Journal of Chemical Physics, Vol.100, No.11, 8109-8124, 1994
Solvent Dynamical Effects on Bond-Breaking Electron-Transfer Reactions
The effects of solvent and intramolecular dynamics on the rates of bond-breaking electron transfer (BBET) reactions is investigated. In the model we adopt, suggested by Saveant [J. Am. Chem. Soc. 109, 6788 (1987)], electron transfer and, bond breaking are considered to occur as a concerted process. Thermal equilibrium rate constants k(ie) [i=1(2) denoting the forward (reverse) reaction] are derived and exhibit a characteristic Marcus form, with the reorganization energy equal to the sum of contributions from the solvent, intramolecular vibrational and bond-breaking coordinates. The effect of dynamics on the BBET rate constants is studied by using diffusion-reaction equations. We assume that the intramolecular vibrational coordinate is in equilibrium and the solvent and the bond-breaking coordinates can be out of equilibrium. The survival probabilities are derived analytically with the use of a decoupling approximation. The single exponential decay of the survival probabilities leads to nonthermal-equilibrium rate constants k(i) that interpolate between the thermal equilibrium k(ie) and diffusion controlled k(id) rate constants (where motion along the nonequilibrium coordinates control the rate) according to k(i)(-1)=k(ie)(-1)+k(id)(-1). The diffusion controlled rate constants k(id) depend on the relaxation times along both the bond-breaking and solvent coordinates. For large activation energies, the fast relaxation will dominate the rate, while for small activation energies, the slow relaxation time will dominate the rate. We also discuss the case of the dynamics along the bond-breaking coordinate being characterized by an energy diffusion process. The rate constant is evaluated for high activation barrier reactions and still has the form given above, with a suitably redefined relaxation time for energy diffusion,
Keywords:POLAR-SOLVENTS;NONEQUILIBRIUM SOLVATION;CHEMICAL-REACTIONS;TRANSITION;FRICTION;MODEL;ACTIVATIONLESS;RELAXATION;REACTIVITY;DEPENDENCE