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

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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.