Switching on oxygen activation by cobalt complexes of pentadentate ligands

The monoanionic N(4)O ligand N-methyl-N,N'-bis(2-pyridylmethyl)ethylenediamine-N'-acetate (mebpena(-)) undergoes oxidative C-N bond cleavage in the presence of Co(II) and O(2). The two resultant fragments are coordinated to the metal ion in the product [Co(III)(2-pyridylformate)(mepena)]ClO(4) (mepena(-) = N-methyl-N'-(2-pyridylmethyl)ethylenediamine-N'-acetato). Bond cleavage does not occur in the presence of chloride ions and [Co(III)(mebpena)Cl](+), containing intact mebpena(-), can be isolated. The oxidative instability of the mebpena(-) in the presence of Co(II) and air stands in contrast to the oxidative stability of the family of very closely related penta- and hexa-dentate ligands in their cobalt complexes. Cyclic voltammetry on the matched pair [Co(III)Cl(mebpena)](+) and [Co(II)Cl(bztpen)](+), bztpen = N-benzyl-N,N',N'-tris(2-pyridylmethyl)ethylenediamine, shows that substitution of a pyridine donor for a carboxylato donor results in a relatively small cathodic shift of 150 mV in the E°(Co(II)/Co(III)) oxidation potential, presumably this is enough to determine the contrasting metal oxidation state in the complexes isolated under ambient conditions. DFT calculations support a proposal that [Co(II)(mebpena)](+) reacts with O(2) to form a Co(III)-superoxide complex which can abstract an H atom from a ligand methylene C atom as the initial step towards the observed oxidative C-N bond cleavage.     

On the mechanism of water oxidation by a bimetallic manganese catalyst: a density functional study

Density functional theory is used to explore possible mechanisms that lead to water oxidation by a bimetallic manganese catalyst developed by McKenzie and co-workers. On the basis of our calculations we propose that the key active intermediate is a mixed valent Mn(III)(μ-O)Mn(IV)-O˙ oxyl radical species, the oxyl centre being the site of nucleophilic attack by water. The mixed-valent species is in equilibrium with an isomeric diamond-core Mn(IV)(μ-O)(2)Mn(IV) structure, which acts as reservoir for the active species. The chemistry appears to be unique to pentadentate ligands because these shift the position of the equilibrium between the Mn(III)(μ-O)Mn(IV)-O˙ and Mn(IV)(μ-O)(2)Mn(IV) isomers, such that significant concentrations of the former are present in solution.     

New results for the formation of a muoniated radical in the Mu + Br2 system: a van der Waals complex or evidence for vibrational bonding in Br-Mu-Br?

New evidence is presented for the observation of a muoniated radical in the Mu + Br(2) system, from μSR longitudinal field (LF) repolarisation studies in the gas phase, at Br(2) concentrations of 0.1 bar in a Br(2)/N(2) mixture at 300 K and at 10 bar total pressure. The LF repolarisation curve, up to a field of 4.5 kG, reveals two paramagnetic components, one for the Mu atom, formed promptly during the slowing-down process of the positive muon, with a known Mu hyperfine coupling constant (hfcc) of 4463 MHz, and one for a muoniated radical formed by fast Mu addition. From model fits to the Br(2)/N(2) data, the radical component is found to have an unusually high muon hfcc, assessed to be ～3300 MHz with an overall error due to systematics expected to exceed 10%. This high muon hfcc is taken as evidence for the observation of either the Br-Mu-Br radical, and hence of vibrational bonding in this H[combining low line]-L[combining low line]-H[combining low line] system, or of a MuBr(2) van der Waals complex formed in the entrance channel. Preliminary ab initio electronic structure calculations suggest the latter is more likely but fully rigorous calculations of the effect of dynamics on the hfcc for either system have yet to be carried out.     

Finitely Related Clones and Algebras with Cube Terms

Aichinger et al. (2011) have proved that every finite algebra with a cube-term (equivalently, with a parallelogram-term; equivalently, having few subpowers) is finitely related. Thus finite algebras with cube terms are inherently finitely related??every expansion of the algebra by adding more operations is finitely related. In this paper, we show that conversely, if A is a finite idempotent algebra and every idempotent expansion of A is finitely related, then A has a cube-term. We present further characterizations of the class of finite idempotent algebras having cube-terms, one of which yields, for idempotent algebras with finitely many basic operations and a fixed finite universe A, a polynomial-time algorithm for determining if the algebra has a cube-term. We also determine the maximal non-finitely related idempotent clones over A. The number of these clones is finite.     

