Dihydrogen and methane elimination from adducts formed by the interaction of carbenium and silylium cations with nucleophiles

Stationary points for reactions R'R' 'HX(+) + YH --> [R'R' 'X-Y](+) + H(2) (I) and R'(CH(3))HX(+) + YH -->[R'HX-Y](+) + CH(4) (II) (R', R' ' = CH(3), H; X = C, Si; Y = CH(3)O, (CH(3))(2)N, and C(6)H(5)) are located and optimized by the B3LYP/aug-cc-pVDZ method. A similar mechanism was found to be operative for both types of reactions with X = C and X = Si. Formation of the intermediate (adduct) results in the transfer of electron density from the electron-rich bases to the X atoms and in the growth of a positive charge on a hydrogen atom attached to Y. This mobile proton may shift from Y to X, and the relative energies of transition states for elimination reactions (Delta) depend on the ability of the X atom to retain this proton. Therefore, Deltagrows on going from Si to C and with increasing numbers of methyl substituents. For X = C, the Deltavalue for both reactions correlates well with the population of the valence orbitals of X in a wide range from -44 kcal/mol (methyl cation/benzene) to 31 kcal/mol (isopropyl cation/methanol). For X = Si this range is more narrow (from -19 to -5.0 kcal/mol), but all Delta values are negative with the exclusion of silylium ion/benzene systems, adducts of which are pi- rather than sigma-complexes. The energy minima for product complexes for H(2) elimination are very shallow, and several are dissociative. However, complexes with methane which exhibit bonding between X and the methane hydrogen are substantially stronger, especially for systems with X = Si. The latter association energy may reach 8 kcal/mol (Si...H distance is 2 A).     

Study of the algorithm for time-frequency analysis of the measurement series of night mesospheric ozone emission spectra at millimeter waves

An algorithm for time–frequency analysis of irregular time data series is developed and tested to study variations of night mesospheric ozone radiation, observed at millimeter waves from the Earth’s surface. Some results of numerical and field experiments are presented.     

On the construction of the Lyapunov function with sign-definite derivative with the help of auxiliary functions with sign-constant derivatives

The short survey of studies of the asymptotic stability with the help of auxiliary functions (positive definite and nonnegative) whose derivatives are nonpositive by virtue of the equations of perturbed motion and the construction of positive definite Lyapunov functions with negative definite derivatives on the basis of these auxiliary functions is given. The example of the construction of the Lyapunov function with the use of an auxiliary nonnegative function with nonpositive derivative is presented.     

Vibrational spectra of hexafluorodisiloxane and internal rotation around the SiO bond. An ab initio study

The structure of hexafluorodisiloxane was optimized at different levels of theory up to MP2/6-31G^*, and the vibrational spectrum was calculated and compared with the experimental one. It was shown that at the Hartree-Fock level the simple SCF/3-21 (O^*) basis set gives satisfactory results. The geometry was also optimized at two C_2v structures which appear to be saddle points on the SiF₃ rotor potential curve. The significant change of the SiOSi angle equilibrium value in the course of the SiF₃ group rotation was explained by assuming repulsion between lone pair electrons of fluorines and oxygen. This effect is also revealed in the predicted change in the v_asSiOSi frequency on going from the C₂ to the C_2v structure. This provides the explanation of some unusual features in the vibrational spectra of hexahalodisiloxanes, namely large gas-solid shifts of v_as SiOSi and splitting of this mode in the matrices.     

On Solutions of the Integrable Boundary Value Problem for KdV Equation on the Semi-Axis

This paper is concerned with the Korteweg–de Vries (KdV) equation on the semi-axis. The boundary value problem with inhomogeneous integrable boundary conditions is studied. We establish some characteristic properties of solutions of the problem. Also we construct a wide class of solutions of the problem using the inverse spectral method.     

Physical Aspects of the Waste of Re-Enrichment Utilization for Recycled Uranium from VVER-1000/1200 Spent Fuel Reprocessing in Molten Salt Reactors

Physics of Atomic Nuclei - The problems of utilization of waste from re-enrichment of regenerated uranium from 232U isotope in a reactor with circulating liquid fuel based on melts of metal...     

Lyapunov's second method in problems of the stability of solutions of systems with impulse effect

A system of ordinary differential equations with impulse effect at fixed moments of time is considered. The system is assumed to have the zero solution. It is shown that the existence of a corresponding Lyapunov function is a necessary and sufficient condition for the uniform asymptotic stability of the zero solution. Restrictions on perturbations of the right-hand sides of differential equations and impulse effects are obtained under which the uniform asymptotic stability of the zero solution of the ‘unperturbed’ system implies the uniform asymptotic stability of the zero solution of the ‘perturbed’ system. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Synthesis,crystal structure and properties of copper(II) complexes with triethanolamine and carboxylic acids (succinic,salicylic, cinnamic)

Transition Metal Chemistry - The interaction of triethanolamine (TEA) with Cu(II) salts of salicylic, cinnamic and succinic acids was studied for the first time. The structure of the synthesized...     

Experimental investigations of fast-proton production in a picosecond laser plasma

Results of experimental investigations of fast-proton production in a laser plasma are presented for the case where the intensity of laser radiation at the targets is 2 × 10¹⁸ W/cm². Three processes of fast-proton acceleration in laser plasma are investigated: (1) the acceleration of protons from the front surface toward the laser pulse, (ii) the acceleration of protons from the front surface of the target toward its interior, and (iii) the acceleration of protons from the rear foil surface in the outward direction. The activation procedure and CR-39 tracker detectors featuring a set of various-thickness aluminum filters were used to record fast protons. It turned out that the proton-acceleration process is the most efficient in the case of proton acceleration from the rear foil surface in the outward direction. Experimental results revealed that about N _p = 10⁷ protons of energy in the region E _p > 1.9 MeV that are accelerated from the target surface toward a laser ray, N _p = 4× 10⁷ protons of energy in the region E _p > 1.9 MeV that are accelerated fromthe front surface of the target toward its interior, and N _p = 4×10⁸ protons of energy in the region E _p > 1.9 MeV that are accelerated from the rear foil surface in the outward direction are generated at a laser-radiation intensity of 2 × 10¹⁸ W/cm² at the surface of aluminum, copper, and titanium targets. Experimental investigations aimed at optimizing the process of proton acceleration from the rear surface of aluminum foils were performed by varying the foil thickness over the range between 1 and 100 μm. The results of these experiments showed that there is an optimum foil thickness of 10 μm, in which case protons of maximum energy 5 MeV are generated.     

Homogeneous polynomials as Lyapunov functions in the stability research of solutions of difference equations

The linear autonomous system of difference equations x(n+1)=Ax(n) is considered, where is a real nonsingular k×k matrix. In this paper it has been proved that if W(x) is any homogeneous polynomial of m-th degree in x, then there exists a unique homogeneous polynomial V(x) of m-th degree such that ΔV=V(Ax)-V(x)=W(x) if and only if where are the eigenvalues of the matrix A. The theorem on the instability has also been proved.