Theory of ozone isotopic effects and various electron transfer reactions

Three separate topics, each stimulated by experiments, are treated theoretically in this dessertation: isotopic effects of ozone, electron transfer at interfaces, and intramolecular directional electron transfer in a supramolecular system.

The strange mass-independent isotope effect for the enrichment of ozone, which has been a puzzle in the literature for some 20 years, and the equally puzzling unconventional strong mass-dependent effect of individual reaction rate constants are studied as different aspects of a symmetry-driven behavior. A statistical (RRKM-based) theory with a hindered-rotor transition state is used. The individual rate constant ratios of recombination reactions at low pressures are calculated using the theory involving (1) small deviation from the statistical density of states for symmetric isotopomers, and (2) weak collisions for deactivation of the vibrationally excited ozone molecules. The weak collision and partitioning among exit channels play major roles in producing the large unconventional isotope effect in "unscrambled" systems. The enrichment studies reflect instead the non-statistical effect in "scrambled" systems. The theoretical results of low-pressure ozone enrichments and individual rate constant ratios obtained from these calculations are consistent with the corresponding experimental results. The isotopic exchange rate constant for the reaction ^(16)O + ^(18)O ^(18)O→+ ^(16)O ^(18)O + ^(18)O provides information on the nature of a variationally determined hindered-rotor transition state using experimental data at 130 K and 300 K. Pressure effects on the recombination rate constant, on the individual rate constant ratios and on the enrichments are also investigated. The theoretical results are consistent with the experimental data. The temperature dependence of the enrichment and rate constant ratios is also discussed, and experimental tests are suggested. The desirability of a more accurate potential energy surface for ozone in the transition state region is also noted.

Electron transfer reactions at semiconductor /liquid interfaces are studied using a tight-binding model for the semiconductors. The slab method and a z-transform method are employed in obtaining the tight-binding electronic structures of semiconductors having surfaces. The maximum electron transfer rate constants at Si/viologen^(2-/+) and InP /Me_(2)Fc^(+/O) interfaces are computed using the tight-binding type calculations for the solid and the extended-Huckel for the coupling to the redox agent at the interface. These electron transfer reactions are also studied using a free electron model for the semiconductor and the redox molecule, where Bardeen's method is adapted to calculate the coupling matrix element between the molecular and semiconductor electronic states. The calculated results for maximum rate constant of the electron transfer from the semiconductor bulk states are compared with the experimentally measured values of Lewis and coworkers, 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.

Photoinduced electron transfer reactions in small supramolecular systems, such as 4-aminonaphthalimide compounds, are interesting in that there are, in principle, two alternative pathways (directions) for the electron transfer. The electron transfer, however, is unidirectional, as deduced from pH-dependent fluorescence quenching studies on different compounds. The role of electronic coupling matrix element and the charges in protonation are considered to explain the directionality of the electron transfer and other various results. A related mechanism is proposed to interpret the fluorescence behavior of similar molecules as fluorescent sensors of metal ions.

High pressure states in condensed matter: I. High pressure behavior of the iron-sulphur system with applications to the earth's core. II. Empirical equation of state for organic compounds at high pressures

Part I:

The earth's core is generally accepted to be composed primarily of iron, with an admixture of other elements. Because the outer core is observed not to transmit shear waves at seismic frequencies, it is known to be liquid or primarily liquid. A new equation of state is presented for liquid iron, in the form of parameters for the 4th order Birch-Murnaghan and Mie-Grüneisen equations of state. The parameters were constrained by a set of values for numerous properties compiled from the literature. A detailed theoretical model is used to constrain the P-T behavior of the heat capacity, based on recent advances in the understanding of the interatomic potentials for transition metals. At the reference pressure of 10⁵ Pa and temperature of 1811 K (the normal melting point of Fe), the parameters are: ρ = 7037 kg/m³, K_S0 = 110 GPa, K_S' = 4.53, K_S" = -.0337 GPa-1, and γ = 2.8, with γ α ρ^-1.17. Comparison of the properties predicted by this model with the earth model PREM indicates that the outer core is 8 to 10 % less dense than pure liquid Fe at the same conditions. The inner core is also found to be 3 to 5% less dense than pure liquid Fe, supporting the idea of a partially molten inner core. The density deficit of the outer core implies that the elements dissolved in the liquid Fe are predominantly of lower atomic weight than Fe. Of the candidate light elements favored by researchers, only sulfur readily dissolves into Fe at low pressure, which means that this element was almost certainly concentrated in the core at early times. New melting data are presented for FeS and FeS₂ which indicate that the FeS₂ is the S-hearing liquidus solid phase at inner core pressures. Consideration of the requirement that the inner core boundary be observable by seismological means and the freezing behavior of solutions leads to the possibility that the outer core may contain a significant fraction of solid material. It is found that convection in the outer core is not hindered if the solid particles are entrained in the fluid flow. This model for a core of Fe and S admits temperatures in the range 3450K to 4200K at the top of the core. An all liquid Fe-S outer core would require a temperature of about 4900 K at the top of the core.

Part II.

The abundance of uses for organic compounds in the modern world results in many applications in which these materials are subjected to high pressures. This leads to the desire to be able to describe the behavior of these materials under such conditions. Unfortunately, the number of compounds is much greater than the number of experimental data available for many of the important properties. In the past, one approach that has worked well is the calculation of appropriate properties by summing the contributions from the organic functional groups making up molecules of the compounds in question. A new set of group contributions for the molar volume, volume thermal expansivity, heat capacity, and the Rao function is presented for functional groups containing C, H, and O. This set is, in most cases, limited in application to low molecular liquids. A new technique for the calculation of the pressure derivative of the bulk modulus is also presented. Comparison with data indicates that the presented technique works very well for most low molecular hydrocarbon liquids and somewhat less well for oxygen-bearing compounds. A similar comparison of previous results for polymers indicates that the existing tabulations of group contributions for this class of materials is in need of revision. There is also evidence that the Rao function contributions for polymers and low molecular compounds are somewhat different.