Adiabatic Electron Transfer: Comparison of Modified Theory with Experiment

Abstract

The radical cations of properly designed bishydrazines allow comparison of observed and calculated electron transfer rate constants. These compounds have rate constants small enough to be measured by dynamic electron spin resonance spectroscopy and show charge transfer bands corresponding to vertical excitation from the energy well for the charge occurring upon one hydrazine unit to that for the electron-transferred species. Analysis of the data for all six compounds studied indicates that the shape of the adiabatic surface on which electron transfer occurs can be obtained from the charge transfer band accurately enough to successfully predict the electron transfer rate constant and that explicit tunneling corrections are not required for these compounds.

Extended Near-Infrared Resonance Raman Investigations of an Organic Mixed-Valence System: Diazatetracyclodiene Radical Cation

“…3 Since electron transfer for 1 was found to be slow on the electron spin resonance (ESR) time scale, 5 more recent work has focused on structural variants in which the electron-transfer rate is increased to be measurable by ESR line broadening. [6][7][8] Related bis-hydrazyl dications (2 2+ ) consisting of two aza moieties separated by four σ bonds have also been studied. 5,9,10 As shown in eq 1, one-electron reduction of these leads to a radical cation in which, again, charge is localized on a dinitrogen unit.…”

Comparisons of Measured Rate Constants with Spectroscopically Determined Electron-Transfer Parameters

“…As V ab increases, the evaluation of the ET rate constant remains a challenge because perturbation theory breaks down, which we believe is the reason for eq 4 predicting the wrong temperature dependence for 1 + and related compounds. 14,15,61 The classical treatment of eq 3 predicts the rate constant as a function of temperature for 1 + and related compounds rather accurately, 53 but it is clear from calculations that this compound cannot be going through a classical transition state for electron-transfer because the electronic coupling would be far too large to be compatible with the observed rate constant. 62 The appropriate electronic coupling to predict the thermal electron-transfer rate constant is that for the ground state geometry, which is that evaluated from the optical absorption spectrum using Hush theory.…”

“…The direction of the change seems reasonable because increasing temperature should slightly increase the average amount of twist about the C-N bonds connecting the hydrazine units to the bridge, which will decrease the electronic coupling. Instead of using the band maxium as λ, as was done previously, 32 the IV band was fit more realistically, using a quartic-enhanced IV band 14 along with higher energy Gaussians as needed to fit the observed spectrum, which upon analyzing substituted naphthalenes that have even more band overlap, 66 we realized will produce more realistic temperature variation of the IV band. The E quart values of Table 2 were used to establish a line for λ(T), which was used to estimate the λ(T) values at the temperatures of the ESR data.…”

“…[55][56][57] Equation 3 works rather well for prediction of k et as a function of temperature for 1 + and related compounds using λ and V ab obtained from Hush theory, and agreement with experiment is better when a refractive index correction is included in evaluating V ab and the diabatic surfaces are allowed to vary from being perfect parabolas by including a quartic term, so that the experimental IV band is properly fit. 14,15 To incorporate the nuclear quantum effects, the BixonJortner approach abandons the idea of an ET barrier as being important and replaces ∆G* with Franck-Condon tunneling factors in their rate expressions. Parabolic diabatic energy surfaces are retained, but the x coordinate for these parabolas only includes the low-frequency contributions to λ that may be treated classically (usually called λ s and identified as the solvent contribution to λ).…”

“…This work led to the rather unsatisfactory result that simple, classical Marcus theory that ignores a quantum mechanical treatment of molecular vibrations 12,13 predicted the observed k et more accurately than more sophisticated methods that incorporated such a treatment. 14 It is the goal of this work to accurately establish the proper vibrational analysis of 1 + , which we have argued has the most accurately determined k et as a function of temperature of the compounds that we have studied, 15 because it has less spin density on the bridge than other cases. Resonance Raman has been used to establish the † Part of the special issue "Norman Sutin Festschrift".…”