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.     

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.     

Modeling of the relationship between electroosmotic flow and separation parameters in capillary zone electrophoresis using artificial neural networks and experimental design

The prediction of migration time of electroosmotic flow (EOF) marker was achieved by applying artificial neural networks (ANN) model based on principal component analysis (PCA) and standard normal distribution simulation to the input variables. The voltage of performance, the temperature in the capillary, the pH and the ionic strength of background electrolytes (BGE) were applied as the input variables to ANN. The range of the performance voltage studied was from 15 to 27 kV, and that of the temperature in the capillary was from 20 to 30 °C. For the pH values studied, the range was from 5.15 to 8.04. The range of the ionic strength investigated in this paper was from 0.040 to 0.097. The prediction abilities of ANN with different pre-processing procedure to the input variables were compared. Under the same performance conditions, the average prediction error of the migration time of the EOF marker was 5.46% with RSD = 1.76% according to 10 parallel runs of the optimized ANN structure by the proposed approach, and that of the 10 parallel predictions of the optimal ANN structure for the different performance conditions was 12.95% with RSD = 2.29% according to the proposed approach. The study showed that the proposed method could give better predicted results than other approaches discussed.     

Diphosphacarbollide analogues of the C5H5- anion: isolation of the nido-di- and triphosphacarboranes 7,8,9-P2CB8H10, [7,8,9-P2CB8H9]-, [7,8,10-P2CB8H9]-, and 7,8,9,10-P3CB7H8

Treatment of a solution of excess PCl(3) and PS (PS = "proton sponge" = 1,8-dimethylamino naphthalene) with arachno-4-CB(8)H(14) (1) in CH(2)Cl(2), followed by hydrolysis of the reaction mixture, resulted in the isolation of the eleven-vertex diphosphacarbaborane nido-7,8,9-P(2)CB(8)H(10) (2) (yield 34%) as the main product. Other products isolated from this reaction were the phosphacarboranes nido-7,8,9,10-P(3)CB(7)H(8) (3) (yield 5%) and closo-2,1-PCB(8)H(9) (4) (yield 15%). Compound 2 can be deprotonated by PS in CH(2)Cl(2) or NaH in diethyl ether to give the [nido-7,8,9-P(2)CB(8)H(9)](-) (2(-)()) anion, which gives back the original compound, 2, upon re-protonation. Thermal rearrangement of anion 2(-) (Na(+) salt) at 350 degrees C for 2 h produced the isomeric [nido-7,8,10-P(2)CB(8)H(9)](-) (5(-)()) anion, which was isolated as a PPh(4)(+) salt (yield 86%). Multinuclear ((1)H, (11)B, (31)P, and (13)C), two-dimensional [(11)B-(11)B] COSY, (1)H{(11)B(selective)}, (1)H{(31)P(selective)}, and gradient-enhanced ([(1)H-(13)C] HSQC) magnetic resonance measurements led to complete assignments of all resonances which are in excellent agreement with the structures proposed. Coupling constants, (1)J((31)P,(13)C), (2)J((31)P,C,(1)H), and (1)J((31)P,(31)P), were calculated using the DFT method B3LYP/6-311+G(d,p). The molecular geometries of all compounds were optimized ab initio at a correlated level of theory (RMP2(fc)) using the 6-31G basis set, and their correctness was assessed by comparison of the experimental (11)B and (13)C chemical shifts with those calculated by the GIAO-SCF/II//RMP2(fc)/6-31G method. The computations also include the structures and chemical shieldings of the still unknown isomers [nido-7,10,8-P(2)CB(8)H(9)](-) (6(-)) and [nido-7,9,8-P(2)CB(8)H(9)](-) (7(-)).