Relation between CIDNP formed upon geminate and bulk recombination of radical pairs

A theoretical approach to time-resolved Chemically Induced Dynamic Nuclear Polarization (CIDNP) is proposed, which allows one to obtain the general relation between polarization formed upon recombination of geminate spin-correlated radical pairs, the so-called G-pairs, and upon recombination of radical pairs formed by encounters of free radicals in solution, the so-called F-pairs. This relation is described by a universal parameter denoted as γ. In this work, the γ value is computed for the arbitrary spin multiplicity, singlet or triplet, of the precursor of the G-pairs as well as for arbitrary recombination rate constants of radical pairs in singlet and triplet states, k_S and k_T, respectively. Furthermore, the treatment is extended to the situation where radicals undergo transformation resulting in different reactivity or magnetic parameters for F-pairs and G-pairs. The proposed theory enables modeling of time-resolved CIDNP data in cases where (i) both recombination channels are active and (ii) fast protonation/deprotonation of radicals changes the effective γ value.