An efficient quantum mechanical method for radical pair recombination reactions

TL;DR

This paper introduces a stochastic quantum mechanical method using spin coherent states to efficiently compute radical pair reaction yields, significantly reducing computational costs compared to traditional deterministic approaches.

Contribution

The authors develop a stochastic trace evaluation method leveraging spin coherent states, enabling faster quantum simulations of radical pair reactions with large nuclear spin spaces.

Findings

Achieved over 5000-fold speedup in calculations

Converged singlet yield with only 200 Monte Carlo samples

Demonstrated method on a radical pair with over 10^6 nuclear states

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 $O(Z^2\log Z)$, 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 $O(MZ\log Z)$, where $M$ is the number of Monte Carlo samples needed for convergence. Example calculations on a strongly-coupled radical pair with $Z>10^6$ show 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.