Instead of using a simple 180° shaped pulse for inversion of the selected resonance, we will use a double PFGSE to excite the selected spins and "destroy" the others. The pulse sequence is as follows (Fig. 8.27): A nonselective 90° pulse rotates all of the sample magnetization onto the —y axis. Then a gradient "twists" the magnetization into a helix. The selective (shaped) 180° pulse is applied to invert the magnetization of the peak of interest, so that its "twist" is now in the reverse direction. A second gradient of equal intensity and duration to the first now unwinds the twist for the peak of interest. But all the other peaks in the spectrum are just twisted twice as far, as their magnetization helix was not reversed by the selective 180° pulse. This destroys this magnetization and leaves only one thing in the sample: the peak of interest with its magnetization aligned along the y axis. A second nonselective 90° pulse is now applied to rotate this magnetization from the y axis to the — z axis. Thus, we have accomplished two things: the peak of interest has been inverted (population inversion) and the rest of the peaks have been destroyed. During the mixing time, the perturbation of populations for the selected resonance (inverted at the start of mixing) propagates to nearby nuclei and perturbs their populations (enhancement of z magnetization, Mz > 0). Finally, a 90° pulse rotates this transferred magnetization into the x-y plane where it precesses and is recorded as an FID. Any signal other than the selected one is an NOE.

8.9.6 Transient NOE of Fumarate-Cyclopentadiene Adduct

Figure 8.33 shows the *H spectrum and a series of transient NOE spectra for a rigid bicy-clo[2.2.1] system formed in a Diels-Alder reaction of dimethyl fumarate and cyclopenta-diene. Assignment of the 1H spectrum depends primarily on through-space (NOE) interactions. The molecule is chiral (racemic) and has no symmetry elements, so all the protons are unique. In this discussion, we will refer to positions in the structure by number and to peaks in the spectrum by letters. In the 1H spectrum (Fig. 8.33, top), we can immediately assign the olefinic protons (H6 and H7) to the two downfield resonances at 6.03 (Hi) and 6.24 ppm (Hj) from their chemical shifts, but we do not yet know which is which. The two three-proton singlets at 3.62 (Hg) and 3.68 (Hh) can be assigned to the two methyl groups H10 and H11. The most upfield signals are due to the protons farthest away from the olefin and ester functional groups: Ha and Hb form an AB system (with one additional small coupling to Ha), corresponding to the geminal pair of protons on C2. By chemical shift arguments, we can tentatively assign the upfield peak Ha to the proton lying directly above the olefin (H2o): The area above and below the olefin is shielded by the "ring current" of the loosely attached n electrons of the double bond. The remaining four peaks, Hc-Hf, are intermediate in chemical shift and will have to be assigned by looking at J couplings and NOEs.

Although this is strictly an NOE experiment, we see strong J-coupling artifacts. Selection of Hj, for example, gives a strong antiphase peak at the Hi resonance due to the vicinal H6-H7 coupling in the olefin functional group. This "zero-quantum" artifact comes from

3.6 3.4 3.2 3.0 2.8 Figure 8.33

coherence transfer via the intermediate ZQC state:

90o J eV0l 90o 90o

Iz - Ix -vo • 2Iy Sz - 2Iy Sy (DQ/ZQ) - 2SyIz where I represents the selected proton and S is a proton J-coupled to I. A gradient can be used during the mixing time to kill the DQC portion (coherence order p = 2) of 2Iy Sy, but the ZQC part (p = 0) is insensitive to gradients and contributes to the final antiphase state. These ZQ artifacts are common in 2D NOE ("NOESY") experiments as well. Because INEPT transfer is very efficient and NOE transfer occurs only to the extent of a few percent, these J-coupling artifacts appear very strong next to the NOE peaks (in Fig. 8.33 they are cut off to avoid messing up the stack of spectra).

Looking at the right-hand side of Figure 8.33, we see that selection of either Hd or He gives equally strong NOEs to Ha and Hb, the geminal pair at C2. This identifies Hd and He as the bridgehead positions H1 and H3. In contrast, selection of Hf gives an NOE to Hb only and selection of Hc does not give an NOE to either Ha or Hb. Looking at the structure, we see that the C2 proton that points toward the ester side (H2e) is close to H5 ("up") and farther from H4 ("down"). Thus, we can assign Hf as the H5 proton that points "up", toward H2e (Hb), and Hc as the H4 proton that points "down", away from H2e. Remember that Ha was assigned by chemical shift arguments to the C2 proton (H2o) that lies over the olefin and away from H4 and H5.

