A unified approach to spin polarization (CIDEP) and relaxation by Heisenberg spin exchange. II. Evaluation of the interradical distance dependence

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Abstract
In paper I, a theory of Heisenberg spin exchange (HSE) was formulated to treat both electron spin polarization (CIDEP) and relaxation. In this paper (II), the expressions have been extended to consider the dependence of the exchange strength J(r) on the interradical distance r. Analytic expressions for the CIDEP enhancement E and the spin exchange frequency νex have been obtained by adopting an exponential model for J(r) and integrating over a distribution of encounter distances r based on a Brownian diffusion model. A semiempirical expression for E has also been developed by replacing the usual diffusion parameters with experimentally measurable properties that are functions of diffusion. The behavior of νex and E on the exchange strength J(r) and the steepness of the distance dependence κr0 is illustrated. The analytic results are consistent with existing numerical calculations and agree remarkably well with recent experimental measurements. The role of viscosity is treated to explain recent results for relaxation (νex) and polarization (E) measurements of (i) acetate radical anion, (ii) H and D atoms, and (iii) acetone photoreduction.