Two-Variable Identities in Groups and Lie Algebras

We study two-variable Engel-like relations and identities characterizing finite-dimensional solvable Lie algebras and, conjecturally, finite solvable groups and introduce some invariants of finite groups associated with such relations. Bibliography: 29 titles.     

α-Fe_2O_3纳米微粒/硬脂酸交替L-B膜的结构表征

纳米微粒(NP)是一个新的物质层次,它具有一系列新异的物理、化学特性,涉及到大块样品中所忽略的,或根本不具有的基本物理、化学问题.用NP 制造新型的人工功能材料具有广泛的潜在应用.一个有意义的挑战是能否对NP 进行有序的组装.Zhao andFendler 等曾利用Fe_3O_4NP 进行有序组装的尝试.我们也在前期的初步研究中利用Langmuir-Blodgett(LB)技术对7nm 的α-Fe_2O_3 NP 进行了有序组装的探索,获得了α-Fe_2O_3 NP-硬脂酸交替LB 多层膜(FNSLF).然而这种交替膜的有序情况还不十分清楚.     

The thermal decomposition of thiirane: a mechanistic study by ab initio MO theory

Using high-level ab initio MO methods, we have identified two reaction pathways with different thermodynamic and kinetic properties for the thermal decomposition of the three-membered heterocycle thiirane (C2H4S) and related derivatives. A homolytic ring opening, followed by attack of the generated diradical on another thiirane molecule, and subsequent elimination of ethene in a fast radical chain reaction results in the formation of disulfur molecules in their triplet ground state (3S2) and requires activation enthalpies of deltaH#(298) = 222 kJ mol(-1) and deltaG#(298) = 212 kJ mol(-1). This reaction mechanism would result in a first-order rate law in agreement with one reported gas-phase experiment but does neither match the experimental activation energy nor does it explain the observed retention of the stereochemical configuration in the thermal decomposition of certain substituted thiiranes. Alternatively, sulfur atoms can be transferred from one thiirane moleculeto another with the intermediate formation of thiirane 1-sulfide (C2H4S2). This molecule can either decompose unimolecularly to ethene and disulfur in its excited singlet state (1S2) or, by means of spin crossover, S2 in its triplet ground state may be formed. On the other hand, the thiirane 1-sulfide may react with itself and transfer one sulfur atom from one molecule to another with formation of thiirane 1,1-disulfide (C2H4S3), which is an analogue of thiirane sulfone; thiirane is formed as the second product. The 1,1-disulfide may then decompose to ethene and S3. In still another bimolecular reaction, the thiirane 1-sulfide may react with itself in a strongly exothermic reaction to give S4 and two equivalents of ethene. This series of reactions results in a second-order rate law and requires activation enthalpies of deltaH#(298) = 109 kJ mol(-1) and deltaG#(298) = 144 kJ mol(-1) for the formation of thiirane 1-sulfide, while the consecutive reactions require less activation enthalpy. Elemental sulfur (S8) is eventually formed by oligomerization of either S2, S3, or S4 in spin-allowed reactions. These findings are in agreement with most experimental data on the thermal desulfurization of thiirane and its substituted derivatives. Thiirane 1-persulfide (C2H4S3) with a linear arrangement of the three sulfur atoms as well as zwitterions and radicals derived from thiirane are not likely to be intermediates in the thermal decomposition of episulfides.     

The role of a vector-valued field in multidimensional universe geometry

For a model of the multidimensional universe we take a smooth manifold S which under the action of a compact Lie group G fibres into orbits of the same type G/H acquiring the structure of a fibre bundle with typical fibre G/H and base-the orbit space S/G (identified with the four-dimensional spacetime). The notion of a connection form on the fibre bundle SS/G is defined and its role for some geometrical structures on S is considered. In the framework of a theory of G-invariant tensor-type fields on S, it is shown that -being itself a field of this type-determines a dimensional reduction of the objects on S to objects on S/G.     

Study on the Kinetics of Non-isothermal Dehydration of Alkaline Earth Metal Selenites

The dehydration kinetics of crystallohydrates of beryllium, magnesium and calcium selenites were studied under non-isothermal conditions. The values of the activation energy of dehydration, the pre-exponential factor in Arrhenius equation and the change of entropy for the formation of the activated complex were calculated using the calculation procedure of Coats and Redfern. Thermal stability and activation energy of dehydration of the crystallohydrates were found to increase by the same order. The relationships observed were interpreted using Klopman’s generalized perturbation theory of chemical reactivity. The same theory was applied to explain the differences in the IR spectra of the selenite crystallohydrates studied.     

Visualisation of interlaboratory comparison results in PomPlots

In this work a novel graphical method is applied to the presentation of intercomparison results. This is demonstrated with the results of a recent intercomparison in measuring the ¹³⁷Cs, ⁴⁰K, and ⁹⁰Sr activity concentration in milk powder. The “PomPlot”, an intuitive graphical method, is used for producing a summary overview of the participants’ results of a common measurand. The “PomPlot” displays (relative) deviations of individual results from the reference value on the horizontal axis and (relative) uncertainties on the vertical axis.     