Although both Hd and He are close to the bridgehead protons Ha and Hb, how can we tell which one corresponds to H1 and which to H3 in the structure (Fig. 8.33, upper left)? Note that selection of He gives a strong ZQ artifact (antiphase peak) at Hf, and the reverse is also true. This places He in a vicinal relationship to Hf, so we can assign it to H1. The other bridgehead proton, Hd, can then be assigned to H3. It is interesting that no such coupling is observed between Hd and Hc (no antiphase peak at Hd when Hc is selected, nor vice versa).

Instead, we see a strong mutual NOE. Apparently, the H3-C3-C4-H4 dihedral angle is very near the minimum in the Karplus curve (90o angle) so that the vicinal coupling constant is very small.

Now we can assign the olefinic pair Hi and Hj and the methyl singlets Hg and Hh. The bridgehead proton H3 (Hd) shows a strong NOE to Hj and not to Hi, so we can assign Hj to the olefinic proton H7, next to H3. The other bridgehead proton H1 (He) gives a strong NOE to Hi but not to Hj. Selection of Hj gives NOEs to Hd (H3) and Hc (H4) on the same side of the molecule as H7, as well as to Ha (H2o). Likewise, Hc (H4) "talks" to Hj (H7), Hf (H5), and Hd (H3). Finally, weak NOEs can be used to assign the Hg/Hh pair. Selection of Hb (H2e) or Hd (H3) gives a very weak NOE to Hh, but only a subtraction artifact at the Hg chemical shift, and selection of Hh gives a very weak NOE to Hj (not shown). This identifies Hh as H10. Likewise, selection of He (H1) or Hf (H5) "lights up" the Hg singlet and not the Hh singlet, so we can assign Hg to H11. This completes the assignments, which are shown on the structure at the upper right-hand side in Figure 8.33.

In contrast to the NOE evidence, the J couplings are rather confusing. Hf appears as a triplet, coupled to He and Hc, but Hc appears as a broad doublet, with resolved coupling only to Hf. The absence of a vicinal Hc-Hd coupling was already noted above. Although we see mostly NOE to Hi and Hj when selecting Ha (H2o), selection of Hb (H2e) gives ZQ artifacts to both olefinic protons, suggesting a long-range J coupling ("W" coupling). Likewise, four-bond "W" couplings can be deduced from ZQ artifacts between Hd and He, Hd and Hi, He and Hj and between Hf and Hi.

8.9.7 NOE Buildup Curve for Sucrose

A study of the NOE intensity as a function of mixing time is called an NOE buildup experiment. The NOE should build up initially at a constant rate (Figs. 8.31 and 8.32) and then level off and eventually decrease to zero as the mixing time is increased. In Chapter 5, we saw the effect of steady-state irradiation of the fructose-1 (CH2OH singlet at 3.62 ppm) resonance of sucrose (Fig. 5.30): strong NOEs are observed to H-g1 (5.36 ppm) and to H-f3 (4.15 ppm). Figure 8.34 shows the NOE buildup curve for selective transient NOE (DPFGSE) of sucrose, selecting the fructose-1 resonance. The upper curve (A) shows the

peak height of the H-g1 peak, and the lower curve (□) shows the peak height of the H-f3 peak as a function of mixing time. The solid curves are simulations of the transient NOE. An accurate measure of the linear buildup rate in the initial phase (proportional to 1/r6) would require a number of data points in the 0-300 ms range of tm. The maximum NOE would be obtained at about 0.7 s mixing for H-g1 and 0.9 s for H-f3. Usually, we set the mixing time of an NOE experiment based on the size of the molecule: longer for smaller molecules and shorter for larger molecules. Because the NOE is a relaxation experiment, the T1 value can give us a rough estimate of the optimal mixing time. The T1 values for sucrose can be estimated from the 1H inversion-recovery experiment (Fig. 5.17), which gives T1 = 120 ms for H-f1, 280 ms for H-g1, and 1.08 s for H-f3. The range of T1 values is very large for these three protons, but the order of magnitude (0.1-1 s) is not far off for setting the mixing time of the transient NOE experiment (Fig. 8.34). As a first guess, use an NOE mixing time of 350 ms for small molecules (200-400 Da), 200 ms for "medium-sized" organic molecules (400-1000 Da), and 100 ms for "large" molecules (1-10 kDa).

