NMR and spectral simplification

For a system of coupled 7=1/2 nuclei, the transition frequencies in the multiple quantum spectra are determined by the dipolar coupling constants, the scalar coupling constants and the chemical shifts of the nuclei. In theory, the spectra of order N— 1 and N—2 contain sufficient transitions to measure all of the dipolar coupling constants and chemical shifts in an 7V-spin system. For additional accuracy and confidence, the A— 3 quantum spectrum can also be analysed to provide redundancy and more reliable estimates of the Dy. 

The number of transitions in an NMR spectrum increases dramatically as the number of interacting nuclei in the spin system increases. The number of transitions appearing in a 1-quantum spectrum of a spin system (without any simplifying symmetry) partially oriented in a nematic phase is expressed by Eq. (2), with some examples shown in Table 1. 

If there is some element of symmetry in the spin system, the number of transitions is reduced. For a 6-spin system with no simplifying symmetry, aligned in an anisotropic solution, there would be 792 transitions in an JH 1-quantum spectrum. However in the spectrum of benzene, C6H6 (a planar hexagonal 6-spin proton spin system) aligned in anisotropic solution there are only 72 transitions in the 1-quantum proton spectrum. 

Severe overlap between transitions in spin systems containing more than about 7 or 8 spins (without simplifying symmetry) makes analysis of the 1-quantum spectra a virtually intractable problem. In larger spin systems, it becomes impossible to resolve or assign individual transitions for an iterative computer analysis. 

The number of M-quantum transitions in a system of TV nuclei (I — 1/2) neglecting symmetry, is given by Eq. (3) and representative values are summarised in Table 2. 

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