Nuclear magnetic resonance (NMR) spectroscopy, also known as magnetic resonance spectroscopy, is a preeminent and noninvasive analytical technique that provides detailed information about the structure, dynamics, reaction state, and chemical environment of molecules. The development of NMR spectroscopy has led to the awarding of many Nobel Prizes, and today NMR spectroscopy serves as an important and irreplaceable tool in physics and chemistry. Two-dimensional (2D) NMR is effective at separating resonances which have similar chemical shifts, although the interpretation of 2D spectra can be challenging. A systematic density operator-based derivation will aid the understanding of the quantitative mechanism of 2D NMR spectroscopy and the interpreting of outcomes of 2D NMR experiments. Therefore, in this study, we systematically analyzed and compared the quantitative basis of 2D and 1D NMR. Meanwhile, as a proof of principle, simulations using the FID Appliance software toolkit were performed and interpreted using a brain phantom, a popular model for studying brain metabolites. The scheme shown in this paper will facilitate the understanding of quantitative 2D NMR spectroscopic analyses in chemistry and biology.

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相关光谱NMR实验的定量密度算子分析

核磁共振（NMR）光谱，也称为磁共振光谱，是一种出色的无创分析技术，可提供有关分子的结构，动力学，反应状态和化学环境的详细信息。NMR光谱学的发展导致获得了许多诺贝尔奖，如今，NMR光谱学已成为物理和化学领域不可或缺的重要工具。二维（2D）NMR有效分离具有相似化学位移的共振，尽管2D光谱的解释可能具有挑战性。系统的基于密度算子的推导将有助于理解2D NMR光谱的定量机制和解释2D NMR实验的结果。因此，在这项研究中 我们系统地分析和比较了2D和1D NMR的定量基础。同时，作为原理证明，使用FID Appliance软件工具包进行了模拟，并使用了脑模型（用于研究脑代谢物的流行模型）进行解释。本文显示的方案将有助于理解化学和生物学中的定量2D NMR光谱分析。