Self-assembly of tetrahedral and trigonal antiprismatic clusters [Fe4(L4)4] and [Fe6(L5)6] on the basis of trigonal tris-bidentate chelators

In a one-pot reaction, the tetranuclear iron chelate complex [Fe4(L4)4] 6 was generated from benzene-1,3,5-tricarboxylic acid trichloride (4), bis-tert-butyl malonate (5a), methyllithium, and iron(II) dichloride under aerobic conditions. Alternatively, hexanuclear iron chelate complex [Fe(L5)6] 7 was formed starting from bis-para-tolyl malonate (5b) by employing identical reaction conditions to those applied for the synthesis of 6. The clusters 6 and 7 are present as racemic mixtures of homoconfigurational (delta,delta,delta,delta)/(lambda,lambda,lambda,lambda)-fac or (delta,delta,delta,delta,delta,delta)/(lambda,lambda,lambda,lambda,lambda,lambda)-fac stereoisomers. The structures of 6 and 7 were unequivocally resolved by single-crystal X-ray analyses. The all-iron(III) character of 6 and 7 was determined by M?ssbauer spectroscopy.     

Modeling features of the non-heme diiron cores in O2-activating enzymes through the synthesis, characterization, and oxidation of 1,8-naphthyridine-based complexes

Multidentate naphthyridine-based ligands were used to prepare a series of diiron(II) complexes. The compound [Fe(2)(BPMAN)(mu-O(2)CPh)(2)](OTf)(2) (1), where BPMAN = 2,7-bis[bis(2-pyridylmethyl)aminomethyl]-1,8-naphthyridine, exhibits two reversible oxidation waves with E(1/2) values at +310 and +733 mV vs Cp(2)Fe(+)/Cp(2)Fe, as revealed by cyclic voltammetry. Reaction with O(2) or H(2)O(2) affords a product with optical and M?ssbauer properties that are characteristic of a (mu-oxo)diiron(III) species. The complexes [Fe(2)(BPMAN)(mu-OH)(mu-O(2)CAr(Tol))](OTf)(2) (2) and [Fe(2)(BPMAN)(mu-OMe)(mu-O(2)CAr(Tol))](OTf)(2) (3) were synthesized, where Ar(Tol)CO(2)(-) is the sterically hindered ligand 2,6-di(p-tolyl)benzoate. Compound 2 has a reversible redox wave at +11 mV, and both 2 and 3 react with O(2), via a mixed-valent Fe(II)Fe(III) intermediate, to give final products that are also consistent with (mu-oxo)diiron(III) species. The paddle-wheel compound [Fe(2)(BBAN)(mu-O(2)CAr(Tol))(3)](OTf) (4), where BBAN = 2,7-bis(N,N-dibenzylaminomethyl)-1,8-naphthyridine, reacts with dioxygen to yield benzaldehyde via oxidative N-dealkylation of a benzyl group on BBAN, an internal substrate. In the presence of bis(4-methylbenzyl)amine, the reaction also produces p-tolualdehyde, revealing oxidation of an external substrate. A structurally related compound, [Fe(2)(BEAN)(mu-O(2)CAr(Tol))(3)](OTf) (5), where BEAN = 2,7-bis(N,N-diethylaminomethyl)-1,8-naphthyridine, does not undergo N-dealkylation, nor does it facilitate the oxidation of bis(4-methylbenzyl)amine. The contrast in reactivity of 4 and 5 is attributed to a difference in accessibility of the substrate to the diiron centers of the two compounds. The M?ssbauer spectroscopic properties of the diiron(II) complexes were also investigated.     

Die metrisierbaren linearen Teilräume des Raumes\mathfrak{O}_M von L. Schwartz

In Schwartz' terminology, a real or complex valued functionf, defined and infinitely differentiable on ? _n , belongs to \(\mathfrak{O}_M \) iff, as well as any of its derivatives, is at most of polynomial growth. The topology of \(\mathfrak{O}_M \) is defined by the seminorms sup{∣?(x)D ^p f(x)∣;x∈? ⁿ }, where ? belongs to \(\mathfrak{S}\) andD ^p is any derivative. It is well-known that \(\mathfrak{O}_M \) is non-metrisable. For any μ: ? ⁿ →?, let \(\mathfrak{B}_\mu \) be the space of all infinitely differentiable functionsf satisfying, for eachp, sup{∣(1+∣x∣²)^?μ(p) D ^p f(x)∣;x∈? ⁿ }<∞, with the obvious topology. These spaces, which are of very little use elsewhere in the theory of distributions, can be conveniently applied to characterise the metrisable linear subspaces of \(\mathfrak{O}_M \) : A linear subspace of \(\mathfrak{O}_M \) is metrisable if and only if it is, algebraically and topologically, a subspace of some \(\mathfrak{B}_\mu \) .     

Condis Crystals of Small Molecules III. Thermal Analysis of Plastic and Condis Crystals of some Cyclosilanes

Three cyclic methyl and ethyl substituted silanes were synthesized and their thermal properties analyzed. All show a plastic crystalline state which permits also ring and/or side-chain conformational motion as judged from the enthalpies of transition to the isotropic state. Heat capacity data and entropies of disordering into the plastic crystal leave open the possibility of a condis (conformationally disordered) state below the plastic crystal state with a continuous, transitionless freezing of the conformational motion at lower temperature.     

From Low- to High-Dimensional Moments Without Magic

We aim to compute the first few moments of a high-dimensional random vector from the first few moments of a number of its low-dimensional projections. To this end, we identify algebraic conditions on the set of low-dimensional projectors that yield explicit reconstruction formulas. We also provide a computational framework, with which suitable projectors can be derived by solving an optimization problem. Finally, we show that randomized projections permit approximate recovery.