Singlet-Triplet Splitting in Diffusing Radical Pairs and the Magnitude of Chemically Induced Electron Spin Polarization

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Abstract
A previous theory of anomalous electron spin resonance spectra of free radicals in solution attributes the electron spin polarizations to the combined effects of singlet‐triplet mixing by magnetic interactions in a diffusing radical pair and singlet‐triplet splitting by the exchange interaction when, and if, the diffusing radicals reencounter each other. This theory is studied in more detail by considering the exchange interaction at all times during the diffusive trajectory of the radical pair, in contrast to the original treatment of approximating it as a rectangular pulse which is nonzero only briefly during the second encounter of the radicals. Time dependent perturbation theory is used to calculate the radical pair wavefunction and the corresponding electron spin polarization to first order in the exchange interaction. The polarization is averaged over all possible diffusion paths of the radicals by averaging the exchange interaction over the distribution of radical pair separations obtained by solution of the diffusion equation with appropriate boundary conditions. These boundary conditions take into account the facts that polarization begins when the radicals separate to a point where the magnetic and exchange interactions are roughly equal, and that the developing polarization is destroyed by spin exchange if the radicals subsequently come too close together. The calculated polarizations are of the right order of magnitude to account for the experimental results, and the dependence of the polarization on the magnetic interactions and the diffusion parameters is essentially the same as predicted by the earlier simpler theory.