Convergence radii of the perturbation expansions for the ground-state energies of finite Hubbard models

The ground state energies of finite Hubbard molecules are calculated by numerically solving the Lieb–Wu equations for a complex Hubbard repulsion parameter U. From the positions of the singular points located in the complex plane, the radii of convergence of the perturbation expansions for the ground state energies are determined.     

Metallurgical factors determining the coercivity of ND-FE-B magnets

In Nd-Fe-B based permanent magnets a high magnetocrystalline anisotropy of the hardmagnetic phase is necessary for a high intrinsic coercivity. In fact, metallurgical parameters (distribution of phases, chemical composition and crystal structures of phases) and processing parameters (alloy preparation, size and shape of particles, sintering and annealing treatments) determine the value of the coercive force of each sintered Nd-Fe-B magnet. Our analytical electron microscope study shows that melt-spun and sintered Nd-Fe-B based magnets contain more or less a distribution of nucleation centres for reversed domains, such as iron-rich phases and-iron precipitates within the hardrnagnetic 2141-grains. A continuous non-magnetic layer phase between the hardrnagnetic 2141-grains increases the expansion field of reversed domains and increase the coercivity. In melt-spun magnets the contribution of the pinning of magnetic domain walls becomes effective during the magnetization reversal process.     

Generalized Hückel treatment of a simple model of transannular interaction and excimer formation

The model of two interacting ethylene molecules having D _2h symmetry was studied using generalized Hückel method. The validity of - separation was tested on this model. The general character of the ground state and lower lying excited states of the model was discussed and the implications drawn concerning transannular interaction and excimer formation. The values obtained for the dissociation energy of the first excited state of our model and corresponding equilibrium intermolecular distance are of right order of magnitude.

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Zusammenfassung Mittels der verallgemeinerten Hückel-Methode wurde das Modell von zwei Äthylenmolekülen mit der Symmetrie D _2h studiert. An diesem Modell wurde die Gültigkeit der - -Separation geprüft. Der allgemeine Charakter des Grundzustandes und der niedriger liegenden angeregten Zustände des Modells wird erörtert und die Folgerungen in Bezug auf transannulare Wechselwirkung und Excimer-Entstehung diskutiert. Die erhaltenen Werte für die Dissoziationsenergie des ersten angeregten Zustandes von unserem Modell und den entsprechenden intermolekularen Gleichgewichtsabstand haben die richtige Größenordnung.

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Résumé Le modèle à symétrie D _2h de deux molécules d'éthylène en interaction a été étudié en utilisant la méthode généralisée de Hückel. On a examiné la validité de la séparation - sur ce modèle. Le caractère général de l'état fondamental et celui des états excités inférieurs du modèle furent discutés et on a fait des déductions sur l'interaction transannulaire et sur la formation d'«excimères». Les valeurs obtenues pour l'énergie de dissociation du premier état excité de notre modèle et la distance intermoléculaire d'équilibre corréspondante ont l'ordre de magnitude correct.

     

Umlagerungsreaktionen von (2′-Propinyl)cyclohexadienolen und -semibenzolen

Rearrangements of (2′-Propinyl)cyclohexadienols and -semibenzenes The acid-catalyzed dienol-benzene rearrangement of 3- and 5-methyl-substituted (2′-propinyl)cyclohexadienols has been investigated. Treatment of the dienols with CF₃COOH in CCl₄ yields allenyl- and (2′-propinyl)benzenes via [3,4]- and [1,2]-sigmatropic rearrangements, respectively. The reaction with H₂SO₄ in Et₂O leeds to a mixture of allenyl-, 2′-propinyl-, 3′-butinyl- and (2′,3′-butadienyl)benzenes (Scheme 3). The latter are products of a thermal semibenzene-benzene rearrangement (cf. Scheme 9). The corresponding semibenzenes have been prepared by dehydration of the cyclohexadienols with H₂SO₄ or POCl₃ (Schemes 6 and 7). Under acidic conditions, the p-(2′-propinyl)semibenzenes 33–35 (Scheme 8) undergo [3,4]- and [1,2]-sigmatropic rearrangements to give again allenyl- and (2′-propinyl)benzenes, whereas the thermal rearrangements to the 3′-butinyl- and (2′,3′-butadienyl)benzenes (Scheme 9) involves a radical mechanism. In contrast, the o-(2′-propinyl)semibenzene b (Scheme 7) leads to (2′,3′-butadienyl)benzene 32 via a thermal [3,3]-sigmatropic rearrangement.     

