George E. McManis

Solvent dynamical effects in electron transfer: Predicted consequences of non‐Debye relaxation processes and some comparisons with experimental kinetics

The consequences of non‐Debye solvent relaxation upon the barrier‐crossing dynamics of adiabatic electron‐transfer processes have been explored numerically using a rate formulation due to Hynes for several common forms of the dielectric response function E(s), with the objective of assessing the likely experimental importance of such effects. For the ‘‘multiple Debye’’ form of E(s), analytic expressions for the required time‐correlation function can be obtained, whereas for the Davidson–Cole and Cole–Cole forms numerical solutions to the inverse Laplace transform were required. Illustrative numerical results are presented of the increases in the adiabatic barrier‐crossing frequency, νn, predicted to be engendered by the presence of higher‐frequency relaxation components for dielectric conditions of likely experimental relevance. Substantial (five‐ to ten fold) rate enhancements are often obtained, resulting from the disproportionately large influence upon νn predicted to arise from the higher‐frequency ...

Solvent dynamical effects in electron transfer: Numerical predictions of molecularity effects using the mean spherical approximation

The influence of solvent molecularity upon the adiabatic barrier‐crossing frequency νn and barrier height ΔG*, for electron–exchange reactions involving only solvent reorganization is examined numerically on the basis of a mean spherical approximation (MSA) treatment of the reaction coordinate time‐correlation function, Δ(t) [Refs. 3(c) and 7(c)] for Debye solvents. The calculated ΔG* values for a spatially isolated redox couple fall increasingly below the corresponding dielectric continuum quantity ΔG*con as the ratio of the solvent to reactant radii (rsol /rre ) increases. For the experimentally common circumstance (rsol /rre )≲2 and for zero and infinite‐frequency dielectric constants e0 and e∞ over the ‘‘typical’’ ranges 20–100 and 1.75–2.5, respectively, the calculated ΔG* values are up to ∼30% below ΔG*con , the deviations tending to be larger for smaller e0 and e∞ values. Two kinetic models are utilized to extract νn values from Δ(t): Hynes’ approach derived from the generalized Langevin equation (...

Solvent dynamical effects on electron‐transfer kinetics: Influence of electronic coupling on weak‐overlap exchange processes

A numerical integration treatment of the appropriate Kramers’ diffusion equation, involving overdamped solvent motion, is employed to estimate adiabatic barrier‐crossing frequencies νos for weak‐overlap electron‐exchange processes featuring only outer‐shell (solvent) reorganization as a function of the electronic matrix coupling element H12. Comparisons are made with estimates of νos obtained from limiting analytical expressions. The competing influence of reaction nonadiabaticity (i.e., electron tunneling) and solvent motion upon the barrier‐crossing frequency is also considered as a function of H12 using a Landau–Zener treatment. The results indicate that the dominant influence of overdamped solvent motion on the preexponential factor, that yields the observed inverse correlation between the reaction rate and the solvent longitudinal relaxation time, requires reactions that feature moderate degrees of electronic coupling, around H12≳0.1 kcal mol−1, in most common polar solvents. These factors are briefl...

Solvent dynamical effects in electron transfer: Predicted influences of electronic coupling upon the rate‐dielectric friction dependence

The predicted dependence of the bimolecular rate constant for outer‐sphere electron exchange kex upon the longitudinal relaxation time τL for Debye solvents is examined numerically on the basis of a suitably combined rate formulation in order to examine the manner and extent to which the rate‐solvent friction dependence, of particular experimental significance, should be sensitive to the degree of donor–acceptor electronic coupling and related factors. The treatment accounts for the contributions to kex from a spatial distribution of reactant pairs as well as for the effects of donor–acceptor interactions upon the unimolecular rate constant, ket (s−1), for each encounter geometry. The latter include the influence of electronic interactions as prescribed by the matrix coupling element H12 upon the effective frequency for adiabatic barrier crossing νn, as well as upon the electronic transmission coefficient κel (i.e., the degree of reaction nonadiabaticity). The anticipated dependence of the free‐energy bar...

Solvent dynamical effects in electron transfer : the solvent inertial limit and the predicted influence of quantum effects

Abstract Analytical continuum formulations for the solvent inertial frequency, constituting the anticipated zero-friction limit for adiabatic barrier crossing in solvent-controlled electron-transfer processes, are derived and discussed. The role of solvent inertia in solvent dynamical effects is discussed with emphasis on the likely modifications brought about by nuclear tunneling. Approximate formulations suitable for assessing the latter correction in the presence as well as absence of solvent friction are outlined and compared. Numerical calculations are provided that illustrate the partly compensatory influence on the rate-solvent friction dependence resulting from nuclear tunneling together with reaction non-adiabaticity. Such combined quantum effects are anticipated typically to mask the clearcut emergence of solvent inertial effects on electron-transfer reaction dynamics in common low-friction media.

Solvent Relaxation in Thermal Electron-Transfer Reactions: Some Comparisons with Real-Time Measurements of Solvation Dynamics.

Abstract The role of solvent dielectric relaxation on the barrier-crossing dynamics for outer-sphere electron transfer (ET), as evaluated from the solvent-dependent kinetics of metallocene self-exchange reactions, is compared with recent real-time measurements of polar solvation dynamics obtained from time-dependent fluorescence Stokes shifts (TDFS) for suitable charge-transfer excited states. While the solvent-dependent kinetics obtained in some aprotic media are consistent with the TDFS measurements, the barrier-crossing dynamics in several associated and/or highly polar liquids are indicative for much faster relaxation than inferred from TDFS. The possible nature, and implications, of these rapid modes are discussed.