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.     

Polynomial Reproduction in Subdivision

We study conditions on the matrix mask of a vector subdivision scheme ensuring that certain polynomial input vectors yield polynomial output again. The conditions are in terms of a recurrence formula for the vectors which determine the structure of polynomial input with this property. From this recurrence, we obtain an algorithm to determine polynomial input of maximal degree. The algorithm can be used in the design of masks to achieve a high order of polynomial reproduction.     

Investigation of acceptor centers in semiconductors with the diamond crystal structure by the μ − SR method

The residual polarization of negative muons in crystal silicon samples with phosphorus (P: 1.6×10¹³ cm⁻³) and antimony (Sb: 2×10¹⁸ cm⁻³) impurities is investigated. The measurements are made in a 1000 G magnetic field oriented in a direction transverse to the muon spin in the temperature range 4–300 K. The relaxation rate and shift of the precession frequency in the silicon sample with the phosphorus impurity are measured more accurately than previously. It is found that in antimony-doped silicon the acceptor center _μ A1 at temperatures below 30 K can be in both ionized and neutral states. The experimental data are interpreted on the basis of spin-lattice relaxation of the magnetic moment of an acceptor center, formation of acceptor-donor pairs, and recombination of charge carriers at the acceptor. Preliminary measurements showed a nonzero residual polarization of negative muons in germanium. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 1, 61–66 (10 July 1998)     

A constructive characterization of the split closure of a mixed integer linear program

Two independent proofs of the polyhedrality of the split closure of mixed integer linear program have been previously presented. Unfortunately neither of these proofs is constructive. In this paper, we present a constructive version of this proof. We also show that split cuts dominate a family of inequalities introduced by Köppe and Weismantel.     

Automorphisms of Green Orders and Their Derived Categories

In an earlier paper, Raphaël Rouquier and the author introduced the group of self-equivalences of a derived category. In the case of a Brauer tree algebra, we determined a nontrivial homomorphism of the Artin braid group to this group of self-equivalences. The class of Brauer tree algebras include blocks of finite group rings over a large enough field with cyclic defect groups. In the present paper we give an integral version of this homomorphism. Moreover, we identify some interesting arithmetic subgroups with natural groups of self-equivalences of the derived category.     

Dynamics in molecular crystals: An application of proton NMR to selectively protonated biphenyl. Do the rings flip together or independently?

The synthesis of a specific isotopomer, C₆D₄H(ortho)-H(ortho)D₄C₆ of biphenyl is reported. The intramolecular dipolar coupling of the protons leads to a well-resolved single-crystal proton nuclear magnetic resonance (NMR) spectrum and allows one to study the dynamics of the phenyl rings in a unique way. At room temperature and above, the most conspicuous dynamical mode consists of 180° ring flips. The present data together with previous measurements of the total flip rate allow us to conclude that the rings flip almost exclusively independently of each other. Between the incommensurate (IC) phase transition of biphenyl at 38 K andT=250 K, the prominent namical mode consists of oscillatory twists ϕ(t) of the two rings. The data allow us to infer the mean square, (φ²), of these twists. (φ²) is found to grow linearly withT for 50<T<200 K. From the slope of (φ²) vs.T the frequency (the wave number[(v)\tilde]\tilde v) is derived. The result is[(v)\tilde] = 20\tilde v = 20 cm⁻¹. ForT<38 K, the spectra give direct evidence of the IC phase transition and its nature (stripelike rather than quiltlike). The temperature dependence of the magnitude of the order parameter of the IC phase is obtained.