A reinterpretation of the mechanism of the simplest reaction at an sp3-hybridized carbon atom: H + CD4 --> CD3 + HD

A comparison between theory and experiment for the benchmark H + CD4 --> HD + CD3 abstraction reaction yields a reinterpretation of the reaction mechanism and highlights the unexpected contribution of a stripping mechanism. Whereas the best analytic surface fails to reproduce experiment, a first-principles direct-dynamics (on the fly) treatment is in good agreement, showing that the H + CD4 reaction exhibits extreme sensitivity to modest differences in the potential energy surface. We find that bent H-D-C transition state geometries play an important role in the dynamics. A simple model that relates the scattering angle impact parameter and cone of acceptance accounts well for the overall reaction dynamics.     

Equivalence of differential operators with a regular singular point

Functional Analysis and Its Applications -     

Magnetic susceptibility and order parameter of the spin-glass-like phase of the double-exchange model

The magnetic susceptibility and Edwards-Anderson order parameter q of the spin-glass-like (SGL) phase of the double-exchange model are evaluated in the weak-coupling or RKKY limit. Dynamical mean-field theory is used to show that q = M(T/T(SGL))2, where M is the classical Brillouin function and T(SGL) is the SGL transition temperature. The correlation length of the SGL phase is determined by a correlation parameter Q that maximizes T(SGL) and minimizes the free energy. The magnetic susceptibility has a cusp at T(SGL) and reaches a nonzero value as T --> 0.     

Reaction of Cl with CD4 excited to the second C-D stretching overtone

The effects of vibrational excitation on the Cl+CD(4) reaction are investigated by preparing three nearly isoenergetic vibrational states: mid R:3000 at 6279.66 cm(-1), |2100> at 6534.20 cm(-1), and |1110> at 6764.24 cm(-1), where |D(1)D(2)D(3)D(4)> identifies the number of vibrational quanta in each C-D oscillator. Vibrational excitation of the perdeuteromethane is via direct infrared pumping. The reaction is initiated by photolysis of molecular chlorine at 355 nm. The nascent methyl radical product distribution is measured by 2+1 resonance-enhanced multiphoton ionization at 330 nm. The resulting CD(3) state distributions reveal a preference to remove all energy available in the most excited C-D oscillator. Although the energetics are nearly identical, the authors observe strong mode specificity in which the CD(3) state distributions markedly differ between the three Cl-atom reactions. Reaction with CD(4) prepared in the |3000> mode leads to CD(3) products populated primarily in the ground state, reaction with CD(4) prepared in the |2100> mode leads primarily to CD(3) with one quantum of stretch excitation, and reaction with CD(4) prepared in the |1110> mode leads primarily to CD(3) with one quantum of C-D stretch excitation in two oscillators. There are some minor deviations from this behavior, most notably that the Cl atom is able to abstract more energy than is available in a single C-D oscillator, as in the case of |2100>, wherein a small population of ground-state CD(3) is observed. These exceptions likely result from the mixings between different second overtone stretch combination bands. They also measure isotropic and anisotropic time-of-flight profiles of CD(3) (nu(1)=1,2) products from the Cl+CD(4) |2100> reaction, providing speed distributions, spatial anisotropies, and differential cross sections that indicate that energy introduced as vibrational energy into the system essentially remains as such throughout the course of the reaction.