Ground state of a spin-phonon system. I. Variational estimates

A study is made of the ground-state energy of a spin-one-half particle in a fieldB and interacting with a phonon bath. The infrared-sensitive case of acoustic phonons with point coupling in three dimensions is characterized by two parameters, a coupling constant andB. Units are used where the high-momentum phonon cutoff is unity. There is a curve (B) separating a symmetry-breaking region with a long-range phonon field from a normal region. Two simple, well-known, approximations are compared. The source theory yields discontinuities in the first derivatives of the energy with respect toB and whenB>e ^–1 and an infinite-order transition whenB<e ^–1, but is trivial in the large- region. The classical theory yields discontinuities in the second derivatives but is trivial in the small- region. An improved variationally fixed ground-state wave function is analyzed. It gives a new (B) curve with an infinite-order transition with continuous energy derivatives whenB<e/(e ²–1/4) and with discontinuous derivatives whenB is larger than this value. It is nontrivial in the entire (B) plane. The crossover to classical behavior occurs near =1/2 forB1. But the wave function does not describe quantum fluctuations in the large- phase. A second way of combining source and classical effects is described. It yields a second-order transition (near =1/2 forB1) everywhere. These theories are special cases of a symmetry-breaking transformation together with a one-mode treatment of quantum fluctuations. The transition is viewed in terms of a single mode with a variable length, coupled dynamically to the spin.     

Nachweise verwandter Elemente nebeneinander in einem Tropfen. II. Mitteilung: Der mikrochemische Nachweis von Aluminium und Beryllium mittels Ammoniummolybdats

Zusammenfassung Entgegen den Auffassungen von van Zijp über den von ihm veröffentlichten Nachweis des Aluminiums mit Ammoniummolybdat wurde gezeigt, daß ein derartiger Nachweis Empfindlichkeit und Störungsfreiheit in hohem Grade vereint.Der Nachweis durch Ammoniummolybdat konnte auf Beryllium ausgedehnt werden. Eine Reihe von Versuchen zeigte, daß Aluminium- und Berylliummolybdat in zwei verschiedenen Krystallformen ohne gegenseitige Beeinträchtigung selbst nebeneinander auszukrystallisieren vermögen.Es ist mir eine angenehme Pflicht, Herrn Prof. Dr. Wilhelm Böttger für sein stets färderndes Interesse und für die mikrochemische Arbeitsmäglichkeit überhaupt zu danken. Zu Dank verpflichtet bin ich auch der Fa. Otto Perutz, München für die freundliche überlassung von Pervola-Platten zu den Mikrophotographien.     

MDGC–MS: A powerful tool for enantioselective flavor analysis

This paper reports the differentiation between the enantiomers of theaspiranes and theaspirones, potent flavor compounds widely used in the flavor industry. Optically pure reference compounds of isomeric theaspiranes were obtained by enantioselective synthesis. Enantiomerically pure reference theaspirones were isolated from quince fruit; their absolute stereochemistry was assigned by CD spectroscopy. For both types of compounds the order of elution was elucidated by using authentic reference compounds. These data enabled the determination of the enantiomeric distribution of both types of compounds in a variety of plant tissues. Because of the complexity of the natural flavor isolates, compounds were identified by mass spectrometry after multidimensional gas chromatography employing a Sichromat 2 double oven chromatograph. After separation of the target compounds on the first, achiral, column (DB-5), they were transferred to a chiral column (C-Dex B) for determination of the enantiomeric distribution. Multiple ion detection (MID) enabled the determination of the enantiomeric distribution even for complex mixtures containing the target compounds at extremely low levels.     

Untersuchungen an reagenzien zur photometrischen zinnbestimmung

The formation of complexes between tin(IV) and o-diphenols, and o-hydroxyquinones, has been studied spectrophotometrically. Simple o-hydroxyquinones do not react with tin(IV), chloranilic acid gives an SnR₂ complex, and o-diphenols give SnR₃ complexes. The reactions of tin(IV) with hydroxyxanthene dyes to give coloured products were considered for their possible analytical utility: the pH range, absorption spectrum, solubility and composition of the complexes were investigated, and the stability constants determined. Analytical procedures have been developed for tin and checked for precision and sensitivity: gallein and hydroxyhydroquinonephthalein (dihydroxyfluorescein) are to be recommended.     

Determination of 1-vinyl-2-pyrrolidone in human serum by high-performance liquid chromatography

Summary A simple method is described which allows the quantification of 1-vinyl-2-pyrrolidone (NVP) in human serum. NVP is extracted from serum with diethylether and determined with HPLC/UV-detection. 1-Cyclohexyl-2-pyrrolidone serves as an internal standard. The detection limit is 0.1 mg/l. The method has shown that NVP can enter the organisms of workers occupationally exposed to this substance.     

Zur Theorie der Chiralitätsfunktionen

The Algebraic Theory of Chirality Functions is derived by means of exclusively qualitative considerations. Hence, the significance of quantitative results is questionable. Moreover the construction of “Näherungsansätze” (”Approximation-Ansatz”), which may be interpreted as semiempirical methods, is achieved on the basis of plausibility and mathematical simplicity. Since physical arguments are not included, the consistency or inconsistency of “Näherungsansätze” with experimental results do not justify direct physical conclusions.     

N-heterocyclic carbenes as ligands in high-valent molybdenum and tungsten complexes

Oxometal complexes of molybdenum and tungsten in high oxidation states from stable adducts with 1,3-dimethylimidazoline-2-ylidene (L) 1. The first ‘carbene’ complexes of molybdenum(VI) [MoO₂Cl(L)₃]Cl (3a) and tungsten(VI) WO₂Cl₂(L)₂ (4b) are reported.     

Microchemical characterization of paintings — A case study

Summary The fundamental importance of scientific research for the preservation and restoration of works of art is uncontestable. The methods described in this paper, such as light microscopy, microchemical tests, emission spectroscopy, chromatography, scanning electron analysis, electron microprobe analysis and infrared spectroscopy, are of special significance in this filed. Nevertheless a better understanding of the problems that arise out of new special questions of art history can be obtained only by the right interpretation of the data obtained by scientific methods.

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Mikrochemische Charakterisierung von Gemälden

Zusammenfassung Die grundlegende Bedeutung wissenschaftlicher Forschung für die Erhaltung und Restaurierung von Kunstwerken ist unbestritten. Die hier beschriebenen Methoden (Lichtmikroskopie, mikrochemische Reaktionen, Emissionsspektroskopie, Chromatographie, Rasterelektronen-Analyse und Infrarotspektroskopie) sind hierfür von zunehmender Bedeutung. Sie ermöglichen ein besseres Verständnis neuerer kunsthistorischer Probleme nur durch die richtige Interpretation der Ergebnisse wissenschaftlicher Methoden.

     

Easy preparation of cobalt corrole and hexaphyrin and isolation of new oligopyrroles in the solvent-free condensation of pyrrole with pentafluorobenzaldehyde

[reaction: see text] Following the discovery that meso-substituted corroles are formed in solvent-free condensation of pyrrole with aldehydes, we demonstrate that a small variation in the methodology is suitable for facile synthesis of cobalt(III) corrole and hexaphyrin. These compounds, as well as three noncyclic products, were fully characterized by spectroscopy and X-ray crystallography.