Fay Thomas P, Lindoy Lachlan P, Manolopoulos David E
Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom.
J Chem Phys. 2021 Feb 28;154(8):084121. doi: 10.1063/5.0040519.
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.
我们表明，随机薛定谔方程（SSE）为模拟自由基对的量子力学自旋动力学提供了一种理想方法。自旋哈密顿量波动引起的电子自旋弛豫效应在此方法中很容易纳入，并且其处理可以与计算实验可观测量所需的核自旋态迹的高效随机评估相结合。这些特性在应用示例中得到了说明，这些示例包括对鸟类磁感受中感兴趣的黄素 - 色氨酸自由基对以及涉及沿分子线的自旋选择性自由基对重组的问题。在这些示例的第一个中，SSE 被证明比最近对林德布拉德方程的随机实现更有效且应用更广泛，后者仅在极窄极限下提供了对弛豫的有效处理。在第二个示例中，精确的 SSE 结果用于评估最近提出的自旋弛豫的中岛 - 茨万齐格理论与自旋动力学的舒尔滕 - 沃利内斯理论相结合的准确性，该理论适用于具有更多核自旋的自由基对。我们还详细分析了迹采样的效率，突出了用 SU(N) 相干态采样的特殊优势。
