N identical particles under quantum confinement: a many-body dimensional perturbation theory approach

Systems that involve N identical interacting particles under quantum confinement appear throughout many areas of physics, including chemical, condensed matter, and atomic physics. In this paper, we present the methods of dimensional perturbation theory, a powerful set of tools that uses symmetry to yield simple results for studying such many-body systems. We present a detailed discussion of the dimensional continuation of the N-particle Schrödinger equation, the spatial dimension D→∞ equilibrium (D⁰) structure, and the normal-mode (D⁻¹) structure. We use the FG matrix method to derive general, analytical expressions for the many-body normal-mode vibrational frequencies, and we give specific analytical results for three confined N-body quantum systems: the N-electron atom, N-electron quantum dot, and N-atom inhomogeneous Bose-Einstein condensate with a repulsive hard-core potential.     

Electrochemical Properties of Vanadium Oxide Aerogels and Aerogel Nanocomposites

The electrochemical properties of high surface area transition metal oxide aerogels are extremely interesting because aerogels serve to amplify surface effects. As a result, the electrochemical properties are dominated by surfaces rather than by bulk behavior. In the case of vanadium oxide aerogels this leads to extraordinary electrochemical properties, including an extremely high capacity for lithium and electrochemical responses that are both battery-like and capacitor-like. By exploiting sol-gel synthesis, it is possible to synthesize nanocomposite electrodes in which aerogels are in intimate contact with carbon nanotubes. The resulting nanocomposites exhibit superior electrochemical properties, especially at high discharge.     

Germacreme derivatives from diverse marine soft-corals (octocorallia)

Examinations of the extracts of 8 taxonomically-diverse marine soft-corals (Orders Gorgonaceae, Alcyonaceae and Stolonifera, Subclass Octocorallia, Phylum Cnidaria), have resulted in the isolation of 4 new sesquiterpenoids (1–4) of the germacrene type. Three previously known germacrene derivatives (5–7), and the elemane 8, have also been isolated, and complete ¹H and ¹³C NMR assignments for these compounds are reported.     

The structure of thorikosite,a naturally occurring member of the bismuth oxyhalide group

Thorikosite, (Pb₃Sb_0.6As_0.4)(O₃0H)Cl₂, is a naturally occurring member of the bismuth oxyhalide group isostructural with LiBi₃O₄Cl₂. The space group isI4/mmm witha = 3.919(1)A?,c = 12.854(5)A?, andZ = 1. A crystal structure analysis showed complete solid solution of Pb²⁺, Sb³⁺, and As³⁺ on the single cation site and large atomic temperature factors indicative of pervasive structural disorder. The latter is due to the structural adjustments necessary to accommodate cations of very different sizes in the same site. Thorikosite is closely related to synthetic tetragonal PbSbO₂Cl through the coupled substitution Sb³⁺O^2? ? Pb²⁺(OH)^?.     

Four levels of pattern recognition

Problems of pattern recognition in chemistry and other subjects can be divided conveniently into four different types depending on the level of scope of the problem.(1) Classification into one of a number of defined classes. As an example blood samples taken from persons known to be either controls or welders are considered. The problem is whether trace element concentrations in these samples contain information on whether or not a person is a welder.(2) Level 1 plus the possibility that an object is an outlier, i.e. does not belong to any of the defined classes. As an example, the üse of ¹³C-n.m.r. data to decide whether 2-substituted norbornanes have the exo or endo structure is discussed. (2A) Level 2, asymmetric. This situation occurs when one class does not have a systematic structure, but another class is homogeneous and can be described by a level 2 model. This occurs in the classification of materials or compounds as good or bad, active or inactive, and in binary classifications. As an example the use of trace element data to classify steel samples as having good or poor properties of strength is discussed.(3) Level 2 plus the ability to relate the variables measured to external properties of continuous character. As an example, the classification of a series of chemical compounds as β -receptor blockers, β -receptor stimulants, or neither, on the basis of their structural variables is discussed. In addition, relations between these structural variables and the measured biological activity are sought within each of the two classes.(4) Level 3 with the difference that several external property variables in the objects are measured. It may be desirable to use variables of the objects both for classification and for relations to several property variables: such examples are numerous in analytical chemistry.