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)，它包含了一系列强大而通用的光谱技术，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得数据所需的射频和/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的自旋少于10个，这通常是相当简单的，并且存在许多有效的算法。然而，对于更大的自旋系统来说，困难出现了，因为所需的时间和存储空间随着自旋数量的增加呈指数级增长。对于自旋超过20个的系统，评估密度算符的时间依赖性所需的Liouvillian矩阵是如此之大，以至于目前没有计算机能够存储它，更不用说对角化了。我们的初步工作表明，可以获得一个高效率的算法，该算法可以按多项式的自旋数量缩放，从而允许对超过20个强耦合自旋进行准确的模拟。这是通过智能地排除不重要的和未填充的状态来降低Liouville矩阵的维度来实现的，例如耦合网络中相互远离的多量子相干的高阶或自旋的纠缠。我们希望对这种仍处于起步阶段的方法进行扩展和改进，并将其应用于磁共振中的两个具体模拟问题。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/这是到目前为止还不可能实现的事情。通过这样做，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计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(广义上定义为核自旋和电子自旋对顺磁分子化学的磁效应)。对这类实验产生的数据的定量解释通常需要模拟短寿命自由基对的相干演化，这些自由基对包括许多耦合的电子和核自旋，受到微弱的静态和/或射频磁场的影响。应用将包括阐明候鸟磁罗盘的生物物理起源，以及确定与溶液中化学反应速率和产率的磁场敏感性有关的自由基的扩散轨迹。

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.