Fixed-nuclei and laboratory-frame formalisms for electron scattering by a spherical top,with full incorporation of symmetry

We discuss molecule-frame and laboratory-frame symmetry-adapted formalisms for electron scattering by a spherical top. The molecule-frame formalism is based on the fixed-nuclear-orientation approximation, both for electronically elastic scattering by a vibrationally rigid molecule and also for the more general case where electronic excitation and vibrational degrees of freedom are included. The laboratory-frame formalism is based on the exact symmetries of the problem, which are carefully related to the approximate symmetries of the molecule-frame treatment. We present both the forward and backward transformations between the two representations.     

Theory of chirality functions,generalized for molecules with chiral ligands

The theory of chirality functions described in a previous publication is generalized to allow for chiral ligands. In the earlier theory, all symmetry operations of the molecular frame could be thought of as permutations of the ligands among the sites; in the present work, improper rotations not only permute the ligands, but convert them into mirror images. The group that generates all isomers from a given ordered molecule belonging to a frame with n sites is now the hyperoctahedral group of order 2ⁿ n! consisting of all possible combinations of permutations and site reflections. The representation theory of these groups is described, and applied to the problem of constructing qualitatively complete chirality functions, and of deciding which ligand partitions, and which isomer mixtures, are chiral. It is found useful to classify chiral representations of the covering group as ligand specific and class specific. The ligand specific representations describe chiral properties which are common to all frames and arise purely from the chirality of the ligands, while the class specific representations describe the chiral properties of the frame. A number of examples are explicitly worked out.     

Energetics of the loss of H2 from [C3H7]+

The internal energies of [C₃H₇]⁺ ions contributing to the metastable peak [C₃H₇]⁺ → [C₃H₅]⁺ + H₂ are higher (by perhaps > 100 kJ mol^?1) than those of the ion contributing to the threshold current in appearance energy measurements on [C₃H₅]⁺. The measured appearance energy may lead to an underestimation of the activation energy, i.e. negative ‘kinetic shift’, due to quantum, mechanical tunnelling. The distribution of energy released in the decomposition can be explained on the basis that much of the reverse activation energy and a statistical proportion of the excess energy is released as translation.     

Synthesis of Quinolines from N-Tosyl-1-azadienes

A route to aryl-substituted quinolines from N-tosyl 1-azadienes is described. The key steps are a [4 + 2] cycloaddition with benzyne followed by base treatment of the 1,4-dihydroquinoline product. The N-tosyl 1-azadienes were prepared from readily accessible cinnamaldehyde and chalcone substrates by condensation with p-TsNH₂.

Supplemental materials are available for this article. Go to the publisher's online edition of Synthetic Communications® to view the free supplemental file.     

Development of Magnesium Anode-Based Transient Primary Batteries

Biodegradable primary batteries, also known as transient batteries, are essential to realize autonomous biodegradable electronic devices with high performance and advanced functionality. In this work, magnesium, copper, iron, and zinc – metals that exist as trace elements in the human body – were tested as materials for biomedical transient electronic devices. Different full cell combinations of Mg and X (where X = Cu, Fe, and Zn and the anodized form of the metals) with phosphate buffered saline (PBS) as electrolyte were studied. To form the cathodes, metal foils were anodized galvanostatically at a current density of 2.0 mA cm⁻² for 30 mins. Electrochemical measurements were then conducted for each electrode combination to evaluate full cell battery performance. Results showed that the Mg−Cu_anodized chemistry has the highest power density at 0.99 mW/cm². Nominal operating voltages of 1.26 V for the first 0.50 h and 0.63 V for the next 3.7 h were observed for Mg−Cu_anodized which was discharged at a current density of 0.70 mA cm⁻². Among the materials tested, Mg−Cu_anodized exhibited the best discharge performance with an average specific capacity of 2.94 mAh cm⁻², which is comparable to previous reports on transient batteries.     

Extended formulations in mixed integer conic quadratic programming

In this paper we consider the use of extended formulations in LP-based algorithms for mixed integer conic quadratic programming (MICQP). Extended formulations have been used by Vielma et al. (INFORMS J Comput 20: 438–450, 2008) and Hijazi et al. (Comput Optim Appl 52: 537–558, 2012) to construct algorithms for MICQP that can provide a significant computational advantage. The first approach is based on an extended or lifted polyhedral relaxation of the Lorentz cone by Ben-Tal and Nemirovski (Math Oper Res 26(2): 193–205 2001) that is extremely economical, but whose approximation quality cannot be iteratively improved. The second is based on a lifted polyhedral relaxation of the euclidean ball that can be constructed using techniques introduced by Tawarmalani and Sahinidis (Math Programm 103(2): 225–249, 2005). This relaxation is less economical, but its approximation quality can be iteratively improved. Unfortunately, while the approach of Vielma, Ahmed and Nemhauser is applicable for general MICQP problems, the approach of Hijazi, Bonami and Ouorou can only be used for MICQP problems with convex quadratic constraints. In this paper we show how a homogenization procedure can be combined with the technique by Tawarmalani and Sahinidis to adapt the extended formulation used by Hijazi, Bonami and Ouorou to a class of conic mixed integer programming problems that include general MICQP problems. We then compare the effectiveness of this new extended formulation against traditional and extended formulation-based algorithms for MICQP. We find that this new formulation can be used to improve various LP-based algorithms. In particular, the formulation provides an easy-to-implement procedure that, in our benchmarks, significantly improved the performance of commercial MICQP solvers.     

The Synthesis and Mechanistic Considerations of a Series of Ammonium Monosubstituted H-Phosphonate Salts

A series of ammonium monosubstituted H-phosphonate salts were synthesized by combining H-phosphonate diesters with amines in the absence of solvent at 80 °C. Variation of the ester substituent and amine produced a range of ionic liquids with low melting points. The products and by-products were analyzed by spectroscopic and spectrometric techniques in order to get a better mechanistic picture of the dealkylation and formal dearylation observed. For dialkyl H-phosphonate diesters, (RO)₂P(O)H (R=alkyl), the reaction proceeds via direct dealkylation with the reactivity increasing in the order R=iPr<Et<Me corresponding to DFT calculated activation enthalpies of 22.6, 20.8, and 17.9 kcal mol⁻¹. For the diphenyl H-phosphonate diesters, (PhO)₂P(O)H, the dearylation was found to proceed via phenol-assisted formation of a 5-coordinate intermediate, (PhO)₃PH(OH), from which P(OPh)₃ and water were eliminated. The presence of an equivalent of water then facilitated the formation of P(OH)₂OPh and the amine, R'NH₂, subsequently abstracted a proton from it to yield [(PhO)PH(O)O]^-[R'NH₃]⁺.