Signal selection with pulsed field gradients

Signal selection with pulsed field gradients 

In the absence of a field gradient pulse, the Larmor frequency, co, of a spin depends upon the applied static field, Bq, such that oo = yBo. When the gradient pulse is applied there is an additional spatially dependent field, Bg(z) associated with the gradient giving rise to a spatially dependent Larmor frequency, co(z)  

If the gradient is applied for a duration ig seconds, the magnetisation vector rotates through a spatially dependent phase angle, 0(z) of 

This modification reflects the fact that a p-quantum coherence dephases at a rate proportional to p. Thus, double-quantum coherences dephase twice as fast as single-quantum coherences yet zero-quantum coherences are insensitive to field gradients. When the eoherence involves different nuclear species, allowance must be made for the magnetogyric ratio and coherence order for each, such that  

This general process is illustrated for a homonuclear spin system in the scheme of Fig. 5.37 in which only double-quantum coherence existing prior to the pulse is to be retained. Thus, prior to the rf pulse p = 2 coherence exists which experiences a gradient of strength Bgi and duration Ti and thus obtains a spatially dependent phase  

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Signal selection with pulsed field gradients... 

Figure 5.37. An illustration of signal selection by pulsed field gradients. Using two gradients with ratio Gi G2 of 1 2 selects only the coherence transfer pathway shown, leaving all others defocused and unobservable.

Figure 6.24. Editing of a proton spectrum according to carbon multiplicities. In (b) only those resonances arising from methylene groups have been selected from the conventional spectrum (a). Clean suppression of all other resonances is achieved with pulsed field gradients, although some phase errors remain on the selected signals.

The HMQC sequence aims to detect only those protons that are bond to a spin- A heteronucleus, or in other words only the satellites of the conventional proton spectrum. In the case of C, this means that only 1 in every 100 proton spins contribute to the 2D spectrum (the other 99 being attached to NMR inactive C) whilst for N with a natural abundance of a mere 0.37%, only 1 in 300 contribute. When the HMQC FID is recorded, all protons will induce a signal in the receiver on each scan and the unwanted resonances, which clearly represent the vast majority, must be removed with a suitable phase cycle if the correlation peaks are to be revealed (the notable exception to this is when pulsed field gradients are employed for signal selection, see Section 6.3.3 below). By inverting the first C pulse on alternate scans, the phase of the C satellites are themselves inverted whereas the C-bound protons remain unaffected (Fig. 6.5). Simultaneous inversion of the receiver will lead to cancellation of the unwanted resonances with corresponding addition of the desired satellites. This two step procedure is the fundamental phase-cycle of the HMQC experiment, as indicated in Fig. 6.3 above. 

Figure 6.8. A comparison of signal suppression methods used in proton-detected heteronuclear correlation experiments (see descriptions in text). Spectrum (a) is taken from a conventional ID proton spectrum without suppression of the parent resonance and displays the required satellites. Other spectra are recorded with (b) phase-cycling, (c) optimised BIRD presaturation, and (d) pulsed field gradients to remove the parent line. All spectra were recorded under otherwise identical acquisition conditions and result from two transients. Complete suppression can be achieved with gradient selection, but at some cost in sensitivity in this case (see text).

Figure 6A8. HMBC spectra recorded under identical conditions but with signal selection through (a) pulsed field gradients and (b) phase cycling alone.

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