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

弗拉基米尔Mandelshtam是由理论和计算化学程序的支持，开发和应用新的理论/计算方法，从数据处理核磁共振（NMR）实验量子化学动力学计算。 将被使用和进一步探讨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），沿着将被设计为针对不同类型的频谱分析问题的变体。 这些研究将包括算法和代码开发，特别是推广到2D，3D和4D NMR实验，以及使用真实的和合成数据的各种测试计算。 此外，将与实验NMR组合作探索FDM数据处理独特可能的新实验的设计。 量子化学动力学数值算法的开发和应用也将继续，重点是物理上重要的问题，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和近似半经典方法，一般的两步方案，包括信号产生，然后信号处理将接近几种方法。 成功的应用程序有可能揭示新的信息或导致显着的计算节省。在光谱分析研究中发展的理论和计算方法在科学和工程中具有广泛的应用前景。 沿着对磁共振光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.