Flat Forms in Banach Spaces

We define a flat partial differential form in a Banach space and show that the space of these forms is isometrically the dual space of the space of flat chains as defined by T. Adams.     

Inter-laboratory exercise with an aim to compare methods for 90Sr and 239,240Pu determination in environmental soil samples

In order to deliver reliable results for a multitude of different scenarios, e.g. emergency preparedness, environmental monitoring, nuclear decommissioning and waste management, there is a constant process of method development in the field of radioanalytical chemistry. This work presents the results of a method comparison exercise aimed at quantifying ⁹⁰Sr and ^239,240Pu in environmental soil samples, with the intention of evaluating the performance and applicability of different methods. From the methods examined in this work, recommendations are given in order to find a radioanalytical measurement procedure, for ⁹⁰Sr and ^239,240Pu analysis, which is fit-for-purpose for a particular scenario.

     

Bonding in Barium Boryloxides,Siloxides, Phenoxides and Silazides: A Comparison with the Lighter Alkaline Earths

Barium complexes ligated by bulky boryloxides [OBR₂]⁻ (where R=CH(SiMe₃)₂, 2,4,6-ⁱPr₃-C₆H₂ or 2,4,6-(CF₃)₃-C₆H₂), siloxide [OSi(SiMe₃)₃]⁻, and/or phenoxide [O-2,6-Ph₂-C₆H₃]⁻, have been prepared. A diversity of coordination patterns is observed in the solid state for both homoleptic and heteroleptic complexes, with coordination numbers ranging between 2 and 4. The identity of the bridging ligand in heteroleptic dimers [Ba(μ₂-X₁)(X₂)]₂ depends largely on the given pair of ligands X₁ and X₂. Experimentally, the propensity to fill the bridging position increases according to [OB{CH(SiMe₃)₂}₂)]⁻<[N(SiMe₃)₂]⁻<[OSi(SiMe₃)₃]⁻<[O(2,6-Ph₂-C₆H₃)]⁻<[OB(2,4,6-ⁱPr₃-C₆H₂)₂]⁻. This trend is the overall expression of 3 properties: steric constraints, electronic density and σ- and π-donating capability of the negatively charged atom, and ability to generate Ba ⋅ ⋅ ⋅ F, Ba ⋅ ⋅ ⋅ C(π) or Ba ⋅ ⋅ ⋅ H−C secondary interactions. The comparison of the structural motifs in the complexes [Ae{μ₂-N(SiMe₃)₂}(OB{CH(SiMe₃)₂}₂)]₂ (Ae = Mg, Ca, Sr and Ba) suggest that these observations may be extended to all alkaline earths. DFT calculations highlight the largely prevailing ionic character of ligand-Ae bonding in all compounds. The ionic character of the Ae-ligand bond encourages bridging coordination, whereas the number of bridging ligands is controlled by steric factors. DFT computations also indicate that in [Ba(μ₂-X₁)(X₂)]₂ heteroleptic dimers, ligand predilection for bridging vs. terminal positions is dictated by the ability to establish secondary interactions between the metals and the ligands.     

Alkoxyallene‐ynes: Selective Preparation of Bicyclo[5.3.0] Ring Systems Including a δ‐Alkoxy Cyclopentadienone

The development of an intramolecular rhodium(I)‐catalyzed Pauson–Khand reaction of alkoxyallene‐ynes with a proximal alkoxy group is reported. This reaction, in the presence of a [Rh(cycloocta‐1,5‐diene)Cl]₂/propane‐1,3‐diylbis(diphenylphosphane) system under a CO atmosphere, constitutes a powerful tool for selectively accessing carbo‐ and heterobicyclo[5.3.0] frameworks featuring an enol ether moiety. Through this procedure, a straightforward access to guaiane skeletons with a tertiary hydroxy group at the C10 position was achieved.