Review of Chemometrics Applied to Spectroscopy: 1985-95, Part 3 — Multi-way Analysis

INTRODUCTION

In this third part of a review on chemometrics in spectroscopy we will describe a recent methodology that has attracted increasing interest in spectroscopy. namely multi-way analysis. The application of multi-way analysis in spectroscopy is still relatively new. hence many methodological improvements are being investigated currently. Part of thls review will also be used to describe the algorithmic improvements gained the last decade.     

Eigenvalues of the difference and product of projections

There is an isomorphism between the matrices over the Boolean algebra of subsets of a k-element set and the k-tuples of Boolean binary (i.e. zero-one) matrices. This isomorphism allows many problems concerning nonbinary Boolean matrices to the referred to the binary ease. However, there are some features of the general (i.e. nonbinary) case that have not been mentioned, although they differ somewhat from the binary case. We exhibit characterizations of the linear operators that preserve several invariants of matrices over finite Boolean algebras to illustrate the differences and similarities of the general vs. the binary cases. We employ a canonical form that is useful in applying the isomorphism.     

Application of low-temperature rapid-scan techniques in the elucidation of inorganic reaction mechanisms

Reactions that occur too rapidly to be monitored by rapid reaction methods at temperatures at or close to ambient can be investigated kinetically by retarding their reaction rates employing very low temperatures. A selection of reactions studied by this approach (low-temperature stopped-flow spectrophotometry) is reported. Details of the reaction mechanisms have been revealed for peroxide activation involving iron(III) porphyrins and cytochrome P450, superoxide activation involving manganese(II) complexes and iron porphyrin complexes, and dioxygen activation and binding by model mono-, and dinuclear copper(I) complexes and dioxygen activation at mono-, and dinuclear non-heme iron complexes. A final section covers progress in unravelling the mechanism of carbon–hydrogen bond activation by platinum complexes.     

Strong Short-Range Cooperativity in Hydrogen-Bond Chains

Chains of hydrogen bonds such as those found in water and proteins are often presumed to be more stable than the sum of the individual H bonds. However, the energetics of cooperativity are complicated by solvent effects and the dynamics of intermolecular interactions, meaning that information on cooperativity typically is derived from theory or indirect structural data. Herein, we present direct measurements of energetic cooperativity in an experimental system in which the geometry and the number of H bonds in a chain were systematically controlled. Strikingly, we found that adding a second H-bond donor to form a chain can almost double the strength of the terminal H bond, while further extensions have little effect. The experimental observations add weight to computations which have suggested that strong, but short-range cooperative effects may occur in H-bond chains.     

Design of a Fragment Library that maximally represents available chemical space

Cheminformatics protocols have been developed and assessed that identify a small set of fragments which can represent the compounds in a chemical library for use in fragment-based ligand discovery. Six different methods have been implemented and tested on Input Libraries of compounds from three suppliers. The resulting Fragment Sets have been characterised on the basis of computed physico-chemical properties and their similarity to the Input Libraries. A method that iteratively identifies fragments with the maximum number of similar compounds in the Input Library (Nearest Neighbours) produces the most diverse library. This approach could increase the success of experimental ligand discovery projects, by providing fragments that can be progressed rapidly to larger compounds through access to available similar compounds (known as SAR by Catalog).     

Organometallic Polymers. XXVII. Radical-Initiated Polymerization and Copolymerization of π-(2, 4-Hexadien-1-yl Acrylate) tricarbonyliron

The novel monomer, π-(2, 4-hexadiene- l-yl acrylate) tricarbonyliron (HATI), has been prepared by two routes. It was homopolymerized and copolymerized with acrylonitrile, vinyl acetate, styrene, and methyl acrylate in benzene solutions. In all cases azobisisobutyronitrile was the initiator. The relative reactivity ratios, where HATI is defined as M₁, were determined: r₁ = 0.34, r₂ = 0.74, M₂ = acrylonitrile; r₁ = 2.0, r₂ = 0.05, M₂ = 0.74, M₂ = acrylonitrile; r₁ = 2.0, r₂ = 0.05, M₂ = vinyl acetate; r₁ = 0.26, r₂ = 1.81, M₂ = styrene; and r₁ = 0.30, r₂ = 0.74, M₂ = methyl acrylate. The homo-and copolymers had high values of T_g. When polymerizations are carried out at high concentrations, a very high molecular weight tail is observed in HATI hompolymerizations and in HATI-methyl acrylate copolymerizations. The polymers were characterized by IR, gel permeation chromatography, viscosity, and differential scanning calorimetry studies. Finally, thermal decompositions carried out in air resulted in decomposition of the Fe(CO)₃ group, producing Fe₂O₃ as a fine powder. Thermal decomposition under nitrogen (in solution and on solids ground into KBr pellets) resulted in slow destruction of the Fe(CO)₃ groups but the resulting polymer mass was insoluble, and the question of what form the iron exists in (Fe metal, oxides, carbides, etc.) has not been answered.     

Polymerization of Methane and Olefin Mixtures over Fluosulfonic Acid and Antimony Pentafluoride

Mixtures of methane and olefins (ethylene, propylene, butenes, butadiene, and styrene) have been polymerized over HSO₃ F-SbF₃ to yield an oily oligomer with a molecular weight ranging from 100 to 700. The NMR spectra of each polymer showed a sharp peak at or near 1.25 &, suggesting the presence of block methylene in the polymer. The formation of block methylene is surprising considering the fact that the polymerization reaction is carbonium ion in nature. A primary cation has been invoked to explain the results. The formation of this primary cation must involve some extraordinary stabilization by some component in the acid.     

Concentration independent calibration of β–γ coincidence detector using 131mXe and 133Xe

Absolute efficiency calibration of radiometric detectors is frequently difficult and requires careful detector modeling and accurate knowledge of the radioactive source used. In the past we have calibrated the β–γ coincidence detector of the Automated Radioxenon Sampler/Analyzer (ARSA) using a variety of sources and techniques which have proven to be less than desirable (Reeder et al., J Radioanal Nucl Chem, 235, 1989). A superior technique has been developed that uses the conversion-electron (CE) and X-ray coincidence of ^131mXe to provide a more accurate absolute gamma efficiency of the detector. The ^131mXe is injected directly into the beta cell of the coincident counting system and no knowledge of absolute source strength is required. In addition, ¹³³Xe is used to provide a second independent means to obtain the absolute efficiency calibration. These two data points provide the necessary information for calculating the detector efficiency and can be used in conjunction with other noble gas isotopes to completely characterize and calibrate the ARSA nuclear detector. In this paper we discuss the techniques and results that we have obtained.     

DIFFRACTION STUDIES OF SOME CONVENTIONAL AND NOVEL MICROPHONE BAFFLES

A directional microphone system for field recording of sounds in the air often involves a parabolic reflector to focus the sound waves on the microphone (transducer) element. Some deficiencies of such a system are noted with respect to reproduction of spectra. The reflector system, involving as it does a structure comparable to a wavelength in linear dimension, is not susceptible to traditional high- or low-frequency approximate methods of computation. Modern numerical techniques now permit precise calculation of the directional responses of small reflectors of various shapes. One result is a proposal for a very economical and effective system involving a plane reflector. Other baffle shapes are also investigated, which may be of interest in special applications.