ALBERT

Notes: Electron transfer reactions at semiconductor/liquid interfaces are studied using the Fermi Golden rule and a free electron model for the semiconductor and the redox molecule. Bardeen's method is adapted to calculate the coupling matrix element between the molecular and semiconductor electronic states where the effective electron mass in the semiconductor need not equal the actual electron mass. The calculated maximum electron transfer rate constants are compared with the experimental results as well as with the theoretical results obtained in Part I using tight-binding calculations. The results, which are analytic for an s-electron in the redox agent and reduced to a quadrature for pz- and dz2-electrons, add to the insight of the earlier calculations. © 2000 American Institute of Physics.

Notes: Electron transfer reaction rate constants at semiconductor/liquid interfaces are calculated using the Fermi Golden Rule and a tight-binding model for the semiconductors. The slab method and a z-transform method are employed in obtaining the electronic structures of semiconductors with surfaces and are compared. The maximum electron transfer rate constants at Si/viologen2+/+ and InP/Me2Fc+/0 interfaces are computed using the tight-binding type calculations for the solid and the extended-Hückel for the coupling to the redox agent at the interface. These results for the bulk states are compared with the experimentally measured values of Lewis and co-workers, and are in reasonable agreement, without adjusting parameters. In the case of InP/liquid interface, the unusual current vs applied potential behavior is additionally interpreted, in part, by the presence of surface states. © 2000 American Institute of Physics.

Notes: A theory is described for the variation in the rate constants for formation of different ozone isotopomers from oxygen atoms and molecules at low pressures. The theory is implemented using a simplified description which treats the transition state as loose. The two principal features of the theory are a phase space partitioning of the transition states of the two exit channels after formation of the energetic molecule and a small (ca. 15%) decrease in the effective density of states, ρ [a "non-Rice–Ramsperger–Kassel–Marcus (RRKM) effect"], for the symmetric ozone isotopomers [B. C. Hathorn and R. A. Marcus, J. Chem. Phys. 111, 4087 (1999)]. This decrease is in addition to the usual statistical factor of 2 for symmetric molecules. Experimentally, the scrambled systems show a "mass-independent" effect for the enrichments δ (for trace) and E (for heavily) enriched systems, but the ratios of the individual isotopomeric rate constants for unscrambled systems show a strongly mass-dependent behavior. The contrasting behavior of scrambled and unscrambled systems is described theoretically using a "phase space" partitioning factor. In scrambled systems an energetic asymmetric ozone isotopomer is accessed from both entrance channels and, as shown in paper I, the partitioning factor becomes unity throughout. In unscrambled systems, access to an asymmetric ozone is only from one entrance channel, and differences in zero-point energies and other properties, such as the centrifugal potential, determine the relative contributions (the partitioning factors) of the two exit channels to the lifetime of the resulting energetic ozone molecule. They are responsible for the large differences in individual recombination rate constants at low pressures. While the decrease in ρ for symmetric systems is attributed to a small non-RRKM effect η, these calculated results are independent of the exact origin of the decrease. The calculated "mass-independent" enrichments, δ and E, in scrambled systems are relatively insensitive to the transition state (TS), because of the absence of the partitioning factor in their case (for a fixed non-RRKM η). They are compared with the data at room temperature. Calculated results for the ratios of individual isotopomeric rate constants for the strongly mass-independent behavior for unscrambled systems are quite sensitive to the nature of the TS because of the partitioning effect. The current data are available only at room temperature but the loose TS is valid only at low temperatures. Accordingly, the results calculated for the latter at 140 K represent a prediction, for any given η. At present, a comparison of the 140 K results can be made only with room temperature data. They show the same trends as, and are in fortuitous agreement, with the data. Work is in progress on a description appropriate for room temperature. © 2000 American Institute of Physics.

