Theory of the magnetic field modulated geminate recombination of radical ion pairs in polar solvents: Application to the pyrene–N,N-dimethylaniline system

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Abstract
Pairs of radical ions generated in polar solvents by photoinduced electron transfer either recombine within a few nanoseconds or separate. The (geminate) recombination process is governed by a hyperfine‐coupling‐induced coherent motion of the unpaired electron spins which can be modulated by weak external magnetic fields. The process which also generates the well‐known CIDNP and CIDEP effects is described theoretically by a stochastic Liouville equation comprising for realistic systems a large set of coupled diffusion equations. For the integration of these equations a finite‐difference algorithm with space and time discretization is developed. By comparison with exact solutions of the Liouville equation for model systems, it is demonstrated that an approximate Liouville equation which entails only two coupled diffusion equations for singlet and triplet radical pairs, respectively, suffices to predict the geminate recombination yields accurately. The approximate Liouville equation is employed then to study on the basis of known hyperfine coupling constants, second‐order recombination rate constants, diffusion coefficients, and dielectric constants, the solvent, temperature, concentration, and magnetic field dependence of the geminate (singlet and triplet) recombination yields for the system pyrene–N,N‐dimethylaniline. The effect of deuteration upon the recombination yield and its magnetic field dependence is also studied. Furthermore, the influence of an exchange interaction acting at small separations of the radicals is investigated for a model system.