Picolinamides as Effective Ligands for Copper‐Catalysed Aryl Ether Formation: Structure–Activity Relationships,Substrate Scope and Mechanistic Investigations

The use of picolinic acid amide derivatives as an effective family of bidentate ligands for copper‐catalysed aryl ether synthesis is reported. A fluorine‐substituted ligand gave good results in the synthesis of a wide range of aryl ethers. Even bulky phenols, known to be very challenging substrates, were shown to react with aryl iodides with excellent yields using these ligands. At the end of the reaction, the first examples of end‐of‐life Cu species were isolated and identified as Cu^II complexes with several of the anionic ligands tested. A preliminary mechanistic investigation is reported that suggests that the substituents on the ligands might have a crucial role in determining the redox properties of the metal centre and, consequently, its efficacy in the coupling process. An understanding of these effects is important for the development of new efficient and tunable ligands for copper‐based chemistry.     

Sulfur‐Functionalized Graphene Oxide by Epoxide Ring‐Opening

The treatment of graphene oxide (GO) with potassium thioacetate followed by an aqueous work‐up yields a new material via the ring‐opening of the epoxide groups. The new material is a thiol‐functionalized GO (GO‐SH) which is able to undergo further functionalization. Reaction with butyl bromide gives another new material, GO‐SBu, which shows significantly enhanced thermal stability compared to both GO and GO‐SH. The thiol‐functionalized GO material showed a high affinity for gold, as demonstrated by the selective deposition of a high density of gold nanoparticles.     

The rotational resonance Raman spectrum of nitrogen dioxide and the determination of electronic state symmetry from resonance Raman selection rules

The pure rotational Raman spectrum of nitrogen dioxide has been observed and shown to be consistent with existing determinations of molecular parameters. Upon observation at 600 Torr pressure and 0.4 cm⁻¹ resolution a well-defined rotational spectrum is obtained. This spectrum is overlaid with a number of fluorescence lines. The fluorescence lines are separated from the Raman spectrum by a comparison of Stokes and anti-Stokes branches of the rotational spectrum. Out of seven strong fluorescence lines seen with 5145 Å excitation, five probably are identifiable with vibration-rotation fluorescence progressions observed by Abe.The most striking feature of these observations is the potential use of the resonance Raman effect for the analysis of complicated electronic spectra. When this rotational spectrum is observed with excitation by 5309 Å or 5145 Å excitation, the Raman spectrum follows a-axis selection rules and the Q-branches are in the noise level or barely out of it. However, at 4880 Å the ΔK = 2Q-branches become a major feature of a spectrum, indicating that an appreciable part of the absorption at this wavelength is occurring through the operation of b- or c-axis selection rules. These findings are consistent with present notions of a ²B₂ excited state dominating absorption at longer wavelengths, while at shorter wavelengths a ²B₁ excited state becomes important. Given a tunable laser, one could map the relative importance of these two possible selection rules for NO₂ without any theoretical analysis more sophisticated than that presented in this paper.A simplified statement of the selection rules for resonance rotational Raman spectra of asymmetric tops has been developed in the course of this investigation. No attempt has been made to refine the rotational parameters of NO₂ since all of the lines seen areunresolved multiplets. Our data should be regarded as a search spectrum preliminary to investigation on a high resolution instrument.     

The Einstein evolution equations as a first-order quasi-linear symmetric hyperbolic system,I

A systematic presentation of the quasi-linear first order symmetric hyperbolic systems of Friedrichs is presented. A number of sharp regularity and smoothness properties of the solutions are obtained. The present paper is devoted to the case ofR ⁿ with suitable asymptotic conditions imposed. As an example, we apply this theory to give new proofs of the existence and uniqueness theorems for the Einstein equations in general relativity, due to Choquet-Bruhat and Lichnerowicz. These new proofs usingfirst order techniques are considerably simplier than the classical proofs based onsecond order techniques. Our existence results are as sharp as had been previously known, and our uniqueness results improve by one degree of differentiability those previously existing in the literature.Partially supported by AEC Contract AT(04-3)-34.Partially Supported by NSF Contract GP-8257.     

Synthesis and characterization of multiply fused dehydrobenzoannulenoannulene topologies

[reaction: see text] From a common precursor, two unusual dehydrobenzoannulene topologies have been synthesized utilizing either Pd-catalyzed or Cu-mediated oxidative homocoupling as the ring-closure step.     

Homothetic and conformal symmetries of solutions to Einstein's equations

We present several results about the nonexistence of solutions of Einstein's equations with homothetic or conformal symmetry. We show that the only spatially compact, globally hyperbolic spacetimes admitting a hypersurface of constant mean extrinsic curvature, and also admitting an infinitesimal proper homothetic symmetry, are everywhere locally flat; this assumes that the matter fields either obey certain energy conditions, or are the Yang-Mills or massless Klein-Gordon fields. We find that the only vacuum solutions admitting an infinitesimal proper conformal symmetry are everywhere locally flat spacetimes and certain plane wave solutions. We show that if the dominant energy condition is assumed, then Minkowski spacetime is the only asymptotically flat solution which has an infinitesimal conformal symmetry that is asymptotic to a dilation. In other words, with the exceptions cited, homothetic or conformal Killing fields are in fact Killing in spatially compact or asymptotically flat spactimes. In the conformal procedure for solving the initial value problem, we show that data with infinitesimal conformal symmetry evolves to a spacetime with full isometry.