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

多项式缩放自旋动力学模拟算法及其在核磁共振和自旋化学中的应用。

• 批准号: EP/F065205/2
• 负责人: Ilya Kuprov
• 金额: --
• 依托单位: University of Oxford
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2009
• 资助国家: 英国
• 起止时间: 2009 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FF065205%2F2
• 关键词: Polynomially; scaling; spin; dynamics; simulation

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.

磁共振，包括核磁共振（NMR）和电子顺磁共振（EPR），包括一个非常强大和多功能的光谱技术范围，用于探索分子的结构，运动和反应性。在许多这些应用中，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少于10个自旋，这通常是相当简单的，并且存在许多有效的算法。然而，对于较大的自旋系统出现困难，因为所需的时间和存储随自旋数量呈指数级变化。对于超过20个自旋的系统，所需的Liouvillian矩阵来评估的密度算子的时间依赖性是如此之大，没有计算机目前能够存储它，更不用说对角化它。我们的初步工作表明，可以得到一个高效的算法，尺度多项式的自旋数，允许精确的模拟进行了许多超过20强耦合自旋。这是通过智能地排除不重要的和未填充的状态，例如高阶的多量子相干性或纠缠的自旋是远离彼此的耦合network.We希望扩展和改进这种方法，这仍然是在它的婴儿期，并开发应用程序的刘维尔矩阵的维数减少磁共振中的两个具体的模拟问题。该算法将适用于蛋白质结构与实验NMR数据的直接拟合，这是迄今为止还不可能的。在这样做的过程中，我们希望建立一个新的范例NMR结构测定，其中原子坐标直接相关的实验光谱的链定义良好的从头计算模拟算法。第二个主要应用将是自旋化学领域（广义上定义为核和电子自旋对顺磁分子化学的磁效应）。对这些实验产生的数据进行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受弱静态和/或射频磁场影响的耦合电子和核自旋。应用将包括阐明候鸟的磁罗盘的生物物理起源，以及确定负责溶液中化学反应的速率和产量的磁场敏感性的自由基的扩散轨迹。

项目成果

Quasioptimality of maximum-volume cross interpolation of tensors

• DOI: 10.1016/j.laa.2014.06.006
• 发表时间: 2013-05
• 期刊: Linear Algebra and its Applications
• 影响因子: 1.1
• 作者: D. Savostyanov

Quantum mechanical NMR simulation algorithm for protein-size spin systems

• DOI: 10.1016/j.jmr.2014.04.002
• 发表时间: 2014-06-01
• 期刊: JOURNAL OF MAGNETIC RESONANCE
• 影响因子: 2.2
• 作者: Edwards, Luke J.;Savostyanov, D. V.;Kuprov, Ilya
• 通讯作者: Kuprov, Ilya

Computation of extreme eigenvalues in higher dimensions using block tensor train format

• DOI: 10.1016/j.cpc.2013.12.017
• 发表时间: 2013-06
• 期刊: Comput. Phys. Commun.
• 作者: S. Dolgov;B. Khoromskij;I. Oseledets;D. Savostyanov

Molecular structure refinement by direct fitting of atomic coordinates to experimental ESR spectra

通过将原子坐标直接拟合到实验 ESR 光谱来细化分子结构

• DOI: 10.48550/arxiv.1109.4815
• 发表时间: 2011
• 作者: Charnock G