Radical pair stochastic Liouville equation

Since the Bia value are less than 10 mT for most organic radical pairs, the magnetically induced changes due to the HFCM are usually saturated below 0.1 T. It is noteworthy that no analytical prediction of the magnetic field dependence of Yc (B) and Ye (B) is possible in the case of the HFCM. On the other hand, the quantitative Yc (B) and Ye (B) values can only be obtained by numerical calculations with the stochastic Liouville equation [27]. 

Combining Spin Dynamics and Radical Pair Dynamics. In a very general form, spin dynamics and radical pair dynamics can be treated simultaneously with the so-called stochastic Liouville equation [10b],... 

Quantitative calculations of the CIDNP effect can be performed as described in Section II.B.5. One has to set up the nuclear spin system of the intermediate radical pair or biradical, choose a diffusional model, compute reaction probabilities for every nuclear spin state by solving the stochastic Liouville equation numerically or approximately, establish a correlation between the nuclear spin states in the paramagnetic intermediates and the nuclear spin states in the products to obtain the populations of the latter, and finally apply Eq. 61 or the formalism of the preceding section to get line intensities. This approach, which for all but the simplest systems is impracticable except on a computer, is often necessary with the usual uncertainty of the parameters entering the calculations of the radical pair mechanism, a reasonable accuracy can be expected. However, qualitative relationships between signal intensities, especially signal phases, and parameters of the reaction mechanism as well as magnetic properties of the intermediates are... 

In a study of phenacylphenylsulfone photolysis, CIDNP data were taken as evidence that the primary radical pairs cannot recombine to regenerate the starting material because the micelle forces a certain orientation of the radicals [63], From low-field 13C CIDNP and SNP measurements on cleavage of benzylic ketones in sodium dodecyl sulfate micelles, it was inferred [64] that the exchange interaction in these systems is several orders of magnitude smaller ( 10lorads 1 at a reduction distance of 6 A cf. the values in Section IV.B) and the distance dependence is much weaker (a x 0.5 A" cf. the discussion of Eq. 10) than generally assumed for radical pairs. By numerical solutions of the stochastic Liouville equation for a model of the micelle where one of the radicals is kept fixed at the center of the micelle while the other radical is allowed to diffuse, the results of MARY experiments, 13C CIDNP experiments at variable fields, and SNP experiments could be reproduced with the same set of parameters [65],... 

An approximative analytical treatment of S-T+-type CIDNP of radical pairs in micelles has recently been given [66]. Comparison with numerical solutions of the stochastic Liouville equation obtained by a finite difference technique showed the accuracy of the approximate solution to be quite good. 

---