We consider a three-electron system in the Impurity Hubbard model with a coupling between nearest-neighbors. Our research aim consists of studying the structure of essential spectrum and discrete spectra of the energy...We consider a three-electron system in the Impurity Hubbard model with a coupling between nearest-neighbors. Our research aim consists of studying the structure of essential spectrum and discrete spectra of the energy operator of three-electron systems in the impurity Hubbard model in the quartet state of the system in a <em>v</em>-dimensional lattice. We have reduced the study of the spectrum of the three-electron quartet state operator in the impurity Hubbard model to the study of the spectrum of a simpler operator. We proved the essential spectra of the three-electron systems in the Impurity Hubbard model in the quartet state is the union of no more than six segments, and the discrete spectrum of the system is consists of no more than four eigenvalues.展开更多
The co-oxidation of a mixture of phenylsulfinylacetic acid (PSAA) and oxalic acid (OxH2) by Cr(VI) in 20% acetonitrile-80% water (v/v) medium follows third order kinetics, first order, each with respect to PSAA, OxH2 ...The co-oxidation of a mixture of phenylsulfinylacetic acid (PSAA) and oxalic acid (OxH2) by Cr(VI) in 20% acetonitrile-80% water (v/v) medium follows third order kinetics, first order, each with respect to PSAA, OxH2 and Cr(VI). The reaction involves nucleophilic attack of sulfur atom of PSAA on chromium of the oxidizing species, Cr(VI)-OxH2 to form a ternary complex, Cr(VI)-OxH2-PSAA followed by a one-step three-electron reduction of Cr(VI) to Cr(III) and simultaneous oxidation of both the substrates. The reaction is catalysed by Mn2+ ion while retarded by Al3+ ion. Electron releasing substituents in the meta- and para-positions of the phenyl ring of PSAA enhance the rate of co-oxidation while electron withdrawing substituents retards the reaction. The Hammett plots at different temperatures exhibit excellent correlation with negative ρ values. The reaction series obey isokinetic relationship and the observed isokinetic temperature is lying below the experimental range of temperature.展开更多
文摘We consider a three-electron system in the Impurity Hubbard model with a coupling between nearest-neighbors. Our research aim consists of studying the structure of essential spectrum and discrete spectra of the energy operator of three-electron systems in the impurity Hubbard model in the quartet state of the system in a <em>v</em>-dimensional lattice. We have reduced the study of the spectrum of the three-electron quartet state operator in the impurity Hubbard model to the study of the spectrum of a simpler operator. We proved the essential spectra of the three-electron systems in the Impurity Hubbard model in the quartet state is the union of no more than six segments, and the discrete spectrum of the system is consists of no more than four eigenvalues.
文摘The co-oxidation of a mixture of phenylsulfinylacetic acid (PSAA) and oxalic acid (OxH2) by Cr(VI) in 20% acetonitrile-80% water (v/v) medium follows third order kinetics, first order, each with respect to PSAA, OxH2 and Cr(VI). The reaction involves nucleophilic attack of sulfur atom of PSAA on chromium of the oxidizing species, Cr(VI)-OxH2 to form a ternary complex, Cr(VI)-OxH2-PSAA followed by a one-step three-electron reduction of Cr(VI) to Cr(III) and simultaneous oxidation of both the substrates. The reaction is catalysed by Mn2+ ion while retarded by Al3+ ion. Electron releasing substituents in the meta- and para-positions of the phenyl ring of PSAA enhance the rate of co-oxidation while electron withdrawing substituents retards the reaction. The Hammett plots at different temperatures exhibit excellent correlation with negative ρ values. The reaction series obey isokinetic relationship and the observed isokinetic temperature is lying below the experimental range of temperature.
