Polynomially scaling spin dynamics simulation algorithms and their application in NMR and Spin Chemistry.

磁共振，包括核磁共振（NMR）和电子顺磁共振（EPR），包含了一个非常强大和通用的光谱技术范围，用于探索分子的结构，运动和反应性。在许多这样的应用中，如果不对自旋系统对获取数据所需的射频和/或微波脉冲序列的响应进行计算机模拟，就不能令人满意地解释光谱。如果感兴趣的系统包含少于10个旋转，这通常是相当直接的，并且存在许多有效的算法。然而，对于更大的自旋系统，困难出现了，因为所需的时间和存储随着自旋的数量呈指数级增长。对于超过20个自旋的系统，评估密度算子的时间依赖性所需的刘维里安矩阵非常大，目前没有计算机能够存储它，更不用说对角化它了。我们的初步工作表明，可以获得一种高效的自旋数多项式缩放算法，允许对超过20个强耦合自旋进行精确模拟。这是通过智能地排除不重要和无人口的状态来降低刘维尔矩阵的维数来实现的，例如高阶的多量子相干或耦合网络中彼此远离的自旋纠缠。我们希望扩展和改进这种仍处于起步阶段的方法，并开发应用于磁共振中的两个特定模拟问题。该算法将适用于蛋白质结构与实验核磁共振数据的直接拟合，这是迄今为止不可能实现的。在此过程中，我们希望建立一种新的核磁共振结构确定范式，其中原子坐标通过一系列定义良好的从头算模拟算法与实验光谱直接相关。第二个主要应用将在自旋化学领域（广义上定义为核和电子自旋对顺磁性分子化学的磁效应）。对此类实验产生的数据进行定量解释通常需要模拟由许多耦合的电子和核自旋组成的短寿命自由基对在弱静态和/或射频磁场作用下的相干演化。应用将包括阐明候鸟磁罗盘的生物物理起源和确定自由基的扩散轨迹，这些自由基对溶液中化学反应的速率和产率的磁场敏感性负责。

Magnetic resonance, which includes Nuclear Magnetic Resonance (NMR) and Electron Paramagnetic Resonance (EPR), comprises an enormously powerful and versatile range of spectroscopic techniques for exploring the structures, motions and reactivity of molecules. In many of these applications, the spectra cannot satisfactorily be interpreted without performing computer simulations of the response of the spin system to the sequence of radiofrequency and/or microwave pulses that are required to obtain the data. If the system of interest contains fewer than about 10 spins, this is usually reasonably straightforward and many efficient algorithms exist. However, difficulties arise for larger spin systems because the time and storage required scales exponentially with the number of spins. For systems with over 20 spins, the Liouvillian matrix required to evaluate the time-dependence of the density operator is so large that no computer is currently able to store it, let alone diagonalise it. Our preliminary work indicates that a highly efficient algorithm can be obtained that scales polynomially in the number of spins, allowing accurate simulations to be performed for many more than 20 strongly coupled spins. This is achieved by reducing the dimension of the Liouville matrix by intelligently excluding unimportant and unpopulated states, for example high orders of multiple quantum coherence or entanglements of spins that are remote from one another in the coupling network.We wish to extend and improve this method, which is still in its infancy, and to develop applications to two specific simulation problems in magnetic resonance. The algorithm will be adapted for the direct fitting of protein structures to experimental NMR data / something that has not so far been possible. In doing so, we hope to establish a new paradigm for NMR structure determination, wherein the atomic coordinates are directly related to the experimental spectra by a chain of well-defined ab initio simulation algorithms. The second major application will be in the field of Spin Chemistry (broadly defined as the magnetic effects of nuclear and electron spins on the chemistry of paramagnetic molecules). Quantitative interpretation of the data produced by such experiments routinely requires simulation of the coherent evolution of short-lived radical pairs comprising many coupled electron and nuclear spins subject to weak static and/or radiofrequency magnetic fields. Applications will include the elucidation of the biophysical origin of the magnetic compass of migratory birds and determination of the diffusive trajectories of radicals responsible for the magnetic field-sensitivity of the rates and yields of chemical reactions in solution.