Theory of chemically induced magnetic polarization. Effects of S–T±1 mixing in strong magnetic fields

Chemically induced magnetic polarization due to mixing of the singlet and MS=±1 triplet sublevels of a diffusing radical pair in a strong magnetic field is investigated by an approximate stochastic Liouville model which considers separately the two-level S–T−1 and S–T1 mixings. As previously found for S–T0 mixing, the stochastic Liouville equations for S–T−1 level mixing can be written as a Bloch-type equation with diffusion, and a similar equation for the S–T1 mixing can be obtained simply by changing the sign of the magnetic field. These equations give a simple vector model of chemically induced polarization by S–T±1 mixing, including the all-important diffusion through the S–T−1 level crossing. For simple Brownian diffusion and an exchange interaction that decays exponentially with radical separation, the stochastic Liouville equations for S–T−1 mixing can be converted to a single integral equation for the resulting polarization, and a similar equation can be derived for the S–T1 case. The polarizations are small and can be well approximated by a single term in the Neumann series solution of the integral equation. Usually the entire S–T±1 polarization comes from S–T−1 mixing in the region where these levels cross. Significant polarizations occur only in those radical pairs where either a very large hyperfine interaction provides rapid singlet–triplet mixing or slow diffusion enables the pair to remain a relatively long time in the level crossing region.