Mutual Orientation Effects on Electron-Transfer Reactions between Porphyrins

Mutual orientation effects on the rate of nonadiabatic electron transfer between several diporphyrin pairs of experimental interest are examined. The electronic matrix element for electron transfer is calculated within a one-electron spheroidal model for a variety of states and orientations which are relevant to both biological and synthetic electron-transfer systems. Both the mutual orientation of the pairs and the nodal structure of the donor and acceptor orbitals can have large effects on calculated rates

A simple classical model of infrared multiphoton dissociation

The classical mechanics of a system of two nonlinearly coupled oscillators driven by an oscillating electric field is studied. The presence of quasiperiodic and chaotic motion in the unforced system is shown to influence the nature of energy absorption. Two essentially different types of behavior are observed. In the first, energy is exchanged in a multiply periodic manner between the system and the forcing field. In the second regime, the energy exchange is erratic and a statistical analysis of a family of trajectories shows the role of the chaotic motion in the unforced system in the dissociation process. A theory for rate of photodissociation is presented and results are compared with those obtained from an ensemble of exact classical trajectories

Theory of Outer-Sphere Electron-Transfer Reactions

Classical, semiclassical and quantum theories of outer-sphere electron-transfer reactions in polar media are discussed. For each, the Franck-Condon overlap factors for the hexaamminecobalt, hexaaquoiron and hexaammineruthenium self-exchange rates and for the cross-reaction of hexaaquoiron(II) with tris(2,2’-bipyridine)ruthenium(III) are evaluated and compared. The quantum effect on the rates is small in the region of moderate driving force; the "normal" ΔGo region. Direct-sum and saddle-point evaluations of the quantum Franck-Condon factors are made and compared. The saddle-point approximation is shown to be an excellent approximation in the cases considered. Quantum effects in homogeneous outer-sphere electron transfer reactions in the region of large negative ΔGo (the "inverted" region) are considered. The results of quantum, semiclassical and classical calculations on model systems are presented. A sequence of highly exothermic photoinduced reactions of tris(2,2'-bipyridyl) complexes is discussed with regard to the possible importance of quantum effects and of alternate reaction pathways in understanding the failure of the sequence of reactions to exhibit pronounced "inverted" behavior. A mechanism leading to electronically excited products provides a possible explanation for the large discrepancy. The theory of highly exothermic homogeneous outersphere electron-transfer reactions is discussed for transfers occurring over a range of distances. A finite rate of diffusion of reactants and their long-range force are treated by solving the reaction-diffusion equation numerically for the reactant pair distribution function. Steady-state solutions are compared with experimental data. On the basis of short-time solutions it is proposed that experiments which measure electron-transfer rates at short times following the onset of reaction improve the possibility of observing the inverted effect in bimolecular systems. The effect of the reactants' relative orientation on the electron-transfer rate is considered. Reactants are modeled as oblate-spheroidal potential wells of constant, finite depth. Energy levels and wavefunctions are obtained for an electron localized in such a well. The electronic matrix elements that govern electron transfer within a nonadiabatic quantum theory are evaluated. Significant orientational preferences are predicted for electron transfer between nonspherical donor and acceptor sites.</p

A model for orientation effects in electron‐transfer reactions

A method for solving the single‐particle Schrödinger equation with an oblate spheroidal potential of finite depth is presented. The wave functions are then used to calculate the matrix element T_BA which appears in theories of nonadiabatic electron transfer. The results illustrate the effects of mutual orientation and separation of the two centers on TBA. Trends in these results are discussed in terms of geometrical and nodal structure effects. Analytical expressions related to T_BA for states of spherical wells are presented and used to analyze the nodal structure effects for T_BA for the spheroidal wells

Further Developments in Electron Transfer

The inverted region in electron transfer reactions is studied for the reaction of electronically-excited ruthenium(II) tris-bipyridyl ions with various metal(III) tris-bipyridyl complexes. Numerical calculations for the diffusion-reaction equation are summarized for the case where electron transfer occurs over a range of distances. Comparison is made with the experimental data and with a simple approximation. The analysis reveals some of the factors which can cause a flattening of the ln k_(obs) versus ΔG^O curve in the inverted region. Ways of improving the chance of observing the effect are discussed

Theory of highly exothermic electron transfer reactions

The theory of highly exothermic homogeneous outer-sphere electron transfer reactions is discussed for transfers occurring over a range of distances. A finite rate of diffusion of reactants and their long-range force are treated by solving the diffusion equation numerically for the reactant pair distribution function. Steady-state solutions for the bimolecular rate constant are compared with experimental data as well as with our recent approximate analytic solution, which is found to agree in the present case. On the basis of short-time solutions, it is proposed that experiments which measure electron transfer rates at short times following the onset of reaction improve the possibility of observing the inverted effect in bimolecular systems. The chance of seeing it in linked systems (unimolecular reactions) is even greater. The relation between the prediction of an “inverted region” in the rate constant vs. ΔG° plot and the existence of a maximum in charge transfer spectral plots of intensity vs. absorption frequency is pointed out