1.5-dimensional scattering barrier

A full six-dimensional PES for the HOCO system has been developed by Schatz and coworkers, particularly L. B. Harding (Kudla et al. 1992 Schatz et al. 1987). This proved to be challenging because of numerous local minima and transition states, and consequently the development of the PES has taken several years. Many points were calculated by using large scale ab initio techniques and the surface was adjusted to reconcile a broad array of experimental data such as nascent product excitations, HOCO decomposition rates, overall bimolecular reaction rates, barrier heights, enthalpy changes, HOCO structural properties, and inelastic scattering data. This PES has been used in several computational studies of the reaction dynamics that employ classical (Kudla and Schatz 1991 Kudla... 

Along the same lines, it is worthwhile mentioning that even the two-dimensional contour plot obscures some important features of the true multidimensional PES. In order to illustrate this fact, consider the following argument. Some of the features in the PES can be probed by experiments the weakly physisorbed, molecularly and atomically chemisorbed species by surface spectroscopies and the activation barriers by molecular beam scattering experiments. Thus, much of the PES can be determined and the reader may wonder why one does not simply join these individual regions together and find the PES ... 

The distinguishing feature of this work, however, is that the activation barrier is allowed to vary with different positions of the H2 in the surface unit cell. This is a clever approach which captures much of the influence of the corrugated surface. Moreover, under these approximations, the dynamical equations become only three-dimensional and, in fact, are identical to those of an atom scattering from a rigid, corrugated surface but with a potential with a sink. The TDSE is solved by the FFT procedure. Hence, it is possible to treat diffraction, tunneling, and dissociative chemisorption by accurate quantum techniques, at least on this simple type of PES. 

The H2 ligand undergoes rapid two-dimensional hindered rotation about the M-H2 axis, that is it spins (librates) in propeller-like fashion with little or no wobbling. This phenomenon has been extensively studied by neutron scattering methods and computationally [19-22], Significantly, there is always at least a small barrier to rotation, AE, brought about by M—>H2 cr backdonation (BD) (Scheme 20.8). The cr-donation from H2 to M cannot give rise to a rotational barrier since it is completely isotropic about the M-H2 bond. The barrier actually... 

Cuccaro et al. (96) interpreted the time delays in Table 2 as resonances and assigned a value of 0 for the third quantum number v without explanation. We identify these resonances as quantized transition states. The analysis presented above of scattering by one-dimensional barriers, with the conclusion that the v = 0 pole is the most important because it is closest to the real energy axis, supplies a justification for the assignment of the third quantum number. 

In HAB molecules the potential surface involves three variables, the molecular angle, the AB distance and the H-AB separation if internal coordinates are chosen. Alternatively a representation is often taken in which, in addition to the AB separation, the H atom is described by its separation from a point on the AB axis (midpoint or center of mass) and the corresponding angle, sometimes referred to as scattering coordinates. Depending on the problem to be solved, the entire three-dimensional surface (very seldom) or a representative section thereof is calculated in ab initio work. The most interesting questions in an HAB study are (1) is the system bent or linear in the various states, (2) what is the energy difference for the two isomers HAB and ABH and what is the barrier to possible unimolecular conversion, and (3) how is the stability situation in the excited states ... 

The results (14)-(17) and (21)-(23) are special cases of a more systematic representation of the conduction and the current-voltage characteristic of a given junction due to Landauer [105, 106]. Lan-dauer s original result was obtained for a system of two one-dimensional leads connecting two macroscopic electrodes ( electron reservoirs ) via a scattering object or a barrier characterized by a transmission function T(E). The zero-temperature conductance, measxu ed as the limit <1> —> 0 of the ratio //< > between the current and the voltage drop between the reservoirs, was found to be... 

PC nanocomposites exhibit exceptional improvement in mechanical properties including stiffness, strength, dimensional stability as well as exhibiting barrier properties far better than conventionally filled polymers. In addition, because of the length scale involved that minimizes scattering, nanocomposites are usually transparent. Furthermore, PC nanocomposites exhibit a significant increase in thermal stability as well as self-extinguishing characteristics and enhanced flame retardancy. 

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