La3Br3Ni: Jahn–Teller Distortion in the Reduced Rare Earth Metal Halide

A ternary lanthanum bromide La₃Br₃Ni was synthesized from lanthanum, LaBr₃ and nickel under argon at 800 °C. It crystallizes in the tetragonal space group I4₁22 (No. 98) with lattice constants a = 12.1758(9) Å and c = 11.744(2) Å. The structure is derived from the cubic Gd₃I₃C type of space group I4₁32 through a tetragonal distortion resulting in a squeezed nickel‐centered La₆ octahedron. Electronic structure and bonding of the compound have been investigated.     

Lundberg’s risk process with tax

In this paper we extend the classical Cramér–Lundberg risk model by including tax payments. The considered tax rule is to pay a certain proportion of the premium income, whenever the portfolio is in a profitable situation. It is shown that the resulting survival probability is a power of the survival probability without tax. Furthermore, an explicit expression for the expected discounted total sum of tax payments until ruin according to this taxation rule is derived and the optimal starting level for taxation is determined. Finally, numerical illustrations of the results are given for the case of exponential claim amounts.     

Cyclo-oligomerization of isocyanates with Na(PH2) or Na(OCP) as “P–” anion sources

We show that the 2-phosphaethynolate anion, OCP^–, is a simple and efficient catalyst for the cyclotrimerization of isocyanates. This process proceeds step-wise and involves five-membered heterocycles, namely 1,4,2-diazaphospholidine-3,5-dionide anions and spiro-phosphoranides as detectable intermediates, both of which were also found to be involved in the catalytic conversion. These species can be considered as adducts of a phosphide anion with two and four isocyanate molecules, respectively, demonstrating that the OCP^– anion acts as a formal “P^–” source. The interconversion between these anionic species was found to be reversible, allowing them to serve as reservoirs for unique phosphorus-based living-catalysts for isocyanate trimerization.     

A tetracoordinated rhodium aminyl radical complex

A [16 + 1] valence electron configured rhodium aminyl radical complex could be synthesized and characterized in detail by pulse EPR spectroscopy and DFT calculations. The unpaired electron is delocalized over the metal center and two adjacent nitrogens. H-abstraction reactions from thiols and triethylsilane show that the spin density is predominantly localized on both nitrogens.     

A synthetic cycle for the ruthenium-promoted formation of 1H-phosphindoles from phosphaalkynes

Beginning with inexpensive and commercially available starting materials, a rational synthesis for the new phosphaalkyne Ph3C-C[triple bond]P (1) is presented. Coordination of 1 to group 8 transition metal centers furnishes the eta1-complexes [MH(dppe)2(Ph3CC[triple bond]P)]OTf, where M = Fe (3) or Ru (4) (dppe = bis-1,2-diphenylphosphinoethane). Treatment of 3 or 4 with a strong acid cyclizes the coordinated phosphaalkyne and is the first example of an electrophilic aromatic substitution reaction in which the electrophile is a low coordinate phosphorus. With the aid of DFT calculations, we were able to gain a more thorough understanding of the energetics and mechanism of this new cyclization reaction. Thermolysis of the iron-3,3-diphenyl-3H-phosphindole adduct (6) in CH3CN results in quantitative formation of the free 3H-phosphindole (7). Alternatively, when ruthenium-3,3-diphenyl-3H-phosphindole adduct (5) is irradiated, a photochemical rearrangement occurs furnishing 2,3-diphenyl-1H-phosphindole (9). Mechanistic work is presented that provides an explanation for this transformation. Compounds 1, 3, 5, and 9 have been characterized by single X-ray diffraction studies. Finally, a synthetic cycle for the conversion of 1 to 1H-phosphindole 9 has been developed that recycles the ruthenium cation [RuH(dppe)2]+.     

KCaEr2CuS5: a new pentanary rare-earth layered chalcogenide without substitutional disorder

A new pentanary rare-earth chalcogenide without substitutional disorder, KCaEr2CuS5, was obtained from reaction of the Er-Ca-Cu-S precursor with KBr flux by either a two-step flux method or a direct reaction of the mixture of the binary components (1Cu2S:2Er2S3:3CaS) with excess KBr as flux. KCaEr2CuS5 crystallizes in the orthorhombic space group Cmcm (No. 63) with a = 3.9327(5) A, b = 13.410(2) A, c = 17.042(2) A, V = 898.8(3) A(3), Z = 4, R = 0.0632, and Rw = 0.0627. The KCaEr2CuS5 structure consists of four different building units: ErS6 octahedra, CaS6 octahedra, CuS4 tetrahedra, and KS6 trigonal prisms; it is characterized by [Er2CuS5]3- layers that are formed by the interconnection of double ErS6 octahedral chains with CuS4 tetrahedral chains in the a-c plane. K+ and Ca2+ cations are located in the cavities defined by S2- anions between the [Er2CuS5]3- layers. KCaEr2CuS5 is a semiconductor with an estimated band gap of 2.4 eV and shows a Curie-Weiss paramagnetic behavior in the 5-300 K range.     

Seifert fibrations of lens spaces

We classify the Seifert fibrations of any given lens space L(p, q). Starting from any pair of coprime non-zero integers \(\alpha _1^0,\alpha _2^0\), we give an algorithmic construction of a Seifert fibration \(L(p,q)\rightarrow S^2(\alpha |\alpha _1^0|,\alpha |\alpha _2^0|)\), where the natural number \(\alpha \) is determined by the algorithm. This algorithm produces all possible Seifert fibrations, and the isomorphisms between the resulting Seifert fibrations are described completely. Also, we show that all Seifert fibrations are isomorphic to certain standard models.