On the Right-Symmetric Algebras with a Unital Matrix Subalgebra

Siberian Mathematical Journal - Under study are the right-symmetric algebras over a field  $ F $ which possess a “unital” matrix subalgebra  $...     

The free Malcev superalgebra on one odd generator and related superalgebras

A base of the universal multiplicative envelope of the free Malcev superalgebra ℳ on one odd generator is constructed. Some corollaries for skew-symmetric functions and central elements in free Malcev and free alternative algebras are obtained. Moreover, a base of the Poisson-Malcev superalgebra of ℳ is constructed. As a corollary, a set of elements that spans the free alternative superalgebra on one odd generator is obtained. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 10, No. 4, pp. 97–106, 2004.     

On the stability of reconstruction of distributions of multivariate random functions from the distributions of their projections

Multivariate random functions belonging to a certain class are considered. A method of reconstruction of distributions of such functions from the distributions of their projections is described and the stability of the method is discussed.     

Geometry and electronic structure of a heterometallic cluster Mo<Subscript>2</Subscript>Mg<Subscript>2</Subscript> in different oxidation states of Mo: a DFT study

Reduction of tetranuclear heterometallic complex Mo₂Mg₂ was simulated using the B3LYP and PBE density functional methods. The results of geometry calculations of the initial complex [Mo^VIO₂Mg(MeOH)₂(OMe)₄]₂ and a partially reduced Mo^V complex are in good agreement with experimental data. The reduced Mo^III complex is characterized by a decrease in the binding energy of aqua ligands. Structural rearrangement of the complex with release of a coordination position at the Mo atoms requires small energy expenditure. One can assume that the reduction of the polynuclear complex causes overcrowding of its coordination sphere, which favors formation of dinitrogen complexes. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 441–457, March, 2008.     

Condensation of Isatoic Anhydride with Hetarylguanidines

Condensation of isatoic anhydride with 4-methylquinazolin-2-yl-, 2-benzoxazolyl-, 2-benzothiazolyl-, and 4,6-dimethylpyrimidin-2-ylguanidines leads to the corresponding 2-hetarylamino-4-hydroxyquinazolines as a result of cyclization of intermediate anthranilic acid hetarylguanidides. These intermediates can be isolated as individual compounds.     

Calculation of the gas hydrate HS-1 framework structure and its energy estimation

Using the Zimmennan-Pimentel potential, we have calculated the basic atomic coordinates of the unit cell of the gas hydrate HS-lframework. A minimum change in the strain energy of hydrogen bonh U_H fakes place in formation of this framework from ice Ih. The dependence of U_H on the lattice parameters is derived.Institute of Inorganic Chemistry, Siberian Branch, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 34, No. 5, pp. 175–178, September–October, 1993.Translated by T. Yudanova     

Methane Hydroxylation by Methane Monooxygenase: On the Problem of the Process Dynamics

Published data on the kinetic isotope effects of the hydroxylation of deuterium-substituted methane molecules (CHD₃, CH₂D₂, and CH₃D) by methane monooxygenase are examined in the framework of the two-step nonradical mechanism through the intermediate formation of a complex containing pentacoordinate carbon. The kinetic schemes with the first step involving one, two, and three hydrogen atoms of the oxidized substrate are considered. Contrary to the widely accepted oxygen rebound mechanism, the experimental results obtained for the oxidation of various substrates by methane monooxygenase and cytochrome P450 can be explained from the viewpoint of the dynamics of a general nonradical mechanism.     

Transition state geometry in radical abstraction reactions: comparison of interatomic distances in the intersecting parabolas and Morse curves models with quantum-chemical calculations

Interatomic distances in the transition state were estimated for the reactions of radical abstraction: H^· + H₂, H^· + HCl, H^· + CH₄, N^·H₂ + NH₃, HO^· + H₂O, HO₂ ^· + HOOH, and C^·H₃ + SiH₄. The calculation was performed by the quantum-chemical density functional method or coupled clusters method (QCH), as well as by the methods of intersecting parabolas (IPM) and Morse curves (IMM), using experimental data (activation energies and reaction enthalpies). The results of the latter two methods are close to the quantum-chemical calculation and differ only by the increment a: r(IPM or IMM) = a + r(QCH), where a = –4.5·10^–12 m for IPM and a = +1.9·10^–12 m for IMM.     

Quantum chemical modeling of CO oxidation by the active site of molybdenum CO dehydrogenase

The catalytic mechanism of molybdenum containing CO dehydrogenase has been studied using hybrid DFT methods with quite large chemical models. The recent high-resolution X-ray structure, showing the surprising presence of copper linked to molybdenum, was used as a starting point. A pathway was initially found with a low barrier for C-O bond formation and CO2 release. However, this pathway did not include the formation of any S-CO2 species, which had been suggested by experiments with an n-butylisocyanide inhibitor. When these SCO2 structures were studied they were found to lead to deep minima, making CO2 release much more difficult. A large effort was spent, including investigations of other spin states, varying the number of protons and electrons, adding water, etc., until a plausible pathway for S-C bond cleavage was found. In this pathway a water molecule is inserted in between molybdenum and the SCO2 group. Full catalytic cycles, including electron and proton transfers, are constructed both with and without S-C bond formation. When these pathways are extended to two full catalytic cycles it can be understood why the formation of the S-C bond actually makes catalysis faster, even though the individual step of CO2 release becomes much more difficult. These results agree well with experimental findings.     

Spin crossover in polyaniline

Solutions of the basic form of polyaniline in m-cresol were studied by ESR and optical spectroscopy in the visible region. m-Cresol can slowly (during one month) protonate polyaniline. For the first time characteristic features of spin crossover were found: sharp changes in the magnetic susceptibility and the ESR line width of polyaniline at ∼200 and 250 K, a smooth decrease in the susceptibility and absorption with the temperature increase from 293 to 423 K, and the temperature hysteresis. The temperature-induced structural rearrangements of polyaniline are caused, most likely, by singlet-triplet transitions in relatively short sections of the polymer chain. The model of short sections permits to explain the origin of the temperature-independent part of susceptibility. Quantum-chemical calculations for the aniline dimers and tetramers describe correctly the singlet-triplet splitting value, thermochromism, and HFS constants in the spectrum of polyaniline. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 1959–1966, October, 2007.