Nanoscale Organolanthanum Clusters: Nuclearity-Directing Role of Cyclopentadienyl and Halogenido Ligands

Tetramethylaluminato/halogenido(X) ligand exchange reactions in half-sandwich complexes [Cp^RLa(AlMe₄)₂] are feasible in non-coordinating solvents and provide access to large coordination clusters of the type [Cp^RLaX₂]_x. Incomplete exchange reactions generate the hexalanthanum clusters [Cp^R₆La₆X₈(AlMe₄)₄] (Cp^R=Cp*=C₅Me₅, X=I; Cp^R=Cp′=C₅H₄SiMe₃, X=Br, I). Treatment of [Cp*La(AlMe₄)₂] with two equivalents Me₃SiI gave the nonalanthanum cluster [Cp*LaI₂]₉, while the exhaustive reaction of [Cp′La(AlMe₄)₂] with the halogenido transfer reagents Me₃GeX and Me₃SiX (X=I, Br, Cl) produced a series of monocyclopentadienyl rare-earth-metal clusters with distinct nuclearity. Depending on the halogenido ion size the homometallic clusters [Cp′LaCl₂]₁₀ and [Cp′LaX₂]₁₂ (X=Br, I) could be isolated, whereas different crystallization techniques led to the aggregation of clusters of distinct structural motifs, including the desilylated cyclopentadienyl-bridged cluster [(μ-Cp)₂Cp′₈La₈I₁₄] and the heteroaluminato derivative [Cp′₁₀La₁₀Br₁₈(AlBr₂Me₂)₂]. The use of the Cp′ ancillary ligand facilitates cluster characterization by means of NMR spectroscopy.     

Cold heteromolecular dipolar collisions

Cold molecules promise to reveal a rich set of novel collision dynamics in the low-energy regime. By combining for the first time the techniques of Stark deceleration, magnetic trapping, and cryogenic buffer gas cooling, we present the first experimental observation of cold collisions between two different species of state-selected neutral polar molecules. This has enabled an absolute measurement of the total trap loss cross sections between OH and ND(3) at a mean collision energy of 3.6 cm(-1) (5 K). Due to the dipolar interaction, the total cross section increases upon application of an external polarizing electric field. Cross sections computed from ab initio potential energy surfaces are in agreement with the measured value at zero external electric field. The theory presented here represents the first such analysis of collisions between a (2)Π radical and a closed-shell polyatomic molecule.     

Concerning the mechanism of a cyanometallate mediated carbonylation reaction

The [Ni(CN)₂(CO)₂]^2? anion (I) reacts with either one or two equivalents of benzyl bromide in either water/acetone or anhydrous acetonitrile to produce mainly 1,3-diphenyl-2-propanone. Excess carbon monoxide inhibits the reaction. These results are interpreted as indicating that I is an intermediate in the reaction of K₄[Ni₂(CN)₆] with CO and PhCH₂Br to form 1,3-diphenyl-2-propanone.     

NH(a1Δ → X3Σ−) emission from the gas-phase photolysis of HN3

During ArF laser (193 nm) photolysis of HN₃, a spectrum of the emission from the highly forbidden NH(a¹Δ → X³Σ^?) transition has     

Mitigation of loss within a molecular Stark decelerator

The transverse motion inside a Stark decelerator plays a large role in the total efficiency of deceleration. We differentiate between two separate regimes of molecule loss during the slowing process. The first mechanism involves distributed loss due to coupling of transverse and longitudinal motion, while the second is a result of the rapid decrease of the molecular velocity within the final few stages. In this work, we describe these effects and present means for overcoming them. Solutions based on modified switching time sequences with the existing decelerator geometry lead to a large gain of stable molecules in the intermediate velocity regime, but fail to address the loss at very low final velocities. We propose a new decelerator design, the quadrupole-guiding decelerator, which eliminates distributed loss due to transverse/longitudinal couplings throughout the slowing process and also exhibits gain over normal deceleration to the lowest velocities.     

Weighted Gaussian entropy and determinant inequalities

Aequationes mathematicae - We produce a series of results extending information-theoretical inequalities (discussed by Dembo–Cover–Thomas in 1988–1991) to a weighted version of...     

Translation groups of Steiner loops

If the order of any product of two different translations of a finite Steiner quasigroup of size n>3 is odd, then the group G generated by the translations of the corresponding Steiner loop of order n+1 contains the alternating group of degree n+1.     

Weighted entropy and optimal portfolios for risk-averse Kelly investments

Following a series of works on capital growth investment, we analyse log-optimal portfolios where the return evaluation includes ‘weights’ of different outcomes. The results are twofold: (A) under certain conditions, the logarithmic growth rate leads to a supermartingale, and (B) the optimal (martingale) investment strategy is a proportional betting. We focus on properties of the optimal portfolios and discuss a number of simple examples extending the well-known Kelly betting scheme. An important restriction is that the investment does not exceed the current capital value and allows the trader to cover the worst possible losses. The paper deals with a class of discrete-time models. A continuous-time extension is a topic of an ongoing study.