title: An efficient quantum mechanical method for radical pair recombination reactions.
abstract: The standard quantum mechanical expressions for the singlet and triplet survival probabilities and product yields of a radical pair recombination reaction involve a trace over the states in a combined electronic and nuclear spin Hilbert space. If this trace is evaluated deterministically, by performing a separate time-dependent wavepacket calculation for each initial state in the Hilbert space, the computational effort scales as O(Z2log⁡Z), where Z is the total number of nuclear spin states. Here we show that the trace can also be evaluated stochastically, by exploiting the properties of spin coherent states. This results in a computational effort of O(MZlog⁡Z), where M is the number of Monte Carlo samples needed for convergence. Example calculations on a strongly coupled radical pair with Z>106show that the singlet yield can be converged to graphical accuracy using just M=200 samples, resulting in a speed up by a factor of >5000 over a standard deterministic calculation. We expect that this factor will greatly facilitate future quantum mechanical simulations of a wide variety of radical pairs of interest in chemistry and biology.
authors.affiliation: Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom.
authors.forename: Alan M
authors.initials: AM
authors.lastname: Lewis
authors.affiliation: Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom.
authors.forename: Thomas P
authors.initials: TP
authors.lastname: Fay
authors.affiliation: Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom.
authors.forename: David E
authors.initials: DE
authors.lastname: Manolopoulos
mesh_terms: D005609:Free Radicals / Q000737:chemistry; D011789:Quantum Theory; D013997:Time Factors
chemical_list: D005609:Free Radicals