Bimolecular reaction rates from ring polymer molecular dynamics: application to H + CH4 → H2 + CH3

In a recent paper, we have developed an efficient implementation of the ring polymer molecular dynamics (RPMD) method for calculating bimolecular chemical reaction rates in the gas phase, and illustrated it with applications to some benchmark atom-diatom reactions. In this paper, we show that the same methodology can readily be used to treat more complex polyatomic reactions in their full dimensionality, such as the hydrogen abstraction reaction from methane, H + CH(4) → H(2) + CH(3). The present calculations were carried out using a modified and recalibrated version of the Jordan-Gilbert potential energy surface. The thermal rate coefficients obtained between 200 and 2000 K are presented and compared with previous results for the same potential energy surface. Throughout the temperature range that is available for comparison, the RPMD approximation gives better agreement with accurate quantum mechanical (multiconfigurational time-dependent Hartree) calculations than do either the centroid density version of quantum transition state theory (QTST) or the quantum instanton (QI) model. The RPMD rate coefficients are within a factor of 2 of the exact quantum mechanical rate coefficients at temperatures in the deep tunneling regime. These results indicate that our previous assessment of the accuracy of the RPMD approximation for atom-diatom reactions remains valid for more complex polyatomic reactions. They also suggest that the sensitivity of the QTST and QI rate coefficients to the choice of the transition state dividing surface becomes more of an issue as the dimensionality of the reaction increases.     

Asymptotics of the Gurevich-Pitaevskii universal special solution of the Korteweg-de Vries equation as |<Emphasis Type="Italic">x</Emphasis>| → ∞

A complete asymptotic expansion as x → ±∞ of the Gurevich-Pitaevskii universal special solution of the Korteweg-de Vries equation u _t + u _xxx + u _ux = 0 is constructed and justified. The expansion is infinitely differentiable with respect to the variables t and x and, together with the asymptotic expansions of all its derivatives with respect to independent variables, is uniform on any compact interval of variation of the time t.     

Synthesis,Structure, and Physicochemical Properties of Lithium Uranovanadate

A new chemical compound, lithium uranovanadate, was synthesized and studied by X-ray diffraction, IR spectroscopy, and thermography. Standard enthalpies of formation of lithium uranovanadate and its dihydrate at 298.15 K were determined by means of reaction and adiabatic vacuum calorimetry. Temperature dependence of heat capacity in the range 80-300 K was obtained for crystalline LiVUO₆·2H₂O and thermodynamic characteristics of its synthesis were calculated.     

Mass-spectrometric an EPR studies of methane interaction with Re?Al?O oxide catalysts

The effect of oxidative-reductive pretreatment of Re–Al–O catalysts on their activity in methane aromatization has been established. Paramagnetic centers have been identified and their contribution to the conversion of methane into benzene over these catalyst is discussed.

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- Re–Al–O . .

     

Temperature-programmed reaction of methane with Re- and Pt-containing oxide contacts

Mass-spectrometric data for the products of temperature-programmed reaction of methane with Re- and Pt-containing Al₂O₃ contacts show that the active sites for methane conversion to benzene over these systems are formed during high-temperature contact of these systems with methane.

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- Re, Pt- , , , .

     

Symmetries of Kadomtsev-Petviashvili equation,isomonodromic deformations,and “nonlinear” generalizations of the special functions of wave catastrophes

A special solution of the Kadomtsev-Petviashvili equation $$u_{tx} + u_{xxxx} + 3u_{yy} + 3(u^2 )_{xx} = 0$$ that is a “nonlinear” analog of the special function of wave catastrophe corresponding to a singularity of swallowtail type is considered. On the basis of a symmetry analysis it is shown that the solution must simultaneously satisfy nonlinear ordinary differential equations with respect to all three independent variables. After “dressing” of the corresponding Ψ function, equations with respect to a spectral parameter arise in a regular manner, and this indicates the possibility of applying the method of isomonodromic deformation.