Definability in substructure orderings, IV: Finite lattices

Let ${\mathcal{L}}$ be the ordered set of isomorphism types of finite lattices, where the ordering is by embeddability. We study first-order definability in this ordered set. Our main result is that for every finite lattice L, the set {?, ? ^opp} is definable, where ? and ? ^opp are the isomorphism types of L and its opposite (L turned upside down). We shall show that the only non-identity automorphism of ${\mathcal{L}}$ is the map ${\ell \mapsto \ell^{\rm opp}}$ .     

Strongly etale extensions and weak henseliziations

Abstract

Since the circulation, in 1974, of the first draft of “The construction D + XD _S [X], J. Algebra 53 (1978), 423–439” a number of variations of this construction have appeared. Some of these are: The generalized D + M construction, the A + (X)B[X] construction, with X a single variable or a set of variables, and the D + I construction (with I not necessarily prime). These constructions have proved their worth not only in providing numerous examples and counter examples in commutative ring theory, but also in providing statements that often turn out to be forerunners of results on general pullbacks. The aim of this paper will be to discuss these constructions and the remarkable uses they have been put to. I will concentrate more on the A + XB[X] construction, its basic properties and examples arising from it.     

Definability in Substructure Orderings,II: Finite Ordered Sets

Let \({{\uppercase {\mathcal{p}}}} \) be the ordered set of isomorphism types of finite ordered sets (posets), where the ordering is by embeddability. We study first-order definability in this ordered set. We prove among other things that for every finite poset P, the set \(\{p,p^{\partial}\}\) is definable, where p and \(p^{\partial}\) are the isomorphism types of P and its dual poset. We prove that the only non-identity automorphism of \({{\uppercase {\mathcal{p}}}}\) is the duality map. Then we apply these results to investigate definability in the closely related lattice of universal classes of posets. We prove that this lattice has only one non-identity automorphism, the duality map; that the set of finitely generated and also the set of finitely axiomatizable universal classes are definable subsets of the lattice; and that for each member K of either of these two definable subsets, \(\{K,K^{\partial}\}\) is a definable subset of the lattice. Next, making fuller use of the techniques developed to establish these results, we go on to show that every isomorphism-invariant relation between finite posets that is definable in a certain strongly enriched second-order language \(\textup{\emph L}_2\) is, after factoring by isomorphism, first-order definable up to duality in the ordered set \({{\uppercase {\mathcal{p}}}}\). The language \(\textup{\emph L}_2\) has different types of quantifiable variables that range, respectively, over finite posets, their elements and order-relation, and over arbitrary subsets of posets, functions between two posets, subsets of products of finitely many posets (heteregenous relations), and can make reference to order relations between elements, the application of a function to an element, and the membership of a tuple of elements in a relation.     

Congruence modularity implies cyclic terms for finite algebras

An n-ary operation f : A ⁿ → A is called cyclic if it is idempotent and ${f(a_1, a_2, a_3, \ldots , a_n) = f(a_2, a_3, \ldots , a_n, a_1)}$ for every ${a_1, \ldots, a_n \in A}$ . We prove that every finite algebra A in a congruence modular variety has a p-ary cyclic term operation for any prime p greater than |A|.     

Clones satisfying the term condition

The term condition considered here is the property of an operation ? that holds iff ? and all of its variants obtained by permuting the variables satisfy (for all x,y,u₁,…v₁,…)$\text{?(x,u}{}_1\text{,…) = ?(x,v}{}_1\text{…)??(y,u}{}_1\text{,…) = ?(y,v)}{}_1\text{,…)}$. Clones consisting entirely of operations satisfying this term condition are called TC clones; algebras whose clone of term operations is a TC clone are called TC algebras; varieties such that every algebra in the variety is a TC algebra are called TC varieties. The paper is a systematic study of these notions, giving primary attention to operations and algebras on finite base sets, and to varieties generated by finite algebras. It is proved, among other results, that the number of n-ary TC operations on a k-element set is logarithmically asymptotic to k^(k?1)n when n increases without bound and k is held fixed; that there exist only countably many TC clones on any finite set; that the maximal TC clones on a finite set are finite in number (for each set). Some necessary conditions for an algebra to generate a TC variety are given, also some sufficient conditions.     

Extraction of structural information from measured transport properties of composites

We describe clearly Milton's bounds on the scalar transport properties of composite materials in the case when no geometrical information is known about the composite, but when a set of measured values of a transport property is available. We consider how the measured values may be used when they are subject to known errors. In this case, a statistical analysis is employed. We illustrate the various conclusions which may result from this analysis by considering six cases involving both two-and three-dimensional composites. In four of the six cases, estimates of the volume fraction of the composite in agreement with the known value are obtained. In the fifth case, the analysis pointed out a possible error in the experimental data, while in the sixth it revealed a critical dependence of transport properties on composite geometry due to filamentary linking between particles.