Interaction of low regularity waves∗

We study the microlocal and local interaction for two low regularity waves using a semilinear system, i.e□u ₁ =u ₁ u ₂where u ₁ and u ₂ are linear wavesu ₁,u ₂ ? H^s (R x Rⁿ) forn ≥ 3, and show that in th lacunau ₃ has higher Sobolev regularity than u ₁ and u ₂. Here s depends on n, and is lower than required in any previous interaction results, (n?1)/2or (n?3/2)     

Non-random perturbations of the Anderson Hamiltonian in the 1-D case

Recently (S. Molchanov and B. Vainberg, Non-random perturbations of the Anderson Hamiltonian, J. Spectral Theory 50 (2) (2011), pp. 179–195), two of the authors applied the Lieb method to the study of the negative spectrum for particular operators of the form H?=?H ₀???W. Here, H ₀ is the generator of the positive stochastic (or sub-stochastic) semigroup, W(x)?≥?0 and W(x)?→?0 as x?→?∞ on some phase space X. They used the general results in several ‘exotic’ situations, among them the Anderson Hamiltonian H ₀. In the 1-D case, the subject of this article, we will prove similar, but more precise results.     

Unraveling the 13C NMR chemical shifts in single-walled carbon nanotubes: dependence on diameter and electronic structure

The atomic specificity afforded by nuclear magnetic resonance (NMR) spectroscopy could enable detailed mechanistic information about single-walled carbon nanotube (SWCNT) functionalization as well as the noncovalent molecular interactions that dictate ground-state charge transfer and separation by electronic structure and diameter. However, to date, the polydispersity present in as-synthesized SWCNT populations has obscured the dependence of the SWCNT (13)C chemical shift on intrinsic parameters such as diameter and electronic structure, meaning that no information is gleaned for specific SWCNTs with unique chiral indices. In this article, we utilize a combination of (13)C labeling and density gradient ultracentrifugation (DGU) to produce an array of (13)C-labeled SWCNT populations with varying diameter, electronic structure, and chiral angle. We find that the SWCNT isotropic (13)C chemical shift decreases systematically with increasing diameter for semiconducting SWCNTs, in agreement with recent theoretical predictions that have heretofore gone unaddressed. Furthermore, we find that the (13)C chemical shifts for small diameter metallic and semiconducting SWCNTs differ significantly, and that the full-width of the isotropic peak for metallic SWCNTs is much larger than that of semiconducting nanotubes, irrespective of diameter.     

Effect of solvent polarity and electrophilicity on quantum yields and solvatochromic shifts of single-walled carbon nanotube photoluminescence

In this work, we investigate the impact of the solvation environment on single-walled carbon nanotube (SWCNT) photoluminescence quantum yield and optical transition energies (E(ii)) using a highly charged aryleneethynylene polymer. This novel surfactant produces dispersions in a variety of polar solvents having a wide range of dielectric constants (methanol, dimethyl sulfoxide, aqueous dimethylformamide, and deuterium oxide). Because a common surfactant can be used while maintaining a constant SWCNT-surfactant morphology, we are able to straightforwardly evaluate the impact of the solvation environment upon SWCNT optical properties. We find that (i) the SWCNT quantum yield is strongly dependent on both the polarity and electrophilicity of the solvent and (ii) solvatochromic shifts correlate with the extent of SWCNT solvation. These findings provide a deeper understanding of the environmental dependence of SWCNT excitonic properties and underscore that the solvent provides a tool with which to modulate SWCNT electronic and optical properties.     

Do male northern elephant seals recognize individuals or merely relative dominance rank?

Vocal recognition was tested in a socially dynamic context where many individuals interact: the female defense polygyny practiced by male northern elephant seals. The goal was to tease apart whether animals recognize other individuals or instead use a simple rule-based category (i.e., relative dominance rank). A total of 67 playback experiments conducted with 18 males at An?o Nuevo State Reserve, California, tested three aspects of recognition: (1) recognition of relative rank; (2) whether such recognition was continuous or categorical; and (3) recognition of familiarity. Results indicate that males recognize familiar individuals although responses are primarily based on relative dominance rank.     

