Electron Exchange between α-Keggin Tungstoaluminates and a Well-Defined Cluster-Anion Probe for Studies in Electron Transfer

Fully oxidized α-AlIIIW12O405- (1ox), and one-electron-reduced α-AlIIIW12O406- (1red), 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 1ox (27Al NMR: 
72.2 ppm relative to Al(H2O)63+; ν1/2 = 0.77 Hz) and 1red (74.1 ppm; ν1/2 = 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 + 2αz1z2μ1/2/(1 + βrμ1/2), where z1 and z2 are the charges of 1ox and 1red, 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 k11 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 PVW12O403- and its
one-electron-reduced form, PVW12O404-. Sutin's semiclassical model reveals that this dramatic difference arises
from the large negative charges of 1ox and 1red. These results, including independent verification of k11, recommend
1red 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 1ox and 1red provide a working model.