Unprecedented ab initio simulations of exchange-affected magnetic field on reaction yield (MARY) spectra of real radical pair (RP) systems are presented which provide a novel, reliable method for the determination of electron self-exchange rate constants by MARY spectroscopy. The MARY technique is an interesting alternative to EPR in the study of short-lived and unstable radicals. A RP lifetime of a few nanoseconds is sufficient compared to at least 100 ms necessary for the CW EPR line broadening technique.