Synthesis of unstrained Criegee intermediates: inverse α-effect and other protective stereoelectronic forces can stop Baeyer–Villiger rearrangement of γ-hydroperoxy-γ-peroxylactones

How far can we push the limits in removing stereoelectronic protection from an unstable intermediate? We address this question by exploring the interplay between the primary and secondary stereoelectronic effects in the Baeyer–Villiger (BV) rearrangement by experimental and computational studies of γ-OR-substituted γ-peroxylactones, the previously elusive non-strained Criegee intermediates (CI). These new cyclic peroxides were synthesized by the peroxidation of γ-ketoesters followed by in situ cyclization using a BF₃·Et₂O/H₂O₂ system. Although the primary effect (alignment of the migrating C–R_m bond with the breaking O–O bond) is active in the 6-membered ring, weakening of the secondary effect (donation from the OR lone pair to the breaking C–R_m bond) provides sufficient kinetic stabilization to allow the formation and isolation of stable γ-hydroperoxy-γ-peroxylactones with a methyl-substituent in the C6-position. Furthermore, supplementary protection is also provided by reactant stabilization originating from two new stereoelectronic factors, both identified and quantified for the first time in the present work. First, an unexpected boat preference in the γ-hydroperoxy-γ-peroxylactones weakens the primary stereoelectronic effects and introduces a ∼2 kcal mol⁻¹ Curtin–Hammett penalty for reacquiring the more reactive chair conformation. Second, activation of the secondary stereoelectronic effect in the TS comes with a ∼2–3 kcal mol⁻¹ penalty for giving up the exo-anomeric stabilization in the 6-membered Criegee intermediate. Together, the three new stereoelectronic factors (inverse α-effect, misalignment of reacting bonds in the boat conformation, and the exo-anomeric effect) illustrate the richness of stereoelectronic patterns in peroxide chemistry and provide experimentally significant kinetic stabilization to this new class of bisperoxides. Furthermore, mild reduction of γ-hydroperoxy-γ-peroxylactone with Ph₃P produced an isolable γ-hydroxy-γ-peroxylactone, the first example of a structurally unencumbered CI where neither the primary nor the secondary stereoelectronic effect are impeded. Although this compound is relatively unstable, it does not undergo the BV reaction and instead follows a new mode of reactivity for the CI – a ring-opening process.

Protecting stereoelectronic effects prevent Baeyer–Villiger rearrangement and stabilize γ-OX-γ-peroxylactones (X = H, OH), the previously elusive non-strained Criegee intermediates.     

The Structure of New Host Molecules that form Channel Inclusion Compounds

1,3-Benzenediamine,N,N′-bis(4,6-dichloro-1,3,5-triazine-2-yl) and 1,3,5-Triazine,2,2′-[2-methyl-1,3-phenylenebis(oxy)] bis(4,6-dichloro) were synthesized as host molecules. The inclusion compound of 1,3-Benzenediamine,N,N′-bis(4,6-dichloro-1,3,5-triazine-2-yl) crystallizes in the monoclinic crystal system in space group C2/c. The host molecule occupies the space group 2-fold special position and packed in the crystal lattice in such a manner as to leave channels running along the c axis of a rectangular cross-section. It crystallizes with two molecules of acetone that are hydrogen bonded to the amino nitrogen atoms. Molecules of 1,3,5-Triazine,2,2′-[2-methyl-1,3-phenylene bis(oxy)]bis(4,6-dichloro) are packed in the crystal in such a manner as to leave channels of a trapezoid cross-section that are running along the a axis. Guest molecules such as metanol, ethanol, and ethyl acetate can be used to fill the channels. The crystal structures of two inclusion compounds are described.     

Thermal and calorimetric investigations on crystalline hydrates of barium hydroxide and their deuterated analogues

The thermal decompositions of Ba(OH)₂ · 8H₂O, Ba(OH)₂ · 8D₂O, Ba(OH)₂ · H₂O and Ba(OH)₂ · D₂O were studied and the phase transitions were identified by DSC and DTA methods. The corresponding enthalpy changes were determined and compared with those calculated from the thermodynamic data. A decrease of the thermal stability was demonstrated for the deuterated crystal hydrates in comparison with the normal ones.

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Zusammenfassung Die thermische Zersetzung von Ba(OH)₂ · 8H₂O, Ba(OH)₂ · 8D₂O, Ba(OH)₂ · H₂O und Ba(OH)₂ · D₂O wurde untersucht. Phasenübergänge wurden mittels DSC und DTA ermittelt. Die entsprechenden Enthalpieveränderungen wurden bestimmt und mit den aus thermodynamischen Daten berechneten Werten verglichen. Die deuterierten Kristallhydrate sind thermisch weniger stabil als die leichtes Kristallwasser enthaltenden Verbindungen.

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()₂ · 8₂, ()₂ · 8D₂O, Ba(OH)₂·H₂O Ba(OH)₂·D₂O. , . .