Role of alkali metal cation size in the energy and rate of electron transfer to solvent-separated 1:1 [(M⁺) (acceptor)] (M⁺ = Li⁺, Na⁺, K⁺) ion pairs

The effect of cation size on the rate and energy of electron transfer to [(M⁺)(acceptor)] ion pairs is addressed by assigning key physicochemical properties (reactivity, relative energy, structure, and size) to an isoelectronic series of well-defined M⁺-acceptor pairs, M⁺ = Li⁺, Na⁺, K⁺. A 1e^- acceptor anion, α-SiV^VW₁₁O₄₀^5- (1, a polyoxometalate of the Keggin structural class), was used in the 2e^- oxidation of an organic electron donor, 3,3′,5,5′-tetra-tert-butylbiphenyl-4,4′-diol (BPH₂), to 3,3′,5,5′-tetra-tert-butyldiphenoquinone (DPQ) in acetate-buffered 2:3 (v/v) H₂O/t-BuOH at 60 °C (2 equiv of 1 are reduced by 1e^- each to 1_red, α-SiV^IVW₁₁O₄₀^6-). Before an attempt was made to address the role of cation size, the mechanism and conditions necessary for kinetically well behaved electron transfer from BPH₂ to 1 were rigorously established by using GC-MS, ¹H, ⁷Li, and ⁵¹V NMR, and UV-vis spectroscopy. At constant [Li⁺] and [H⁺], the reaction rate is first order in [BPH₂] and in [1] and zeroth order in [1_red] and in [acetate] (base) and is independent of ionic strength, μ. The dependence of the reaction rate on [H⁺] is a function of the constant, K_a1, for acid dissociation of BPH₂ to BPH^- and H⁺. Temperature dependence data provided activation parameters of ΔH‡ = 8.5 ± 1.4 kcal mol^-1 and ΔS‡ = -39 ± 5 cal mol^-1 K^-1. No evidence of preassociation between BPH₂ and 1 was observed by combined ¹H and ⁵¹V NMR studies, while pH (pD)-dependent deuterium kinetic isotope data indicated that the O-H bond in BPH₂ remains intact during rate-limiting electron transfer from BPH₂ and 1. The formation of 1:1 ion pairs [(M⁺)(SiVW₁₁O₄₀^5-)]^4- (M⁺1, M⁺ = Li⁺, Na⁺, K⁺) was demonstrated, and the thermodynamic constants, K_M1, and rate constants, k_m1, associated with the formation and reactivity of each M⁺1 ion pair with BPH₂ were calculated by simultaneous nonlinear fitting of kinetic data (obtained by using all three cations) to an equation describing the rectangular hyperbolic functional dependence of k_obs values on [M⁺]. Constants, K_M1red, associated with the formation of 1:1 ion pairs between M⁺ and 1_red were obtained by using K_M1 values (from k_obs data) to simultaneously fit reduction potential (E_1/2) values (from cyclic voltammetry) of solutions of 1 containing varying concentrations of all three cations to a Nernstian equation describing the dependence of E_1/2 values on the ratio of thermodynamic constants K_M1 and K_M1red. Formation constants, K_M1, and K_M1red, and rate constants, k_M1, all increase with the size of M⁺ in the order K_Li1 = 21 < K_Na1 = 54 < K_K1 = 65 M^-1, K_Li1red = 130 < K_Na1red = 570 < K_K1red = 2000 M^-1, and k_Li1 = 0.065 < k_na1 = 0.137 < k_K1 = 0.225 M^-1 s^-1. Changes in the chemical shifts of ⁷Li NMR signals as functions of [Li₅1] and [Li₆1_red] were used to establish that the complexes M⁺1 and M⁺1_red exist as solvent-separated ion pairs. Finally, correlation between cation size and the rate and energy of electron transfer was established by consideration of K_M1, k_M1, and K_M1red values along with the relative sizes of the three M⁺1 pairs (effective hydrodynamic radii, r_eff, obtained by single-potential step chronoamperometry). As M⁺ increases in size, association constants, K_M1, become larger as smaller, more intimate solvent-separated ion pairs, M⁺1, possessing larger electron affinities (q/r), and associated with larger k_M1 values, are formed. Moreover, as M⁺1 pairs are reduced to M⁺1_red during electron transfer in the activated complexes, [BPH₂, M⁺1], contributions of ion pairing energy (proportional to -RT ln(K_M1red/K_M1) to the standard free energy change associated with electron transfer, ΔG°_et, increase with cation size: -RT ln(K_M1red/K_M1) (in kcal mol^-1) = -1.2 for Li⁺, -1.5 for Na⁺, and -2.3 for K⁺.