Theory of solid-state photo-CIDNP in the earth's magnetic field

To date, solid-state photo-CIDNP experiments have been performed only using magic angle spinning NMR in a high-field regime, which is not associated with physiologically relevant spin dynamics. Here, we predict that nuclear spin polarization up to 10%, almost 9 orders of magnitude larger than thermal equilibrium polarization, can arise in cyclic photoreactions at the earth field due to a coherent three-spin mixing mechanism in the S-T(-) or S-T(+) manifold. The effect is maximal at a distance of about 30 Å between the two radicals, which nearly coincides with the separation between the donor and secondary acceptor in natural photosynthetic reaction centers. Analytical expressions are given for a simple limiting case. Numerical computations for photosynthetic reaction centers show that many nuclei in the chromophores and their vicinity are likely to become polarized. The theory predicts that only modest hyperfine couplings of a few hundred kilohertz are required to generate polarization of more than 1% for radical-radical distances between 20 and 50 Å, that is, for a large number of radical pairs in electron-transfer proteins.