Theory of chemically induced dynamic electron polarization. II

Abstract

The earlier theoretical analysis for chemically induced dynamic electron polarization (CIDEP), based on the stochastic‐Liouville equation, is generalized to explicitly include the spin‐dependent exchange forces in the diffusive trajectories, thus permitting a consistent analysis of the simultaneous effects of exchange on both the spin‐selective chemical reaction and CIDEP effects. The semiclassical treatment of diffusion under a ``classical'' force field due to the valence interactions requires the introduction of spin‐dependent diffusive and reactive trajectories, and this is discussed for the Brownian‐motion model utilized. Our results show that the polarization generated per fractional probability that singlets react ${\mathrm{(P\hspace{0.17em}}}^{\infty }/\mathcal{F})$ , is not sensitive to the actual details of the spin‐selective reactive process (although the absolute polarization P^∞ is sensitive to the reactive process), due presumably to the spatial distinction between interradical separations (r) for which the reaction may occur vs those for which CIDEP polarizations are developed. The former require ℏ|J(r)|/kT > 1 while for the latter ℏ|J(r)|/kT < 1, where J(r) is the exchange interaction. It is found that differences in the (nonreactive) diffusive trajectories for singlets and triplets give polarizations that are generally negligible compared to those which develop as a result of the spin‐selective reaction (for our overdamped diffusive model). However, our results for more long‐range Coulomb interactions between charged radicals show they can produce significant changes on ${\mathrm{P\hspace{0.17em}}}^{\infty }/\mathcal{F}$ that are quite sensitive to the magnitude of J. Thus ionic‐concentration effects on $P^{\infty }/\mathcal{F}$ should be an important indicator of the CIDEP mechanism. Results are also given for the spin‐depolarization process, whereby the effects of spin exchange on a radical pair, which initially collide with residual nonthermal polarization, are to destroy this polarization. The effective range of the spin exchange is found to be weakly enhanced as the range of J(r) is increased. Also, it is shown that, for several variations of a simple exponential dependence of J(r) on r, $P^{\infty }/\mathcal{F}$ is hardly affected, although nonexponential dependences can introduce marked changes.