Size-Controlled Hapticity Switching in [Ln(C9H9)(C8H8)] Sandwiches

Sandwich complexes of lanthanides have recently attracted a considerable amount of interest due to their applications as Single Molecule Magnet (SMM). Herein, a comprehensive series of heteroleptic lanthanide sandwich complexes ligated by the cyclononatetraenyl (Cnt) and the cyclooctatetraenyl (Cot) ligand [Ln(Cot)(Cnt)] (Ln=Tb, Dy, Er, Ho, Yb, and Lu) is reported. The coordination behavior of the Cnt ligand has been investigated along the series and shows different coordination patterns in the solid-state depending on the size of the corresponding lanthanide ion without altering its overall anisotropy. Besides the characterization in the solid state by single-crystal X-ray diffraction and in solution by ¹H NMR, static magnetic studies and ab initio computational studies were performed.     

An Elastic Frictional Contact Problem with Unilateral Constraint

We consider a mathematical model which describes the equilibrium of an elastic body in contact with two obstacles. We derive its weak formulation which is in a form of an elliptic quasi-variational inequality for the displacement field. Then, under a smallness assumption, we establish the existence of a unique weak solution to the problem. We also study the dependence of the solution with respect to the data and prove a convergence result. Finally, we consider an optimization problem associated with the contact model for which we prove the existence of a minimizer and a convergence result, as well.     

Infinitesimal non-crossing cumulants and free probability of type B

Free probabilistic considerations of type B first appeared in the paper of Biane, Goodman and Nica [P. Biane, F. Goodman, A. Nica, Non-crossing cumulants of type B, Trans. Amer. Math. Soc. 355 (2003) 2263-2303]. Recently, connections between type B and infinitesimal free probability were put into evidence by Belinschi and Shlyakhtenko [S.T. Belinschi, D. Shlyakhtenko, Free probability of type B: Analytic aspects and applications, preprint, 2009, available online at www.arxiv.org under reference arXiv:0903.2721]. The interplay between “type B” and “infinitesimal” is also the object of the present paper. We study infinitesimal freeness for a family of unital subalgebras A₁,…,Ak in an infinitesimal noncommutative probability space (A,φ,φ^′) and we introduce a concept of infinitesimal non-crossing cumulant functionals for (A,φ,φ^′), obtained by taking a formal derivative in the formula for usual non-crossing cumulants. We prove that the infinitesimal freeness of A₁,…,Ak is equivalent to a vanishing condition for mixed cumulants; this gives the infinitesimal counterpart for a theorem of Speicher from “usual” free probability. We show that the lattices NC(B)(n) of non-crossing partitions of type B appear in the combinatorial study of (A,φ,φ^′), in the formulas for infinitesimal cumulants and when describing alternating products of infinitesimally free random variables. As an application of alternating free products, we observe the infinitesimal analogue for the well-known fact that freeness is preserved under compression with a free projection. As another application, we observe the infinitesimal analogue for a well-known procedure used to construct free families of free Poisson elements. Finally, we discuss situations when the freeness of A₁,…,Ak in (A,φ) can be naturally upgraded to infinitesimal freeness in (A,φ,φ^′), for a suitable choice of a “companion functional” .     

On the Two Closely Related Phases of [Ru(C5Me5)(η6-1,3-(Me2NCH2)2C6H4)](BF4) and the Reversible Solid–Solid Order–Disorder Phase Transition

