Development and Applications of Computational Methods of Spectral Analysis: From Quantum Dynamics Calculations to NMR Data Processing.

Vladimir Mandelshtam由理论和计算化学项目支持，开发和应用新的理论/计算方法，范围从核磁共振（NMR）实验中的数据处理到量子化学动力学计算。将使用并进一步探索的核心技术是用于时间信号频谱分析的滤波器对角化方法（FDM），以及针对不同类型频谱分析问题而设计的变体。研究将包括算法和代码开发，特别是2D、3D和4D核磁共振实验的推广，以及使用真实和合成数据的各种测试计算。此外，将与实验核磁共振小组合作探索FDM数据处理独特可能的新实验设计。量子化学动力学数值算法的发展和应用也将继续，重点关注物理上重要的问题，如隧道分裂和能量转移（由环境或同位素取代引起）。对于数值精确的量子方法和近似半经典方法，一般的两步方案涉及信号产生和信号处理，将采用几种方法进行处理。成功的应用程序具有揭示新信息或节省大量计算的潜力。在光谱分析研究中发展的理论和计算方法在科学和工程上具有广泛的应用前景。随着磁共振波谱数据分析的重大改进，这项研究的结果可能会影响通信科学和经济学等多个领域。

Vladimir Mandelshtam is supported by the Theoretical and Computational Chemistry Program to develop and apply novel theoretical/computational methods, ranging from data processing in nuclear magnetic resonance (NMR) experiments to quantum chemical dynamics calculations. The central technique that will be used and further explored is the Filter Diagonalization Method (FDM) for spectral analysis of time signals, along with variants that will be designed to target different types of spectral analysis problems. The studies will include algorithm and code development, in particular the generalization to 2D, 3D, and 4D NMR experiments, and various test calculations using real and synthesized data. Moreover, the design of new experiments that are uniquely possible with FDM data processing will be explored in collaboration with experimental NMR groups. The development and applications of numerical algorithms for quantum chemical dynamics will continue as well, focusing on physically important problems such as tunneling splittings and energy shifts (caused by the environment or isotope substitution). For both numerically exact quantum and approximate semiclassical approaches, the general two-step scheme involving signal generation followed by signal processing will be approached with several methodologies. Successful applications have the potential to reveal new information or lead to dramatic computational savings. The theoretical and computational methods developed in this spectral analysis research have broad application possibilities in science and engineering. Along with enabling major improvements to data analysis in magnetic resonance spectroscopy, outcomes from this research can potentially impact diverse areas such as communications science and economics.