Ensemble averaged spin pair dynamics of doublet and triplet molecules

Analytical expressions are presented which describe the spin dynamics of random ensembles of pairs of molecules, the partners being either of doublet (²D) or of triplet (³T) type. The spin dynamics are induced either by the hyperfine coupling (²D) or by the zero-field splitting (³T). The three spin transitions ¹( ²D₁+²D₂)→³( ²D₁+²D₂), ⁴( ³T₁+²D₂)→²( ³T₁+²D₂), and ^3,5( ³T₁+³T₂)→(³T ₁+³T₂) are considered at low and high magnetic fields. The ensemble average is taken over all nuclear spin configurations (²D), over all molecular orientations (³T) and over possible histories which may include nuclear spin realignments by paramagnetic-diamagnetic exchange (²D) or molecular reorientations by rotational diffusion or exciton migration in random matrices (³T). The results obtained demonstrate that magnetic fields influence the processes of triplet quenching by radicals and triplet-triplet annihilation and thereby can provide information on the rotational diffusion of triplet molecules, exciton migration, and paramagnetic-diamagnetic exchange. Such effects predicted earlier by us for processes involving doublets [J. Chem. Phys. 71,1878 (1979)] and discussed here, were recently demonstrated experimentally [F. Nolting, H. Staerk, and A. Weller, Chem. Phys. Lett. 88, 523 (1983)]. The results presented are also of general interest as the spin systems considered provide a solvable model to describe the degree of randomization in ensembles of quantum systems.