Monte-Carlo wavefunction approach for the spin dynamics of recombining radicals

Abstract

We adapt the Monte-Carlo wavefunction (MCWF) approach to treat the open-system spin dynamics of radical pairs subject to spin-selective recombination reactions. For these systems, non-Lindbladian master equations are widely employed, which account for recombination via the non trace-preserving Haberkorn superoperator in combination with reaction-dependent exchange and singlet–triplet dephasing terms. We show that this type of master equation can be accommodated in the MCWF approach, by introducing a second type of quantum jump that accounts for the reaction simply by suitably terminating the propagation. In this way, we are able to evaluate approximate solutions to the time-dependent radical pair survival probability for systems that have been considered untreatable with the master equation approach until now. We explicate the suggested approach with calculations for radical pair reactions that have been suggested to be relevant for the quantum compass of birds and related phenomena.

Spin relaxation in radical pairs from the stochastic Schrödinger equation

“…Here we demonstrate the utility of the SSE applied to radical pair spin dynamics by considering two sets of model problems. The first is based on a recent study by Keens & Kattnig into relaxation effects on FAD •− -Z • and FAD •− -W •+ radical pairs, 34 and the second is based on our own recent study 36 of the DMJ •+ -An -Ph n -NDI •− radical pairs investigated experimentally by Scott et al 4 A. FAD •− -X • radical pairs As a first example application of the SSE with coherent state sampling, we consider a set of FAD •− -X • radical pairs with random fields relaxation. Here X • is either W •+ , a tryptophan radical, or Z • , a radical with no hyperfine coupled nuclear spins, both of which are commonly examined model radical pairs in the context of avian magnetoreception.…”

“…( 9), which we have thus far not specified. We shall now present two methods for sampling, one based on the spin coherent states we have used before, 34,35,45,[57][58][59] and the other based on 𝑆𝑈 (𝑍) coherent states. Ideally, the choice of |𝜓(𝝃) will yield a sampling method that is self-averaging, meaning that the statistical error in the sampled trace is O (1/ √ 𝑀 𝑍) and therefore exponentially convergent in the number of nuclear spins.…”

“…Carlo wavefunction approach can be modified to find solutions to the Lindblad equation for recombining radicals, 34 and that this approach can be combined with a coherent state sampling scheme introduced by us to reduce the computational cost of spin dynamics calculations in systems without spin relaxation. 35 This makes spin dynamics simulations including relaxation feasible for realistic models of radical pairs, provided the relaxation can be treated accurately with a Lindblad equation.…”

“…In the SSE approach, the stochastic fluctuations in the spin interactions are directly included in the spin state dynamics. This can be viewed as a way to extend the Keens & Kattnig Monte Carlo wavefunction method 34 to treat relaxation beyond the Lindblad approximation, an idea which we have already suggested in several papers. 35,36,45 Indeed, the direct use of stochastic fluctuations to model relaxation in spin dynamics is not new: it has previously been applied, for example, in the context of simulating both EPR spectra [46][47][48] and radical pair recombination.…”

“…Firstly we consider the effect of random field relaxation on some model FAD •− -W •+ and FAD •− -Z • radical pairs of relevance to the avian magnetoreception problem, extending the model systems treated by Keens & Kattnig in Ref. 34 to include non-Markovian effects which cannot be captured with the Lindblad equation. Secondly we simulate the spin dynamics of DMJ •+ -An -Ph n -NDI •− "molecular wire" radical pairs with a more realistic rotational Brownian motion model of relaxation.…”