Spin relaxation in radical pairs from the stochastic Schrödinger equation

Abstract

We show that the stochastic Schrödinger equation (SSE) provides an ideal way to simulate the quantum mechanical spin dynamics of radical pairs. Electron spin relaxation effects arising from fluctuations in the spin Hamiltonian are straightforward to include in this approach, and their treatment can be combined with a highly efficient stochastic evaluation of the trace over nuclear spin states that is required to compute experimental observables. These features are illustrated in example applications to a flavin–tryptophan radical pair of interest in avian magnetoreception and to a problem involving spin-selective radical pair recombination along a molecular wire. In the first of these examples, the SSE is shown to be both more efficient and more widely applicable than a recent stochastic implementation of the Lindblad equation, which only provides a valid treatment of relaxation in the extreme-narrowing limit. In the second, the exact SSE results are used to assess the accuracy of a recently proposed combination of Nakajima–Zwanzig theory for the spin relaxation and Schulten–Wolynes theory for the spin dynamics, which is applicable to radical pairs with many more nuclear spins. We also analyze the efficiency of trace sampling in some detail, highlighting the particular advantages of sampling with SU(N) coherent states.

Magnetic field effects on radical pair reactions: estimation ofB1/2for flavin-tryptophan radical pairs in cryptochromes

“…To determine B 1/2 with anisotropic hyperfine and dipolar interactions included, we have used a method proposed by Fay et al to model spin relaxation in radical pairs. 42 The initial singlet state of the radical pair was propagated in 1 ns time-steps to 5 μs and then integrated (using k = 10 6 s −1 ) to obtain Φ T ( B ). The initial nuclear spin space was trace-sampled using a single SU ( Z ) coherent state 42 with averaging over 16 randomly distributed directions of the magnetic field.…”

“…42 The initial singlet state of the radical pair was propagated in 1 ns time-steps to 5 μs and then integrated (using k = 10 6 s −1 ) to obtain Φ T ( B ). The initial nuclear spin space was trace-sampled using a single SU ( Z ) coherent state 42 with averaging over 16 randomly distributed directions of the magnetic field. The relative orientation of the two radicals and the dipolar coupling parameter ( D = −0.511 mT) were appropriate for FAD and Trp318 in the crystal structure of pigeon cryptochrome 4a.…”

“…The relative orientation of the two radicals and the dipolar coupling parameter ( D = −0.511 mT) were appropriate for FAD and Trp318 in the crystal structure of pigeon cryptochrome 4a. 32 We refer to this method here as SU ( Z ) (instead of stochastic Schrödinger equation, SSE 42 ) because we do not use it to model spin relaxation.…”

Spin selective charge recombination in chiral donor-bridge-acceptor triads

“…The spin density operator framework used here can be extended straightforwardly to include other important physics of spin-correlated charge separated states necessary to understand real systems, such as hyperfine coupling effects and spin relaxation. 5,[36][37][38][39][40] We anticipate that this framework for understanding spin selective charge recombination in chiral systems will be useful in numerous contexts involving molecular CISS, such as in devising systems exploiting CISS for quantum information science and in studies of CISS effects in biological electron transfer.…”

Driven Radical Motion Enhances Cryptochrome Magnetoreception: Toward Live Quantum Sensing

“…This assessment is further corroborated by our observations that damped oscillations can be even more effective and that, for the low-frequency modes, sustained oscillations are not a necessity as a single oscillation can already produce a significant enhancement. In the SI we have additionally considered a more realistic treatment of protein mediated radical motion with a Brownian dynamics model implemented via the stochastic Schrödinger equation 45 (see Figure S13 ). This model calculation demonstrates that for weak velocity damping, the compass sensitivity can be enhanced over the static limit and even the idealized undamped harmonic model, suggesting that more realistic models could be better amplifiers.…”