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Figure 8.22

spectrometer) from the center. If we put the center of the spectral window on the water peak (4.755 ppm), we see a maximum at 4.755 + 3.833 = 8.588 ppm and at 4.755 - 3.833 = 0.922 ppm. The nulls occur at the water frequency (4.755 ppm) and at twice the optimal offset: 4.755 + 2(3.833) = 12.421 ppm and 4.755 - 2(3.833) = -2.911 ppm. The advantage of Watergate is the flatness of the curve around the optimal frequency (7-11 ppm and — 1 to 3 ppm), where there is little or no loss of signal. The 7-11 ppm region for proteins and peptides corresponds to the amide NH region and most of the aromatic region, and the — 1 to 3 ppm region covers most of the aliphatic side chain resonances. The problem is the Ha proton region, which gets really "slammed" in the process of knocking down the water signal. Compared to presaturation, Watergate cuts a very wide "swath" around the water peak and there is a lot of collateral damage done to the Ha resonances. Generally, for experiments that focus on the amide NH resonances, we use Watergate because it avoids "bleaching" these signals, and for looking at the Ha resonances we use presaturation or prepare a sample in D2O, which removes the amide NH peaks but makes water suppression much easier. We will come back to the unique properties of 90% H2O and other methods to suppress water in Chapter 12.

Figure 8.24

Figure 8.23 shows the Watergate sequence applied to a sample of sucrose in D2O. When the HOD peak is put on-resonance (Fig. 8.23, center) the HOD peak disappears with some loss of intensity for the peaks closest to HOD. When we move the reference frequency to the triplet at 3.99 ppm, we see that nearby peaks such as the doublet at 4.15 ppm are almost completely destroyed, whereas the faraway g1 peak at 5.36 ppm is restored to its original intensity because it is now in the "plateau" region of the Watergate extinction profile (Fig. 8.22). We can map out the extinction profile of Watergate by applying it to a sample of H2O alone and moving the reference frequency in small steps (0.1 ppm), repeating the experiment and plotting the spectra side by side. Figure 8.24 shows the results using a t delay of 240 |xs. The two additional nulls occur close to the calculated null points of 11.70 and -2.19 ppm (1/t = 4166.7 Hz = 6.94 ppm), and we see the wide swath cut out around the water resonance (3.4-6.2 ppm). We have a relatively flat response from 6 to 10 ppm, which includes the majority of amide NH protons and aromatic protons.

8.7 COHERENCE ORDER: USING GRADIENTS TO SELECT A COHERENCE PATHWAY

How sensitive is a particular spin state to being twisted by a pulsed field gradient? For example, Iz is completely unaffected by a PFG because it has no coherence. Without magnetization in the x'-y' plane, there is no precession and the gradient has nothing to "twist." The same goes for 2Iz Sz, as neither Iz nor Sz is affected by a gradient. In fact, this is a common strategy for "cleaning up" coherence transfer by INEPT: The INEPT

Gradient-enhanced INEPT

Gradient-enhanced INEPT

Figure 8.25

transfer is separated into two parts with 2Iz Sz as an intermediate state and between the two pulses a gradient is applied to "scramble" any magnetization that is in the x'-y' plane (Fig. 8.25):

Any coherences that did not make it to the 2Iz Sz state will be killed by the gradient.

We know that Iy is twisted by a gradient. How much is Sy(I = 1H, S = 13C) twisted? The change in Larmor frequency during the gradient is vg = yzGz/2n, and the amount of "twist" or phase change at any given level of the gradient is determined by vg times the duration of the gradient, t . So the twist resulting from a given gradient strength and duration is proportional to y, the strength of the nuclear magnet. We know that y H is about four times as large as yC, so we can say that 1H single-quantum coherence (SQC) is about four times more sensitive to twisting by a gradient than 13C SQC. We could exploit this difference in sensitivity to gradients in an INEPT experiment by using a gradient to "twist" the 1H SQC spin state 2Iy Sz before the coherence transfer, and then using a gradient of opposite sign and four times the magnitude to "untwist" the 13C SQC (2SxIz) after the coherence transfer (Fig. 8.26). This "gradient selection" would destroy any coherence that is not 1H SQC before the transfer and 13C SQC after the transfer! We can have an amazingly "clean" INEPT transfer using gradients to enforce the pathway 1H SQC ^ 13C SQC. Twisting of antiphase coherences is just like chemical shift evolution (Fig. 7.8): The double arrow pointing in opposite directions in the x'-y' plane just rotates as a unit, without changing the 180° angle between them. For example, 2Iy Sz is twisted by a gradient of intensity Gz and duration tg into 2IySz cos(yHzGztg) - 2IxSz sin(yHzGztg), ignoring the chemical shift evolution that would occur during t if the I (proton) peak is not on-resonance. Just like with chemical shift evolution, the Sz part is not affected because it is on the z axis.

In general, the sensitivity to twisting of a particular spin state can be classified by something called its coherence order. Thus an ordinary magnetization vector in the x'-y' plane has coherence order of 1 (single-quantum coherence, p = 1) and a magnetization vector along the z axis has coherence order zero (p = 0). Only the coherence order of 1

Figure 8.26

can be observed during the FID. There is also double-quantum coherence, which corresponds to a transition in a /-coupled system of two spins (e.g., Ha and Hb), where both spins flip together in the same direction: aa to pp (H^H£ to Ha Hp) or pp to aa. This coherence for the homonuclear (two protons) system has a coherence order of 2 (p = 2). Zero-quantum coherence results from a transition where both spins flip together but in opposite directions (e.g., ap to Pa or Pa to aP). Like magnetization along the z axis, it has a coherence order of zero (p = 0) for a homonuclear system. It turns out that the "twisting" effect of a gradient pulse depends precisely on the coherence order. For example, during a gradient a double-quantum coherence (p = 2) rotates twice as fast in the x'-y' plane as a single-quantum coherence (p = 1) and will acquire twice as many "turns" of twist during the gradient. We saw in Chapter 7 that DQC precesses in the x'-y' plane at a rate equal to the sum of the two offsets (QI + QS); this applies equally to twisting in a gradient—the twist is equal to the sum of the twists that would result for each of the nuclei alone. For z-magnetization and homonuclear zero-quantum coherence (both p = 0), the gradient has no effect.

In heteronuclear experiments, we need to consider that different types of nuclei have different "magnet strengths" or magnetogyric ratios y. For example, the magnetogyric ratio of proton (1H) is about four times as large as the magnetogyric ratio of carbon (13C). This means that in a gradient the proton magnetization rotates (and accumulates a helix twist in the x-y plane) four times faster than the carbon magnetization under the influence of the same gradient. This is extremely useful when we want to select only proton or only carbon coherence (SQC) at a particular point in a pulse sequence. We can put all of this together by including the magnetogyric ratio as part of the coherence order. Thus, for single-quantum coherence we can use p = 1 for 13C and p = 4 for 1H. For heteronuclear double-quantum coherence (1H, 13C pair), we have p = 5 (pH + pC) and for zero-quantum coherence we have p = 3 (pH — pC). This means that in addition to z magnetization (p = 0), there are four separate things we can select with a gradient pulse.

A simple way to view a pulsed field gradient experiment is to add up the "twist" acquired by the sample magnetization in each gradient pulse and make sure they add up to zero for the desired pathway. If the "twist" is not zero at the beginning of acquisition of the FID, there will be no observable signal. For example, in the INEPT experiment (Fig. 8.26)

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