The charge capacitance of the chemical bond: Application to bonds containing metals

The charge capacitance of metal containing complexes are studied. For molecules with multiple bonding between the metal atoms it is found that the charge capacitance is correlated to the maximum bond order, natural bond order, and to some extent the effective bond order. Furthermore the charge capacitance of some methylidene metal dihydride complexes are studied. These molecules have agostic interactions of varying strength, and it is concluded that this strength is very well reflected in the charge capacitances of the systems. In accordance with the definition of agostic interactions it is therefor concluded that the charge capacitance holds information about the strength of covalent interactions. The effect therefore on the agostic interactions upon substitution of one of the hydrogen atoms with fluorine in the methylidene metal complexes is studied, and found to reduce the agostic interactions. It is also demonstrated that there is an agostic interaction in an ArCrCrAr complex. The distance dependence of the charge capacitance is also discussed. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Secondary-Phase Formation in Spinel-Type LiMn<Subscript>2</Subscript>O<Subscript>4</Subscript>-Cathode Materials for Lithium-Ion Batteries: Quantifying Trace Amounts of Li<Subscript>2</Subscript>MnO<Subscript>3</Subscript> by Electron Paramagnetic Resonance Spectroscopy

Spinel-type lithium manganese oxides are considered as promising cathode materials for lithium-ion batteries. Trace amounts of Li₂MnO₃ usually occur as a secondary phase in lithium-manganese spinels in the common high-temperature, solid-state synthesis, affecting the overall Li–Mn stoichiometry in the spinel phase and thereby the electrochemical performance. However, the formation of Li₂MnO₃ lower than 1 wt.% can hardly be quantified by the conventional analytical techniques. In this work, we synthesized lithium-manganese spinels with different Li/Mn molar ratios and demonstrate that electron paramagnetic resonance (EPR) enables quantifying trace amounts of Li₂MnO₃ below 10^?2 wt.% in the synthesized products. The results reveal that the formation of Li₂MnO₃ secondary phase is favored by lithium excess in the synthesis. Based on the quantitative evaluation of the EPR data, precise determining Li–Mn stoichiometry in the spinel phase in Li_1+xMn_2?xO₄ materials can be assessed. Accordingly, it is possible to estimate the amount of lithium on 16d-sites in the Li-rich manganese spinels.     

Cryobiology, wildlife conservation and reality

Conservation is about protecting and nurturing species so that they can survive, not only now but also into the future. Ideally this means protecting genetically diverse populations and not simply breeding a few individuals. In principle, cryobiology offers the means to help maintain genetic diversity by storing genetically important germplasm that could reinvigorate populations in the future. Unfortunately the technical problems associated with this ideal goal still provide a major barrier to the practical use of cryopreservation technology. Sometimes these are technical problems with the cryobiology, but lack of basic biological information about unusual species, coupled with difficulties in obtaining such information, means that progress will be possible with only a few species that are subject to intensive scrutiny. The opportunities nevertheless exist for cryobiologists and reproductive biologists to make useful and global contributions to species conservation. I argue here that there are often two mutually suspicious groups of biologists, who do not interact or even understand each others goals. If conservation biologists and biotechnologists were more prepared to join forces and share their expertise, there would be much improved prospects for achieving lasting success in the conservation of a small, but well targeted, number of threatened species.     

Hydroxy-directed fluorination of remote unactivated C(sp3)–H bonds: a new age of diastereoselective radical fluorination

We report a photochemically induced, hydroxy-directed fluorination that addresses the prevailing challenge of high diastereoselectivity in this burgeoning field. Numerous simple and complex motifs showcase a spectrum of regio- and stereochemical outcomes based on the configuration of the hydroxy group. Notable examples include a long-sought switch in the selectivity of the refractory sclareolide core, an override of benzylic fluorination, and a rare case of 3,3′-difluorination. Furthermore, calculations illuminate a low barrier transition state for fluorination, supporting our notion that alcohols are engaged in coordinated reagent direction. A hydrogen bonding interaction between the innate hydroxy directing group and fluorine is also highlighted for several substrates with ¹⁹F–¹H HOESY experiments, calculations, and more.

