Solvent dynamical effects in electron transfer: evaluation of electronic matrix coupling elements for metallocene self-exchange reactions

Abstract

The functional dependence of the rate constants for self-exchange, kex, for a series of metallocene redox couples to solvent-induced variations in the nuclear frequency factor, vn, engendered by alterations in the longitudinal solvent relaxation time, tl, are utilized to deduce values of the electronic matrix coupling element, Hn, for electron exchange. The analysis exploits the sensitivity of the kex-rL"' dependence to the degree of reaction adiabaticity and hence Hn for a given electron-exchange reaction. Six metallocene couples are examined: Cp2Co+',°, Cp2Fe+,,cl (Cp = cyclopentadienyl), the decamethyl derivatives Cp'2Co+/°a nd Cp'2Fe+/°s crutinized previously, with additional solvent-dependent kex values for (carboxymethyl)cobaltocenium-(carboxymethyl)cobaltocene [Cpe2Co+/°, e = "ester"] and (hydroxymethyl)ferrocenium-(hydroxymethyl)ferrocene [HMFc+/0], Kinetic data are examined in 15 solvents, including 11 "Debye" solvents for which it is anticipated that t>" * tl"'. Corrections to kcx for the solvent-dependent variations in the barrier height were obtained by corresponding measurements of the optical electron-transfer energies for the related binuclear complex biferrocenylacetylene, yielding "barrier-corrected" rate constants, k'sx. The k'^-rU1 dependencies, as well as the kex values in a given solvent, are markedly dependent on the redox couple. The log k 'ex-log tl"* plots for the most facile couple, Cp,2Co+/0, exhibit slopes approaching unity for smaller tl"* values. The less facile couples yield smaller slopes, diminishing in the same sequence that k'ex decreases in a given solvent: Cp'2Co+/0 > Cpc2Co+/0 > Cp2Co+/°> Cp'2Fe+/°> Cp2Fe+/0 £ HMFc+/0. These findings are consistent with Hl2 decreasing in the same order. Comparison of such rate-solvent friction dependencies with corresponding plots calculated using a combined solvent friction-electron tunneling model yields the following approximate values of the matrix coupling element for reactant "closest approach", H°n (kcal mol"1): Cp'2Co+/°, 1.0; Cpe2Co+/°, 0.5-1.0; Cp2Co+/°, 0.5; Cp'2Fe+/°, 0.2; Cp2Fe+/°, 0.1; HMFc+/°, 0.075. Reasonable concordance is seen with recent theoretical estimates of H°12 for Cp2Co+',°a nd Cp2Fe+/°. The relationship between H°n and metallocene electronic structure is briefly discussed. The analysis also enables effective solvent relaxation times for adiabatic barrier crossing in non-Debye media, including primary alcohols, to be extracted.

Solvent dynamical effects in electron transfer: molecular dynamics simulations of reactions in methanol

“…Given that the LR approximation is noticeably less valid for the 5 A anion than for the cation reactant ( Figure 7, vide supra), the free energy-reaction coordinates should be decidedly nonparabolic, so that disparate AM values might be expected for these systems. It is worth noting that the effective diameters of the majority of ET reactants commonly utilized to probe solvent dynamical effects are somewhat larger than 5 A; for example, a = 7-8 A for simple metallocenes [9][10][11].…”

“…Barrier-crossing frequencies that are markedly 2 accelerated above TL- 1 have been observed for a number of outer-sphere ET reactions in primary alcohols [9][10][11][12][13][14][15][16]. Part of the often large (-10 fold) rate accelerations can be accounted for[15J in terms of a continuum-based formulation due to Hynes [17].…”

Some Electronic and Dynamical Factors in Electron-Transfer Chemistry: Metal Complexes, Clusters, and Surfaces

“…An example of this approach, involving self exchanges of metallocenium-metallocene (Cp2M + 1") redox couples in various polar Debye solvents is worth highlighting here since ET rate-solvent dependencies are observed that span the limits of nonadiabatic and adiabatic behavior [12]. For ferrocenium-ferrocene couples, the rate constants k'ex (corrected for AG*-solvent variations) are almost independent of the solvent dynamics, as discerned by tL• 1 .…”

“…Interestingly, substantial (up to ca 50 fold) variations in .L are observed in such media, from ca. 0.25 to 10 ps [12]. Since analytic theories predict commonly that vn,-T -1, correspondingly large variations in Vn are anticipated to be achieved by suitable alterations in -5-the solvent medium.…”

Simple and Ultrasensitive Chemically Amplified Electrochemical Detection of Ferrocenemethanol on 4-Nitrophenyl Grafted Glassy Carbon Electrode

“…3B). The similar electrode potential of ferrocyanide and ferrocenemethanol (less than 10 mV apart), thermoneutral character, and rapid electron self-exchange rate constants allow desirable electron transfer and thus make this pair of reactants suitable for a chemically amplified electrochemical detection scheme [18][19][20][21].…”