R. C. Dorfman

The influence of diffusion on photoinduced electron transfer and geminate recombination

The influence of diffusion on photoinduced electron transfer and geminate recombination in solutions of randomly distributed donors and acceptors is explored. The focus is on the effect diffusional motion has on geminate recombination. The reactive state (state following photoinduced electron transfer) probability is calculated as a function of diffusion constant and relative permittivity for three intermolecular potential cases: attractive, repulsive, and no Coulomb potentials. Also calculated are the reactive state yield and reactive state survival fraction. Both forward and back electron‐transfer rates are distance dependent (not contact transfer). Any diffusion constant can be investigated, and donor–acceptor and acceptor–acceptor excluded volumes are taken into account. The model developed here is compared with slow and fast diffusion limits as well as with the theories of Smoluchowski, and Collins and Kimball.

Time dependence of donor–acceptor electron transfer and back transfer in solid solution

Electron transfer from an optically excited donor to randomly distributed acceptors followed by electron back transfer is treated theoretically for donors and acceptors in a rigid solution. The forward electron transfer process is described in terms of the excited state population probabilityPex(t) of the donor molecules, while the electron back transfer from the radical anion to the radical cation is characterized by Pct(t), the donor cation state population probability. Exact expressions for the ensemble averages 〈Pex(t)〉 and 〈Pct(t)〉 are derived. Numerical calulations are presented for the cation probabilities, the average cation–anion separation distance 〈R(t)〉, and the average cation existence time 〈τ(R)〉, using parameters which characterize the forward and back transfer distance dependent rates. Relationships among 〈Pex(t)〉, 〈Pct(t)〉 and the intermolecular interaction parameters provide detailed insights into the distance and time dependence of the flow of electron probability in an ensemble of dono...

Solvent relaxation effects on the kinetics of photoinduced electron transfer reactions

The three‐potential surface problem of electron transfer in solution is analyzed using Zusman‐type kinetic equations. The model describes ultrafast formation and recombination of radical–ion pairs limited by solvent dielectric relaxation. The problem begins with a donor on an electronic excited state surface. The system evolves with crossing to the radical–ion pair surface (with the possibility of recrossing to the excited donor surface included). Solvent relaxation moves the system to lower energy on the radical–ion pair surface where crossing to the ground state neutral surface occurs (with the possibility of recrossing to the radical–ion surface included). Model calculations of the transient radical–ion pair populations are presented. The time dependent results that are presented show a dramatic dependence on the relative free energy differences (ΔG’s) among the three potential surfaces. Comparisons to other formalisms and to less detailed approximations are made. The mean populations of the transient ...

Forward and back photoinduced electron transfer in solid solutions: a comparison of theoretical methods

Abstract Several methods for calculating the excited-state and radical-ion probabilities in systems undergoing photoinduced electron transfer are presented and compared. These calculations are for solid solution where there are donors present at low concentration surrounded by a random distribution of acceptors at any concentration. The transfer rate depends exponentially on distance and is time independent (no solvent relaxation). This problem forms the basis for more complex situations including molecular diffusion and solvent relaxation. For each method the range of applicability and the underlying assumption are discussed.

Solvent relaxation and electron back transfer following photoinduced electron transfer in an ensemble of randomly distributed donors and acceptors

The role of solvent relaxation in electron back transfer following electron transfer from an optically excited donor to randomly distributed acceptors is treated theoretically. The solvent dynamics are included by using a time dependent electron back transfer rate function, Keff(R,t). The solvent relaxation is parameterized by τr, the relaxation time, D, the solvent energy diffusion constant, and Δq, the potential barrier height difference between the nonequilibrium solvent state formed upon ion creation and the relaxed solvent state. The expression for the ensemble averaged donor cation state population probability, 〈Pct(t)〉, as a function of these solvent relaxation parameters is derived. Numerical calculations are presented. Relationships among 〈Pct(t)〉, the intermolecular interaction parameters, and solvent relaxation parameters provide detailed insights into the distance and time dependence of the flow of electron probability in an ensemble of donors and acceptors. The theoretical expressions can be ...

Electron Transfer in Solution: Theory and Experiment

Photoinduced electron transfer is a fundamental chemical process. Following the transfer of an electron from an electronically excited donor to an acceptor, the resulting radical ions can go on to do useful chemistry. Electron back transfer (geminate recombination), however, quenches the ions and prevents further chemistry from occurring. The initial steps of photosynthesis involve excitation of a donor followed by electron transfer. Electron back transfer to the primary donor would stop the photosynthetic process. However, a specialized spatial array of consecutive acceptors eliminates the back transfer problem and is responsible for the efficiency of photosynthesis [1, 2, 3]. In systems of randomly distributed donors and acceptors (liquid or solid solutions) geminate recombination can be very rapid [4]. In liquid solutions, geminate recombination competes with diffusional separation of the photoinduced ions and limits chemical yields. Therefore, understanding phenomena which influence back transfer is not only an important basic problem, but is a problem of considerable practical significance.