We report a photochemical, hydroxy-directed fluorination that addresses the prevailing challenge of high diastereoselectivity. Numerous motifs showcase a range of regio- and stereochemical outcomes based on the configuration of the hydroxy group.

The hydroxy (OH) group is treasured and versatile in chemistry and biology.¹ Its ubiquity in nature and broad spectrum of chemical properties make it an attractive source as a potential directing group.² The exploitation of the mild Lewis basicity exhibited by alcohols has afforded several elegant pathways for selective functionalization (e.g., Sharpless epoxidation,³ homogeneous hydrogenation,⁴ cross-coupling reactions,⁵ among others⁶). Recently, we reported a photochemically promoted carbonyl-directed aliphatic fluorination, and most notably, established the key role that C–H⋯O hydrogen bonds play in the success of the reaction.⁷ Our detailed mechanistic investigations prompt us to postulate that other Lewis basic functional groups (such as –OH) can direct fluorination in highly complementary ways.⁸ In this communication, we report a hydroxy-directed aliphatic fluorination method that exhibits unique directing properties and greatly expands the domain of radical fluorination into the less established realm governing high diastereoselectivity.⁹Our first inclination that functional groups other than carbonyls may influence fluorination regiochemical outcomes was obtained while screening substrates for our published ketone-directed radical-based method (Scheme 1).^8a In this example, we surmised that oxidation of the tertiary hydroxy group on substrate 1 cannot occur and would demonstrate functional group tolerance (directing to C11, compound 2). Surprisingly, the two major regioisomers (products 3 and 4) are derivatized by Selectfluor (SF) on C12 and C16 – indicative of the freely rotating hydroxyl directing fluorination. Without an obvious explanation of how these groups could be involved in dictating regiochemistry, we continued the mechanistic study of carbonyl-directed fluorination (Scheme 2A). We established that the regioselective coordinated hydrogen atom abstraction occurs by hydrogen bonding between a strategically placed carbonyl and Selectfluor radical dication (SRD).⁷ However, we noted that the subsequent radical fluorination is not diastereoselective due to the locally planar nature of carbonyl groups. Thus, we posed the question: are there other directing groups that can provide both regio- and diastereoselectivity? Such a group would optimally be attached to a sp³ hybridized carbon; thus the “three dimensional” hydroxy carbon logically comes to mind as an attractive choice, and Scheme 1 illustrates the first positive hint.Open in a separate windowScheme 1Observed products for the fluorination of compound 1.Open in a separate windowScheme 2(A) Proposed mechanism, (B) β-caryophyllene alcohol hypochlorite derivative synthetic probe, (C) isodesmic relation of transition states showing the general importance of the hydroxy group to reactivity (ωB97xd/6-31+G*), and (D) ¹H NMR experiment with Selectfluor and various additives at different concentrations.We began our detailed study with a simple substrate that contains a tertiary hydroxyl group. Alcohol 5 was synthesized stereoselectively by the reaction of 3-methylcyclohexanone, FeCl₃, and 4-chlorophenylmagnesium bromide;¹⁰ the 4-chlorophenyl substituent allows for an uncomplicated product identification and isolation (aromatic chromophore). We sought to determine optimal reaction conditions by examination of numerous photosensitizers, bases, solvents, and light sources (7 Although we utilize cool blue LEDs (sharp cutoff ca. 400 nm), CFLs (small amount of UVB (280–315 nm) and UVA (315–400 nm)) are useable as well.¹¹ A mild base additive was also found to neutralize adventitious HF and improve yields in the substrates indicated (