Molecular Mechanics Calculation of Inner-Shell Activation Barriers to Heterogeneous Electron Transfer in M(tacn)_2~(3+/2+) Redox Couples (M = Fe, Co, Ni; tacn = 1,4,7-Triazacyclononane)

摘要

M(tacn)_2~(3+/2+) redox couples (M = Fe, Ni, Co; tacn = 1,4,7-triazacyclononane) exhibit different extents of M-N bond lengthening upon electrochemical reduction and standard heterogeneous rate constants (k_(s,h)) that decrease systematically in accord with this structural feature. Inner-shell enthalpies of activation (ΔH_(is)) obtained from temperature-dependent measurements of k_(s,h) [Crawford, P. W.; Schultz, F. A. Inorg. Chem. 1994, 33, 4344] equal 1.7, 1.9, and 13.2 kcal mol~(-1) for M = Fe, Ni, and Co, respectively, in contrast with values of 0.2, 2.2, and 6.0 kcal mol~(-1) calculated by the harmonic oscillator model of M-N bond elongation. In an attempt to resolve this discrepancy we have carried out molecular mechanics calculation of ΔH_(is) for M(tacn)_2~(3+/2+) couples using MMX and CHARMM force fields. The procedure for doing so involves intersecting potential energy curves of oxidized and reduced reactants generated from the force field parameters required to optimize the ground state structure of each oxidation state. MMX barrier heights estimated in this way are in close correspondence with the harmonic oscillator approximation widely used in Marcus theory calculation of inner-shell reorganization energies. The vibrational entropies of the molecules are calculated, and differences in these quantities correlate with the half-reaction entropy (ΔS°_(rc)) of the M(tacn)_2~(3+/2+) couples. Non-zero, metal-dependent values of ΔS°_(rc) for these complexes are thought to arise from changes in M-N frequencies upon reduction [Richardson, D. E.; Sharpe, P. Inorg. Chem. 1991, 30, 1412]. Poor correspondence between measured and calculated activation enthalpies remains in cases where the electrode reaction exhibits a large half-reaction entropy. The molecular mechanics force fields are used to partition the energy of the molecules into component terms, and it is found that the majority of the inner-shell barrier derives from M-N bond stretching.