The Role of Methoxy Group in the Nazarov Cyclization of 1,5-bis-(2-Methoxyphenyl)-1,4-Pentadien-3-one in the Gas Phase and Condensed Phase

ESI-protonated 1,5-bis-(2-methoxyphenyl)-1,4-pentadien-3-one (1) undergoes a gas-phase Nazarov cyclization and dissociates via expulsions of ketene and anisole. The dissociations of the [M + D]⁺ ions are accompanied by limited HD scrambling that supports the proposed cyclization. Solution cyclization of 1 was effected to yield the cyclic ketone, 2,3-bis-(2-methoxyphenyl)-cyclopent-2-ene-1-one, (2) on a time scale that is significantly shorter than the time for cyclization of dibenzalacetone. The dissociation characteristics of the ESI-generated [M + H]⁺ ion of the synthetic cyclic ketone closely resemble those of 1, suggesting that gas-phase and solution cyclization products are the same. Additional mechanistic studies by density functional theory (DFT) methods of the gas-phase reaction reveals that the initial cyclization is followed by two sequential 1,2-aryl migrations that account for the observed structure of the cyclic product in the gas phase and solution. Furthermore, the DFT calculations show that the methoxy group serves as a catalyst for the proton migrations necessary for both cyclization and fragmentation after aryl migration. An isomer formed by moving the 2-methoxy to the 4-position requires relatively higher collision energy for the elimination of anisole, as is consistent with DFT calculations. Replacement of the 2-methoxy group with an OH shows that the cyclization followed by aryl migration and elimination of phenol occurs from the [M + H]⁺ ion at low energy similar to that for 1.

Affine-Invariant Distances, Envelopes and Symmetry Sets

Affine invariant symmetry sets of planar curves are introduced and studied in this paper. Two different approaches are investigated. The first one is based on affine invariant distances, and defines the symmetry set as the closure of the locus of points on (at least) two affine normals and affine-equidistant from the corresponding points on the curve. The second approach is based on affine bitangent conics. In this case the symmetry set is defined as the closure of the locus of centers of conics with (at least) 3-point contact with the curve at two or more distinct points on the curve. This is equivalent to conic and curve having, at those points, the same affine tangent, or the same Euclidean tangent and curvature. Although the two analogous definitions for the classical Euclidean symmetry set are equivalent, this is not the case for the affine group. We present a number of properties of both affine symmetry sets, showing their similarities with and differences from the Euclidean case. We conclude the paper with a discussion of possible extensions to higher dimensions and other transformation groups, as well as to invariant Voronoi diagrams.     

Bifurcations of affine equidistants

The bifurcations of so-called affine equidistants for a surface in three-space are classified and described geometrically. An affine equidistant is formed by the points dividing in a given ratio the segment with the endpoints lying on a given surface provided that the tangent planes to the surface at these endpoints are parallel. The most interesting case corresponds to segments near parabolic lines. All singularities turn out to be stable and simple.     

Generic equi-centro-affine differential geometry of plane curves

We study the equi-centro-affine invariants of plane curves from the view point of the singularity theory of smooth functions. We define the notion of the equi-centro-affine pre-evolute and pre-curve and establish the relationship between singularities of these objects and geometric invariants of plane curves.     

Recognition of centre symmetry set singularities

Let M be a smooth surface in real affine 3-space. Consider the pairs of points of this surface at which the tangent planes are parallel and in particular the chords (infinite lines) joining these pairs. We study in detail and classify the singularities of the envelope of these chords, that is a (singular) surface tangent to all of them. This is called the Centre Symmetry Set (CSS) of M. The study is local in character and is based upon a more general investigation by the authors of the n-dimensional case. The construction of the CSS is affinely invariant and generalises the focal set of a surface in euclidean space and the affine focal set of a surface in affine space. Many standard and some unusual singularities occur in a natural way as the singularities of the CSS. There are illustrations of the various cases by means of concrete examples.      

Singularities of Families of Chords

A chord is a straight line joining two points of a pair of hypersurfaces in an affine space such that the tangent hyperplanes at these points are parallel. We classify the singularities of envelopes of the families of chords determined by generic pairs of plane curves and surfaces in three-space. The list contains all bifurcation diagrams of simple boundary singularities (of the corresponding multiplicity).     

