Electron exchange between α-Keggin tungstoaluminates and a well-defined cluster-anion probe for studies in electron transfer

Fully oxidized α-Al^IIIW₁₂O₄₀ ^5- (1_ox), and one-electron-reduced α-Al ^IIIW₁₂O₄₀^6- (1_red), are well-behaved (stable and free of ion pairing) over a wide range of pH and ionic-strength values at room temperature in water. Having established this, ²⁷Al NMR spectroscopy is used to measure rates of electron exchange between 1_ox (²⁷Al NMR: 72.2 ppm relative to Al(H ₂O)₆³⁺; ν_1/2 = 0.77 Hz) and 1_red (74.1 ppm; ν_1/2v2 = 0.76 Hz). Bimolecular rate constants, k, are obtained from line broadening in ²⁷Al NMR signals as ionic strength, μ, is increased by addition of NaCl at the slow-exchange limit of the NMR time scale. The dependence of k on μ is plotted using the extended Debye-Hückel equation: log k = log k₀ + 2αz ₁z₂μ^1/2/(1 + βrμ^1/2), where z₁ and z₂ are the charges of 1_ox and 1_red, α and β are constants, and r, the distance of closest contact, is fixed at 1.12 nm, the crystallographic diameter of a Keggin anion. Although not derived for highly charged ions, this equation gives a straight line (R² = 0.996), whose slope gives a charge product, z₁z₂, of 29 ± 2, statistically identical to the theoretical value of 30. Extrapolation to μ = 0 gives a rate constant k ₁₁ of (6.5 ± 1.5) × 10^-3 M^-1 s^-1, more than 7 orders of magnitude smaller than the rate constant [(1.1 ± 0.2) × 10⁵ M^-1 s^-1] determined by ³¹P NMR for self-exchange between P^VW ₁₂O₄₀^3- and its one-electron-reduced form, P^VW₁₂O₄₀^4-. Sutin's semiclassical model reveals that this dramatic difference arises from the large negative charges of 1_ox and 1_red. These results, including independent verification of k₁₁, recommend 1_red as a well-behaved electron donor for investigating outer-sphere electron transfer to molecules or nanostructures in water, while addressing a larger issue, the prediction of collision rates between uniformly charged nanospheres, for which 1_ox and 1_red provide a working model.