Quantitative density operator analysis of correlation spectroscopy NMR experiments

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.