Gravitational wave production at the end of inflation

We consider gravitational wave production due to parametric resonance at the end of inflation, or "preheating." This leads to large inhomogeneities that source a stochastic background of gravitational waves at scales inside the comoving Hubble horizon at the end of inflation. We confirm that the present amplitude of these gravitational waves need not depend on the inflationary energy scale. We analyze an explicit model where the inflationary energy scale is approximately 10{9} GeV, yielding a signal close to the sensitivity of Advanced Laser Interferometer Gravitational Wave Observatory and Big Bang Observer. This signal highlights the possibility of a new observational "window" into inflationary physics and provides significant motivation for searches for stochastic backgrounds of gravitational waves in the Hz to GHz range, with an amplitude on the order of Omega_{gw}(k)h{2} approximately 10{-11}.     

Solution-based II-VI core/shell nanowire heterostructures

We demonstrate the solution-phase synthesis of CdS/CdSe, CdSe/CdS, and CdSe/ZnTe core/shell nanowires (NWs). On the basis of bulk band offsets, type-I and type-II heterostructures are made, contributing to the further development of low-dimensional heteroassemblies using solution-phase chemistry. Core/shell wires are prepared by slowly introducing shell precursors into a solution of premade core NWs dispersed in a noncoordinating solvent at moderate temperatures (215-250 degrees C). Resulting heterostructures are characterized through low- and high-resolution transmission electron microscopy, selected area electron diffraction, and energy dispersive X-ray analysis. From these experiments, initial shell growth appears to occur through either Stranski-Krastanov or Volmer-Weber island growth. However, beyond a critical shell thickness, nucleation of randomly oriented nanocrystals results in a polycrystalline coat. In cases where overcoating has been achieved, corresponding elemental analyses show spatially varying compositions along the NW radial direction in agreement with expected element ratios. Electronic interactions between the core and shell were subsequently probed through optical studies involving UV-vis extinction spectroscopy, photoluminescence experiments, and transient differential absorption spectroscopy. In particular, transient differential absorption studies reveal unexpected shell-induced changes in core NW Auger kinetics at high carrier densities. Previously seen three-carrier Auger kinetics in CdS (bimolecular in CdSe) NWs were suppressed by the presence of a CdSe (CdS) shell. These observations suggest the ability to influence NW optical/electrical properties by coating them with a surrounding shell, a method which could be important for future NW optical studies as well as for NW-based applications.     

Structural determination of oxofatty acids by charge-remote fragmentations

A strategy is described to locate the carbonyl position in oxofatty acids by utilizing charge-remote fragmentations of various molecular ions that are desorbed by fast atom bombardment (FAB). Oxofatty acids were cationized with alkali metal ions (Li⁺, Na⁺, K⁺, Rb⁺, and Cs⁺) to form [M+2Met?H]⁺ or alkaline earth metal ions (Mg²⁺, Ca²⁺, Sr²⁺ or Ba²⁺) to form [M+Met?H]⁺ in the gas phase. The cationized acids undergo charge-remote fragmentations upon high-energy activation, giving a product-ion pattern that has a gap corresponding to the oxo position and bordered by two high-intensity peaks. One of the peaks corresponds to an ion that is formed by the cleavage of the C-C bond β to the oxo position and proximal to the charge (β ion), whereas the other is formed from the cleavage of the C-C bond γ to the oxo position and distal to the charge (γ′ ion). The oxo position is easily determined by identifying the gap and the β and γ′ ions. Furthermore, there are two competing patterns of fragments in a CAD spectrum of an oxofatty acid or ester [M+Li]⁺ ion. These arise because Li⁺ attaches to either the oxo or the carboxylic end, as was confirmed by ab initio molecular orbital calculations. The results demonstrate that control of the fragmentation can be guided by an understanding of metal-ion affinities. Collisional activation of the anionic carboxylates gives results that are similar to those for positive ions, showing that the process is not related to the charge status. Collisional activation of [M+H]⁺ ions does not give structural information because the charge migrates, leading to charge-mediated fragmentations.