Coherence Pathway Selection In Nmr Experiments

An NMR experiment (pulse sequence) consists of a precisely defined series of radio frequency pulses and delays. Pulses create coherence from z magnetization or convert one coherence into another. They usually lead to multiple changes in coherence order (p), so that after a number of pulses there can be a bewildering array of different coherences. Delays cause coherences to undergo evolution, resulting from either chemical shift differences or J couplings. During a delay, a single coherence can lead to as many as four different components depending upon whether chemical-shift evolution, J-coupling evolution, both or neither has occurred during the delay. Delays can also lead to relaxation (T1 and T2) and cross relaxation (NOE). Of the myriad coherences present at the end of the pulse sequence (beginning of the FID), we are only interested in one. This coherence gives us the information we want from the experiment: specific relationships between spins that we have selected with the pulse sequence. All other coherences are artifacts: They will lead to false crosspeaks, ugly streaks that interfere with the desired information, or phase distortions in the desired peaks. The desired coherence follows a specific pathway throughout the pulse sequence, defined by the coherence order (p) at each stage of the experiment. In general, delays conserve the coherence order, whereas 180° pulses change its sign and 90° pulses cause coherences to split into several different coherence orders. To select the desired coherence pathway and to eliminate the many artifacts resulting from alternative pathways, we use coherence pathway selection.

Two methods are available for coherence pathway selection: phase cycling and pulsed field gradients. We can also use both methods working together to get even better suppression of artifacts. Phase cycling focuses on the effect of pulses on the coherence order. By changing the phase of the RF pulse, which corresponds to the orientation of the B1 field vector in the x'-y' plane in the rotating frame of reference, we can cause the desired coherence in the FID to add together in the sum-to-memory with each successive transient or scan. The undesired signals (artifacts) can be made to cancel in the sum-to-memory with a series of scans. Gradients operate in a different way: the "twist" (position-dependent phase shift) that a gradient pulse gives to a coherence depends on its coherence order (p). A series of gradient pulses placed at strategic places within the pulse sequence leads to a combined "twist" that depends on the coherence order at each stage of the pulse sequence. If the gradient strength is properly adjusted for each gradient in the sequence, only the desired coherence can arrive at the beginning of the FID with no "twist." All other coherences (the artifacts) will be "twisted" and therefore not contribute to the FID.

Figure 10.29

10.6.1 The Coherence Level Diagram

Below the pulse sequence we can show the desired coherence level, p, at each stage of the pulse sequence. This diagram defines the coherence pathway that is desired for a particular NMR experiment. Coherence order is mixed for Cartesian product operators

Ix, Iy p = ±1; {DQ}x, {DQ}y p = ±2 (homonuclear) but it is pure for the spherical (raising and lowering) operators

The Cartesian operators have mixed coherence order because they are linear combinations of the spherical operators

Using spherical operators we can see that a 90o pulse can "explode" the coherence order into several different levels. For example, a 90X pulse converts the pure coherence level p = +1 into three different coherences, at coherence levels of +1,0, and —1 (Fig. 10.29). After several pulses and delays there can be a very large number of coherences, each of which has traveled a different coherence order pathway through the experiment. The ideal coherence pathway selection will choose only one of the coherence levels after each pulse, thus defining the events of the experiment clearly and producing a clearly interpretable result in the FID. After all, the purpose of every NMR experiment is to make the spins "dance" in a particular way that reveals to us clearly their relationships and interactions: J couplings, distances, and so on. As this information can be very complex and overlapping, it is very important to select only certain pieces of information in each experiment to make the data interpretation simple. Coherence pathway selection is the editing process by which we get clean and simple results. The coherence pathway diagram summarizes the sequence of events we are interested in for the spins according to the information we want. The task of coherence pathway selection, whether by phase cycling or by gradients, is to select this desired pathway and to block all other coherence pathways.

10.6.2 Coherence Order Pathway Selection by Phase Cycling

There is a key observation that makes coherence pathway selection possible by phase cycling. Starting with a pure I+ (p = 1) coherence, consider the effect of changing the phase of a 90° pulse on the phases of the resulting coherences:

Ap : 0 - 2 -1

I+

90° -

11+ 2 I

+ 21-

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