Determination of radical re-encounter probability distributions from magnetic field effects on reaction yields

Measurements are reported of the effects of 0-23 mT applied magnetic fields on the spin-selective recombination of Py*- and DMA*+ radicals formed in the photochemical reaction of pyrene and N,N-dimethylaniline. Singlet <--> triplet interconversion in [Py*- DMA*+] radical pairs is probed by investigating combinations of fully protonated and fully deuterated reaction partners. Qualitatively, the experimental B1/2 values for the four isotopomeric radical pairs agree with predictions based on the Weller equation using known hyperfine coupling constants. The amplitude of the "low field effect" (LFE) correlates well with the ratio of effective hyperfine couplings, aDMA/aPy. An efficient method is introduced for calculating the spin evolution of [Py*- DMA*+] radical pairs containing a total of 18 spin-1/2 and spin-1 magnetic nuclei. Quantitative analysis of the magnetic field effects to obtain the radical re-encounter probability distribution f (t )-a highly ill-posed and underdetermined problem-is achieved by means of Tikhonov and maximum entropy regularization methods. The resulting f (t ) functions are very similar for the four isotopomeric radical pairs and have significant amplitude between 2 and 10 ns after the creation of the geminate radical pair. This interval reflects the time scale of re-encounters that are crucial for generating the magnetic field effect. Computer simulations of generalized radical pairs containing six spin-1/2 nuclei show that Weller's equation holds approximately only when the radical pair recombination rate is comparable to the two effective hyperfine couplings and that a substantial LFE requires, but is not guaranteed by, the condition that the two effective hyperfine couplings differ by more than a factor of 5. In contrast, for very slow recombination, essentially any radical pair should show a significant LFE.