Coupling and Poisson approximation

We give an overview of the Stein-Chen method for establishing Poisson approximations of various random variables. Couplings of certain variables are used to gives explicit bounds for the total variation distance between the distribution of a random variable and a Poisson variable. Some applications are given. In some cases, explicit couplings may be used to obtain good estimates; in other applications it suffices to show the existence of couplings with certain monotonicity properties.Supported by the Göran Gustafsson Foundation for Research in Natural Sciences and Medicine.     

Study of DNA coated nanoparticles as possible programmable self-assembly building blocks

Nanoparticles coated with single stranded DNA have been shown to efficiently hybridize to targets of complementary DNA. This property might be used to implement programmable (or algorithmic) self-assembly to build nanoparticle structures. However, we argue that a DNA coated nanoparticle by itself cannot be used as a programmable self-assembly building block since it does not have directed bonds. A general scheme for assembling and purifying nanoparticle eight-mers with eight geometrically well-directed bonds is presented together with some preliminary experimental work.     

Vibrational and lifetime line broadenings in ESCA

The line profile of the narrow, symmetric 1s line from neon, recorded with the new ESCA instrument with X-ray monochromatization, is analyzed. The natural linewidth of this line is found to be 0.23 ± 0.02 eV, in good agreement with theoretical calculations of the oscillator strengths for Auger transitions and X-ray emission. Spectra from molecules show frequently asymmetric core electron lines under high resolution. This rules out previous explanations based on a chemical influence on the natural lifetime. Contrary to earlier assumptions, vibrational excitations are shown to be important in core electron spectra. For methane, the vibrational energy spacing is large enough to allow the vibrational lines to be partly resolved. Recent results from accurate PNO CI calculations on methane agree well with the experimental findings. The Franck-Condon transitions in the C1s and N1s lines from CO and N₂ are shown to be well described in the harmonic approximation and approximating the potential curves of the highly excited core hole states with the potential curve for the ground state of NO⁺, X¹ Σ⁺. Knowledge of vibrational excitations in core electron spectra is shown to be valuable in the analysis of high resolution X-ray emission spectra of free molecules.     

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.     

N-Vinyl as N-H protecting group. Synthesis of cyclic imines from N-vinyllactams and organolithium reagents

On reaction with organolithium reagents followed by hydrolysis and distillation, N-vinylpyrrolidone ( 1 ) gives five-membered ring imines 3-8 , whereas N-vinylcaprolactam ( 2 ) gives mixtures of seven-membered ring imines and the corresponding ∈-amino ketones.     

Oxoniobates Containing Metal Clusters

Metal clusters, discrete or condensed, are characteristic of the structures of many compounds which contain transition metals in low oxidation states. The highly reduced oxoniobates support the concept of condensed clusters. They contain Nb₆O₁₂ clusters which are either isolated or linked at the apices of the Nb₆ octahedra to form oligomeric chains or networks. The analysis of the bonding relationships allows the identification of different types of Nb atoms and thus the quantitative prediction of valence electron concentrations for finite or infinite structures composed of these condensed M₆X₁₂ clusters.