Analytische Aspekte der Oxydation organischer Stickstoffverbindungen mit Chromsäure. XXIII

Zusammenfassung Die früher beschriebene Halbmikromethode zur Bestimmung von Isonitrosogruppen in organischen Verbindungen wurde in den Mikromaßstab übergeführt. Sie beruht auf der Reaktion der Substanz mit Eisen(III)-sulfat in verd. Schwefelsäure. Dabei wird der Oximstickstoff als Distickstoffoxid frei, das mit Kupfer zu elementarem Stickstoff reduziert und im Mikroazotometer gemessen wird. Für die Berechnung des Oximstickstoffgehaltes aus den abgelesenen Gasvolumina wurden Werte für die konstante und proportionale Volumenkorrektur mit Hilfe der Methode der Regressionsgeraden experimentell festgestellt. Beide Werte sind den bei der N-N-Gruppenbestimmung benützten Volumenkorrekturen fast gleich. Die Bestimmung von Oximgruppen ist durch die Anwesenheit von Nitro- oder Aminogruppen nicht gestört. Diese Gruppen können aus derselben Einwaage durch nachfolgende Oxydation mit Chromsäure bestimmt werden.

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Analytical aspects of the oxidation of organic nitrogen compounds with chromic acid. XXIII

Summary The semimicro method previously described for the determination of isonitroso groups in organic compounds has been converted to the microscale. It is based on the reaction of the material with iron(III)-sulfate in dilute sulfuric acid. The oxime nitrogen is thus liberated as dinitrogen oxide, which is reduced to elementary nitrogen by copper and measured in the mieroazotometer. To calculate the oxime nitrogen content from the read-off gas volume, values for the constant and proportional volume correction with the aid of the regression lines were established experimentally. Both values are almost equal in the case of the determination of the volume corrections employed in the determination of the N-N-groups. The presence of nitro-or amino groups does not interfere with the determination of oxime groups. These groups may be determined from the same sample by subsequent oxidation with chromic acid.

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XXII. Mitteilung s.¹.     

Organosilicon compounds VI. The preparation of silylaziridines and silyldiaziridines by silicon-carbon cleavage

The preparation of several 2-furyl-, 2-thienyl-, benzyl-, and allylsubstituted silanes is reported. Such derivatives, when treated with aziridine in the presence of a metal catalyst, afford good yields of silylaziridines and silyldiaziridines. A qualitative study of electronic and steric requirements of the displacement reaction is reported.     

The speciation of rhodium(III) in hydrochloric acid media by capillary zone electrophoresis

A fast and effective method to study the aquation of rhodium(III) chlorocomplex in hydrochloric solutions using capillary zone electrophoresis (CZE) is developed. At least five species, some of which seem to be oligomeric, are formed in solution during the aquation process at pH>1. The fast hydration of RhCl₆³⁻ makes this species impossible to detect. The first species detected in the optimised conditions is RhCl₅(H₂O)²⁻ although RhCl₄(H₂O)₂⁻ is the main species during the first stage of the aquation process. When equilibrium is reached either RhCl₃(H₂O)₃ or a cationic complex, RhCl₂(H₂O)₄⁺, is formed as the main species. Matrix Assisted Laser Desorption Ionisation Time of Flight Mass Spectrometry (MALDI-TOF MS) is used as a novel technique to elucidate the structure of the rhodium aqua/chloro complexes formed in solution. Results obtained by CZE are confirmed by spectrophotometry.