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The standard quantum mechanical expressions for the singlet and tripletsurvival probabilities and product yields of a radical pair recombinationreaction involve a trace over the states in a combined electronic and nuclearspin Hilbert space. If this trace is evaluated deterministically, by performinga separate time-dependent wavepacket calculation for each initial state in theHilbert space, the computational effort scales as $O(Z^2\log Z)$, where $Z$ isthe total number of nuclear spin states. Here we show that the trace can alsobe evaluated stochastically, by exploiting the properties of spin coherentstates. This results in a computational effort of $O(MZ\log Z)$, where $M$ isthe number of Monte Carlo samples needed for convergence. Example calculationson a strongly-coupled radical pair with $Z>10^6$ show that the singlet yieldcan be converged to graphical accuracy using just $M=200$ samples, resulting ina speed up by a factor of $>5000$ over a standard deterministic calculation. Weexpect that this factor will greatly facilitate future quantum mechanicalsimulations of a wide variety of radical pairs of interest in chemistry andbiology.

An efficient quantum mechanical method for radical pair recombination reactions