Separation of multiple-quantum signals with different orders along with frequency axis in Raman magnetic resonance spectroscopy in heteronuclear systems

One-dimensional multiple-quantum spectroscopy with Raman magnetic resonance (RMR) in heteronuclear systems was described by the product operator formalism in detail. The effects of the field strength and the frequency offset of the irradiation introduced during the detection period on the intensities and the resonant frequencies of the multiple-quantum signals in RMR spectra were investigated extensively by this product operator formalism. The results predicted by the formalism showed that the multiple-quantum signals in RMR spectroscopy had a higher sensitivity when a smaller frequency offset of irradiation field was employed. However, this situation would complicate the assignment and the separation of the multiple-quantum signals in different orders along the frequency axis in RMR spectra. On the other hand, a larger strength of the irradiation field would result in decoupling and therefore would obscure the detection of the multiple-quantum signals. In the meantime, a much weaker RF field might greatly decrease the intensities of the multiple-quantum signals in RMR spectra, though in this case the assignment and the separation of the multiple-quantum signals would be easier to be carried out. Hence, a moderate irradiation field strength with an adequate offset would be necessary for detecting and separating the multiple-quantum signals in different orders in the RMR experiments. These theoretical predictions were in good agreement with the RMR experiments in the heteronuclear spin systems AXn (n = 1, 2 and 3) when the protons were irradiated and the signals from the carbon-13 nuclei in those spin systems were detected.