Notes: Ion transfer across the interface of two immiscible liquids involves a mechanism for initiating desolvation from the first liquid, A, and concerted solvation by the second, B. In the present article a mechanism is considered in which this initiation is facilitated by the ion attaching itself to the tip of a solvent protrusion of B into A. (Protrusions have been observed in computer simulations and termed "fingers" or "cones.") It is presumed that the most effective protrusion represents a balance between two opposing effects: the more convex the protrusion the less probable the ion/protrusion formation but also the less the resistance to extrusion of the intervening liquid between the ion and the surface. An analogy of the latter to hydrodynamics is noted, namely, the more convex the surface the less the frictional force it exerts on the approaching ion. After diffusion in coordinate and solvation space across the interfacial region, the final detachment of the ion from solvent A is assumed to occur from a protrusion of A into B. Existing data on ion transfer rates are discussed, including the question of diffusion vs kinetic control. Computer simulations that correspond to the experimental conditions in realistic liquids for measurement of the electrochemical exchange current rate constant k0 are suggested. They can be used to test specific theoretical features. With a suitable choice of systems the need (and a major barrier to the simulations) for having a base electrolyte in such simulations can be bypassed. An experiment for the real-time observation of an ion leaving the interface is also suggested. © 2000 American Institute of Physics.

Notes: A modified ab initio potential energy surface (PES) is used for calculations of ozone recombination and isotopic exchange rate constants. The calculated low-pressure isotopic effects on the ozone formation reaction are consistent with the experimental results and with the theoretical results obtained earlier [J. Chem. Phys. 116, 137 (2002)]. They are thereby relatively insensitive to the properties of these PES. The topics discussed include the dependence of the calculated low-pressure recombination rate constant on the hindered-rotor PES, the role of the asymmetry of the potential for a general X+YZ reaction (Y≠Z), and the partitioning to form each of the two recombination products: XYZ and XZY. © 2002 American Institute of Physics.

Notes: Applications of the z-transform were made earlier to interfacial electron transfer involving semi-infinite solids, e.g., semiconductor/liquid and metal/liquid interfaces and scanning tunneling microscopy. It is shown how the method is readily adapted to treat composite materials, such as solid/solid interfaces or "molecular wire"/solid interfaces. © 2001 American Institute of Physics.

Notes: The strange mass-independent isotope effect for the enrichment of ozone and the contrastingly unconventional strong mass-dependent effect of individual reaction rate constants are studied using statistical (RRKM)-based theory with a hindered-rotor transition state. Individual rate constant ratios of recombination reactions and enrichments are calculated. The theory assumes (1) an "η-effect," which can be interpreted as a small deviation from the statistical density of states for symmetric isotopomers, compared with the asymmetric isotopomers, and (2) weak collisions for deactivation of the vibrationally excited ozone molecules. A partitioning effect controls the recombination rate constant ratios. It arises from small differences in zero-point energies of the two exit channels of dissociation of an asymmetric ozone isotopomer, which are magnified into large differences in numbers of states in the two competing exit channel transition states. In enrichment experiments, in contrast, this partitioning factor disappears exactly [Hathorn and Marcus, J. Chem. Phys. 112, 9497 (2000)], and what remains is the η-effect. Both aspects can be regarded as "symmetry driven" isotopic effects. The two experiments, enrichments and rate constant ratios, thus reveal markedly different theoretical aspects of the phenomena. The calculated low-pressure ozone enrichments, the low-pressure recombination rate constant ratios, the effects of pressure on the enrichment, on the individual recombination rate constant ratios, and on the recombination rate constant are consistent with the experimental data. The temperature dependence of the enrichment and of the recombination rate constant ratios is discussed and a variety of experimental tests are proposed. The negative temperature dependence of the isotopic exchange rate constant for the reaction 16O+18O18O→16O18O+18O at 130 K and 300 K is used for testing or providing information on the nature of a variationally determined hindered-rotor transition state. The theory is not limited to ozone formation but is intended to apply to other reactions where a symmetrical stable or unstable gas phase molecule may be formed. © 2002 American Institute of Physics.

Notes: The treatment of pressure effects on bimolecular recombinations and unimolecular dissociations is discussed. The analysis of recombination and dissociation reactions is made by showing how the nonequilibrium energy (E) and angular momentum (J)-dependent steady-state population distribution functions for the two reactions are related to each other and to the equilibrium population distribution function at the given E and J. As a special case a strong collision model is then used for the collisional rotational angular momentum transfer, and a ladder model for the collisional energy transfer. An analytical result is obtained for states below the dissociation threshold. The extension to recombinations with two exit channels is described, for application to ozone formation and isotopic effects. © 2001 American Institute of Physics.