Extrinsic Killing spinors

 Under intrinsic and extrinsic curvature assumptions on a Riemannian spin manifold and its boundary, we show that there is an isomorphism between the restriction to the boundary of parallel spinors and extrinsic Killing spinors of non-negative Killing constant. As a corollary, we prove that a complete Ricci-flat spin manifold with mean-convex boundary isometric to a round sphere, is necessarily a flat disc. Received: 2 February 2002; in final form: 1 August 2002 / Published online: 1 April 2003 Mathematics Subject Classification (1991): 53C27, 53C40, 53C80, 58G25 The authors would like to thank Lars Andersson for helpful discussions and for bringing to our knowledge the information regarding Remark 4. We are also grateful to the referee for pointing out that Corollary 5 and Corollary 6 are only valid when the boundary is at least 2-dimensional. Research of S. Montiel is partially supported by a Spanish MCyT grant No. BFM2001-2967     

Absolute rate calculations: atom and proton transfers in hydrogen-bonded systems.

We calculate energy barriers of atom- and proton-transfer reactions in hydrogen-bonded complexes in the gas phase. Our calculations do not involve adjustable parameters and are based on bond-dissociation energies, ionization potentials, electron affinities, bond lengths, and vibration frequencies of the reactive bonds. The calculated barriers are in agreement with experimental data and high-level ab initio calculations. We relate the height of the barrier with the molecular properties of the reactants and complexes. The structure of complexes with strong hydrogen bonds approaches that of the transition state, and substantially reduces the barrier height. We calculate the hydrogen-abstraction rates in H-bonded systems using the transition-state theory with the semiclassical correction for tunneling, and show that they are in excellent agreement with the experimental data. H-bonding leads to an increase in tunneling corrections at room temperature.     

Effects of Aqueous and Organic Solvents on the Conformational Properties of the Helix-Forming alpha-Methyl-beta-L-aspartamyl Residue

The conformational preferences of N-acetyl-N'-methyl-alpha-methyl-beta-L-aspartamide, which is the model compound for helical poly(beta-L-aspartate)s, have been determined by ab initio SCF-MO computations. Two driving patterns have been found for the existing 13 minimum energy conformations: (i) intramolecular hydrogen bonding interactions of both amide-amide and amide-ester type; and (ii) repulsive interactions between the four oxygen atoms contained in the molecule. Self-consistent reaction-field (SCRF) calculations based on the method proposed by Miertus, Scrocco, and Tomasi have been performed in order to evaluate the effect of the solvent on the conformational preferences of the compound subject of study. Water and carbon tetrachloride were the solvents chosen for this purpose, and results have been discussed and interpreted on the basis of their electronic structures. The conclusions drawn from this study are of assistance to understand some features of the conformational transitions experimentally found in poly(beta-L-aspartate)s.     

The Dienone–Phenol Rearrangement of Santonin: A Comprehensive Laboratory Experiment for Advanced Undergraduate Organic Chemistry Students

A comprehensive laboratory experiment suitable for advanced undergraduate organic chemistry students has been designed. The experiment is based on the dienone-phenol rearrangement reaction of the sesquiterpene santonin to give -desmotroposantonin acetate. It challenges students to solve an earlier controversial stereochemical problem. The students carry out the reaction and analyze spectroscopic data to determine the stereochemistry of the starting material and the product. In addition, they perform simple molecular modeling calculations, which enable them to rationalize the stereochemical outcome of the transformation and discuss the mechanism of the dienone-phenol rearrangement and related rearrangements reported in the literature.     

Preparation and characterization of theβ-cyclodextrin inclusion complex with phenylpropiolic acid

The preparation of a 1:1 complex involving-cyclodextrin (-CD) and phenylpropiolic acid (PPA) is reported. The new inclusion complex of-CD has been characterized on the basis of its chemical analysis, thermal behavior, infrared spectrum, X-ray powder pattern and¹³C-NMR spectrum in DMSO solution.     

Covalent Cross-Linking of 2H-MoS2 Nanosheets

The combination of 2D materials opens a wide range of possibilities to create new-generation structures with multiple applications. Covalently cross-linked approaches are a ground-breaking strategy for the formation of homo or heterostructures made by design. However, the covalent assembly of transition metal dichalcogenides flakes is relatively underexplored. Here, a simple covalent cross-linking method to build 2H-MoS₂–MoS₂ homostructures is described, using commercially available bismaleimides. These assemblies are mainly connected vertically, basal plane to basal plane, creating specific molecular sized spaces between MoS₂ sheets. Therefore, this straightforward approach gives access to the controlled connection of sulfide-based 2D materials.     

Phosphorus-Containing Dendrimers: Synthesis and Properties

Several series of phosphorus-containing dendrimers have been designed to study the variation of their properties, depending on the type, the location (surface, branches, core, and cavities), and the number of functions implied.