphism between these monoids is a homeomorphism. For the same two structures, the automorphism groups and polymorphism clones are isomorphic, but not topologically isomorphic. In particular, there exists a countable ω-categorical structure in a finite relational language which can neither be reconstructed up to first-order biinterpretations from its automorphism group, nor up to existential positive bi-interpretations from its endomorphism monoid, nor up to primitive positive bi-interpretations from its polymorphism clone.     

Data Analysis: Keeping Pace with Extraordinary Change

It is a very exciting time in the field of macromolecular crystallography for those of us who are fortunate enough to be involved in the development of instrumentation and software methods. The driver for much of this change has been the remarkable developments in synchrotron light sources and beamline instrumentation over the last two decades. In the 1990s, the ESRF, APS, and SPring-8 set the tone for many of these developments and the 2000s capitalized on them by seeding a host of medium-energy national light sources around the world.     

Regioselectivity in the Intramolecular Heck Reaction of a Series of Cyclic Sulfonamides: An Experimental and Computational Study

Regioselectivity in the intramolecular Heck reaction of a series of N‐sulfonyl‐2,5‐dihydro‐3‐substituted pyrroles was studied. These substrates are unbiased in terms of the formed ring size of the new heterocycle. Results indicate that high levels of regioselectivity are observed under a range of conditions, and that there is an underlying propensity for carbon–carbon bond formation at the most hindered end of the alkene. For two examples (3‐Me and 3‐tBu), DFT calculations were performed and indicate that in both cases, the modelled transition state for carbopalladation is energetically lower for the experimentally preferred isomer.     

Discrete Morse Theory for Computing Cellular Sheaf Cohomology

Sheaves and sheaf cohomology are powerful tools in computational topology, greatly generalizing persistent homology. We develop an algorithm for simplifying the computation of cellular sheaf cohomology via (discrete) Morse theoretic techniques. As a consequence, we derive efficient techniques for distributed computation of (ordinary) cohomology of a cell complex.