INNER-SHELL EFFECTS ON HETEROGENEOUS ELECTRON-TRANSFER RATES OF BIS(1,4,7-TRIAZACYCLONONANE) (TACN) REDOX COUPLES, M(TACN)(2)(3+/2+) (M=FE, CO, NI, RU)

Heterogeneous electron-transfer rates and activation parameters are reported for M(tacn)(2)(3+/2+) (M = Fe, Co, Ni, Ru; tacn = 1,4,7-triazacyclononane) complexes in aqueous sodium fluoride solution. The M(tacn)(2)(3+/2+) couples are chemically reversible, outer-sphere, one-electron transfers whose redox-induced changes in metal-nitrogen bond distance range from 1 to 18 pm depending on the identity of M. Double-layer corrected standard heterogeneous rate constants decrease in a sequence (Ru approximate to Fe > Ni >> Co) that is qualitatively in accord with this structural feature. Inner-shell contributions to the electrochemical activation process are obtained from temperature-dependent measurement of the standard heterogeneous rate constants and subtraction of an outer-shell contribution of 15 kJ mol(-1) calculated by the mean spherical approximation. Values of Delta H-isis(double dagger) = 1, 7-12, 8, and 55 kJ mol(-1) are determined for Ru, Fe, Ni, and Co, respectively, in contrast to values of 0, 1, 9, and 25 kJ mol(-1) calculated from a simple harmonic oscillator expression for M-N bond stretching. The M(tacn)2(3+)/(2+) couples exhibit half-reaction entropies (Delta S degrees(rc)) and entropies of activation (Delta S-double dagger which correlate with the experimental inner-shell barriers. The origin of the entropic terms, the discrepancies in Delta H-is(double dagger) values, and the metal dependence of these quantities are attributed to differences in vibrational partition functions between products and reactants (Richardson, D. E.; Sharpe, P. Inorg. Chem. 1991, 30, 1412) which become significant when inner-shell frequencies are low and change significantly upon redox.