Lanthanide SMMs Based on Belt Macrocycles: Recent Advances and General Trends

Enhancement of axial magnetic anisotropy is the central objective to push forward the performance of Single-Molecule Magnet (SMM) complexes. In the case of mononuclear lanthanide complexes, the chemical environment around the paramagnetic ion must be tuned to place strongly interacting ligands along either the axial positions or the equatorial plane, depending on the oblate or prolate preference of the selected lanthanide. One classical strategy to achieve a precise chemical environment for a metal centre is using highly structured, chelating ligands. A natural approach for axial-equatorial control is the employment of macrocycles acting in a belt conformation, providing the equatorial coordination environment, and leaving room for axial ligands. In this review, we present a survey of SMMs based on the macrocycle belt motif. Literature systems are divided in three families (crown ether, Schiff-base and metallacrown) and their general properties in terms of structural stability and SMM performance are briefly discussed.     

Liouville theorem for weighted p-Lichnerowicz equation on smooth metric measure space

In this paper, let $(M^n,g,d\mu )$ be n-dimensional noncompact metric measure space which satisfies Poincaré inequality with some Ricci curvature condition. We obtain a Liouville theorem for positive weak solutions to weighted p-Lichnerowicz equation

${△}_{p,f}v+c{v}^{\sigma }=0,$

where $c\le 0,m>n\ge 1,1<p<\frac{m?1+\sqrt{(m?1)(m+3)}}{2},\sigma \le p?1$ are real constants.     

Mononuclear and Dinuclear Copper Complexes of Tridentate Redox-active Ligands with Tunable H-bonding Donors: Structure,Spectroscopy and H+/e− Reactivity

In this research article, we describe the synthesis and characterization of mononuclear and dinuclear Cu complexes bound by a family of tridentate redox-active ligands with tunable H-bonding donors. The mononuclear Cu-anion complexes were oxidized to the corresponding “high-valent” intermediates by oxidation of the redox-active ligand. These species were capable of oxidizing phenols with weak O−H bonds via H-atom abstraction. Thermodynamic analysis of the H-atom abstractions, which included reduction potential measurements, pK_a determination and kinetic studies, revealed that modification of the anion coordinated to the Cu and changes in the H-bonding donor did not lead to major differences in the reactivity of the “high-valent” CuY complexes (Y: hydroxide, phenolate and acetate), which indicated that the tridentate ligand scaffold acts as the H⁺ and e⁻ acceptor.     

The character and the wave front set correspondence in the stable range

We relate the distribution characters and the wave front sets of unitary representation for real reductive dual pairs of type I in the stable range.     

Extended Open-Chain Polyenides as Versatile Delocalized Anion Ligands for Metal Chain Clusters

Although small cyclic- and open-chain unsaturated hydrocarbon anions such as cyclopentadienide and open-chain pentadienide are used as the strongly electron-donating auxiliary ligands for metal complexes, more extended π-conjugated unsaturated hydrocarbon anions have rarely been used in coordination chemistry, despite their potential ability to serve as the multiply bridging π-ligands for metal clusters. This work reports isolation of metal chain clusters bearing the multi-dentate, open-chain extended unsaturated hydrocarbon anion ligands. The extended open-chain π-conjugated polyenyl ligands could effectively stabilize oxidized palladium chains, including an unprecedented [Pd₄]⁴⁺ chain.     

New ligands for the Fe(III)‐mediated reverse atom transfer radical polymerization of methyl methacrylate

A series of (di)picolinic acids and their derivates are investigated as novel complexing tridentate or bidentate ligands in the iron‐mediated reverse atom transfer radical polymerization of methyl methacrylate in N,N‐dimethylformamide at 100 °C with 2,2′‐azobisisobutyrontrile as an initiator. The polymerization rates and polydispersity indices (1.32–1.8) of the resulting polymers are dependent on the structures of the ligands employed. Different iron complexes may be involved in iron‐mediated reverse atom transfer radical polymerization, depending on the type of acid used. ¹H NMR spectroscopy has been used to study the structure of the resulting polymers. Chain‐extension reactions have been performed to further confirm the living nature of this catalytic system. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2912–2921, 2006     

On the realization of Riemannian symmetric spaces in Lie groups

In this paper we give a realization of some symmetric space G/K as a closed submanifold P of G. We also give several equivalent representations of the submanifold P. Some properties of the set gK∩P are also discussed, where gK is a coset space in G.     

Challenging Students to View the Concept of Area in Triangles in a Broad Context: Exploiting the Features of Cabri-II

This study focuses on the constructions in terms of area and perimeter in equivalent triangles developed by students aged 12–15 years-old, using the tools provided by Cabri-Geometry II [Labore (1990). Cabri-Geometry (software), Université de Grenoble]. Twenty-five students participated in a learning experiment where they were asked to construct: (a) pairs of equivalent triangles “in as many ways as possible” and to study their area and their perimeter using any of the tools provided and (b) “any possible sequence of modifications of an original triangle into other equivalent ones”. As regards the concept of area and in contrast to a paper and pencil environment, Cabri provided students with different and potential opportunities in terms of: (a) means of construction, (b) control, (c) variety of representations and (d) linking representations, by exploiting its capability for continuous modifications. By exploiting these opportunities in the context of the given open tasks, students were helped by the tools provided to develop a broader view of the concept of area than the typical view they would construct in a typical paper and pencil environment.