Theory of chemically induced dynamic electron polarization. I

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Abstract
A general and detailed analysis is given of the phenomenon of chemically‐induced dynamic electron polarization (CIDEP) by means of the stochastic‐Liouville method in accordance with the earlier preliminary report. The finite‐difference technique employed permits rapid and convergent solutions without requiring any untoward assumptions on the nature of the models. The dependence of the polarization on the exchange interaction J(r), the Larmor frequency differences between the interacting pair of radicals, diffusion rates, and rates of spin‐selective chemical reactions are given in detail. It is shown that models in which J(r) is taken to decay exponentially with r, the radical‐separation distance of the radical pair, yield results which are distinctly different from those for a contact exchange model, when J0 [the value of J(r) when r is at the distance of closest approach] is appreciable. The former, more realistic model yields substantial polarizations asymptotically independent of J0, but larger the slower the decrease of J(r) with r; the contact exchange model, however, rapidly goes to zero with increasing J0. These asymptotic values of polarization are predicted to be as high as 10–40 times the equilibrium polarizations (Peq) for sensible values of the relevant parameters, while for values of J0 yielding maximum polarizations (generated at the formative reaction), they can be greater than 100 Peq. These results are of the correct order for agreement with recent experiments. The polarizations have been related to the CIDEP intensities that one may observe for typical schemes of radical production, reaction, and relaxation in order to allow a comparison of the theoretical predictions with experiment.