Abstract  

Crystals of the complex [Ru(C₅Me₅)(η⁶-1,3-(Me₂NCH₂)₂C₆H₄)](BF₄) have been examined over the temperature range 150–300 K via X-ray diffraction measurements. This study shows that the Ru complex is a two-phase system in this T-range and the solid–solid transition is reversible. At 150 K, phase II (P2₁/c, Z′ = 4) is ordered and non-merohedrally twinned, a = 16.4396 (9) ?, b = 17.3226 (4) ?, c = 32.1874 (11) ?, β = 91.375 (2)°. At 295 K, phase I (Pbca, Z′ = 1) is disordered, a = 8.5071 (3) ?, b = 17.1567 (3) ?, c = 32.8250 (8) ?. The relationship between the two phases is obvious because the packing remains similar in the two phases. The greatest structural changes between the two phases are found in the rows of adjacent cations [Ru(C₅Me₅)(η⁶-1,3-(Me₂NCH₂)₂C₆H₄)]⁺ packed along the a direction. These rows are ordered in phase II but are disordered in phase I. The phase transition is first order. Significant changes in thermal motion for the cations are considered as being the driving force for the occurrence of this phase transition.     

Binding energies in benzene dimers: Nonlocal density functional calculations

The interaction energy and minimum energy structure for different geometries of the benzene dimer have been calculated using the recently developed nonlocal correlation energy functional for calculating dispersion interactions. The comparison of this straightforward and relatively quick density functional based method with recent calculations provides a promising first step to elucidate how the former, quicker method might be exploited in larger more complicated biological, organic, aromatic, and even infinite systems such as molecules physisorbed on surfaces and van der Waals crystals.     

Relevance of linked dye‐coinitiator in visible three‐component photoinitiating systems: Application to red light photopolymerization

A new visible light photoinitiating system (PIS) containing a linked dye‐coinitiator dyad and a nondissociative electron donor was evaluated and compared with unlinked three components systems. Our results show that in the physical mixture of the three component PIS, addition of the nondissociative donor decreased the Rp to a great extent, whereas in combination with the dyads an increase in Rp is observed. The results were explained based on faster intramolecular electron transfer in linked pairs and point out the importance of linked initiator in three‐component PIS for the first time. This system is the first example of three‐components system with a nondissociative donor that would be useful for long life coating formulation. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 4325–4330     

Dioxygen Activation by a Macrocyclic Copper Complex Leads to a Cu2O2 Core with Unexpected Structure and Reactivity

We report the Cu^I/O₂ chemistry of complexes derived from the macrocylic ligands 14‐TMC (1,4,8,11‐tetramethyl‐1,4,8,11‐tetraazacyclotetradecane) and 12‐TMC (1,4,7,10‐tetramethyl‐1,4,7,10‐tetraazacyclododecane). While [(14‐TMC)Cu^I]⁺ is unreactive towards dioxygen, the smaller analog [(12‐TMC)Cu^I(CH₃CN)]⁺ reacts with O₂ to give a side‐on bound peroxo‐dicopper(II) species (^SP), confirmed by spectroscopic and computational methods. Intriguingly, 12‐TMC as a N4 donor ligand generates ^SP species, thus in contrast with the previous observation that such species are generated by N2 and N3 ligands. In addition, the reactivity of this macrocyclic side‐on peroxo‐dicopper(II) differs from typical ^SP species, because it reacts only with acid to release H₂O₂, in contrast with the classic reactivity of Cu₂O₂ cores. Kinetics and computations are consistent with a protonation mechanism whereby the TMC acts as a hemilabile ligand and shuttles H⁺ to an isomerized peroxo core.     

Cooperative Veratryle and Nitroindoline Cages for Two‐Photon Uncaging in the NIR

Tandem uncaging systems in which a two‐photon absorbing module and a cage moiety, linked via a phosphorous clip, that act together by Förster resonance energy transfer (FRET) have been developed. A library of these compounds, using different linkers and cages (7‐nitroindolinyl or nitroveratryl) has been synthesized. The investigation of their uncaging and two‐photon absorption properties demonstrates the scope and versatility of the engineering strategy towards efficient two‐photon cages and reveals surprising cooperative and topological effects. The interactions between the 2PA module and the caging moiety are found to promote cooperative effects on the 2PA response while additional processes that enhance the uncaging efficiency are operative in well‐oriented nitroindoline‐derived dyads. These synergic effects combine to lead to record two‐photon uncaging cross‐section values (i.e., up to 20 GM) for uncaging of carboxylic acids.