8.9.8 A Demonstration of Selectivity: Cholesterol

To show the selectivity of the DPFGSE-NOE experiment, consider the H4ax and H4eq protons of cholesterol (Fig. 8.35). Because C4 is flanked on both sides by downfield-shifting functional groups (C3-OH and C5=C6), the two H4 protons are pulled downfield to 2.2-2.4 ppm, away from the "pack" of overlapped resonances in the 1H spectrum. At 500 MHz, the H4ax and H4eq protons are just barely resolved from each other, with H4eq (downfield) appearing as a "doublet" (plus two small couplings) and H4ax (upfield) appearing as a "triplet" (actually a double doublet plus three small, nearly equal long-range couplings to H6, H7eq, and H7ax). If we focus on the large couplings only, we see that H4eq has only one: the geminal coupling to H4ax. This gives it the "doublet" appearance. H4ax has two large couplings: the geminal coupling back to H4eq and the axial-axial coupling to H3. This gives it the "triplet" appearance. The "doublet" and "triplet" lean strongly toward each other due to their strong coupling (Av in hertz similar in magnitude to J). H4ax is close in space to the angular methyl group (C19) at the A-B ring juncture, and H4eq is close to the H6 olefinic proton in the equatorial plane. So if we could selectively excite mostly H4ax, we would expect a strong NOE (H4ax to H19 = 2.39 A) to the H19 methyl peak (singlet)

Figure 8.36

and a weak NOE (H4ax to H6 = 3.32 A) to the H6 peak. Likewise, selective excitation of mostly H4eq would give a strong NOE to the H6 peak (2.32 A) and a weak NOE to the H19 methyl peak (3.89 A).

These distances come from an X-ray crystal structure of cholesterol hydrate, with hydrogen positions added. Because cholesterol is a rigid molecule with the four rings locked in place by the trans ring junctures, energy minimized model structures also give fairly accurate distances. The distance to H19 is measured to the nearest of the three hydrogens in the C19 methyl group. The NOE intensity will actually be the sum of the NOEs from the three protons of the methyl group, but because of the 1/r6 dependence it will be dominated by the closest proton.

Figure 8.36 shows the results of these two experiments, using a mixing time of 350 ms. In the insets, we see the inverted H4 peaks: in the top spectrum, we have excited mostly the H4eq peaks ("doublet") along with the downfield part of the H4ax peak, and in the bottom spectrum we see mostly the H4ax peaks ("triplet") with some intensity due to the upfield half of the H4eq peak ("doublet"). This is not bad for selectivity considering how close the two chemical shifts are to each other. In the rest of the spectrum we see the NOE peaks, integrated relative to an integral value of -100 for the inverted H4 peak. Selecting H4eq gives NOEs of 2.83% for H6 and 0.27% for H19-Me, whereas selecting H4 ax gives values of 1.38% for H6 and 0.88% for H19-Me (integral values are divided by the number of protons represented by each peak). These numbers are strictly qualitative, but they are consistent with our expectations based on the structure. They also confirm our assignments of H4ax and H4eq, and allow us to assign which of the two CH3 singlet peaks is H19-Me.

8.9.9 Details, Details, Details

The DPFGSE-NOE experiment is a very elegant demonstration of excitation sculpting using the combined power of shaped pulses and gradients. The DPFGSE allows us to destroy all magnetization on the other, nonselected spin, so that any signal that we observe in the spectrum has to derive from NOE transfer from the selected spin. In the NOE difference experiment, our result is the difference of two very similar numbers: 103% minus 100%, for example. In the transient NOE experiment using DPFGSE, we see only the 3%. This is however, only a first approximation and now it is time to face up to the nitty-gritty details.

First of all, although it is true that at the end of the DPFGSE sequence there is no overall net magnetization on the nonselected spins, if we look at the sample in detail, we see that the net magnetization alternates between Iz and —Iz as we move up in the tube (Fig. 8.27, bottom). At this moment they all cancel perfectly, but during the mixing time the —Iz levels begin to recover whereas the Iz levels remain at equilibrium. They no longer cancel and we begin to see net magnetization (Iz) overall for the nonselected spins. So at the end of the mixing time, our 90° "read" pulse will rotate this recovered z magnetization into the x-y plane, producing peaks in the spectrum that have nothing to do with the NOE. Furthermore, although the selected peak is perturbed radically by inversion (Iz ^ —Iz), the nonselected peaks are perturbed half as much on average by inversion for half of the levels. So we would expect the levels that were inverted to generate NOEs to their nearest neighbors, although the unperturbed levels would not generate any NOEs. This would create a whole bunch of signals in the final spectrum, coming from the nonselected spins (one-half as strong) and from the selected spins.

The solution to both problems—recovery of z magnetization of the nonselected spins and NOEs developed from these same spins—is to phase-cycle (—x, x) the 90° pulse at the end of the DPFGSE, the one that flips the selected spin's magnetization down to the —z axis. If we reverse the phase of this pulse, it flips the selected spin's magnetization up, back to +z. There will be no NOE from the selected spin, but the nonselected spins will experience exactly the same perturbations, with the levels that were previously inverted now at equilibrium and the levels that were previously at equilibrium now inverted. Overall, the same artifact signals (recovery and NOE) will be generated from the nonselected spins. If we alternate the phase of this pulse and alternate the receiver phase with it (add, subtract, add, subtract, ...), we are essentially running a control experiment on every other scan and subtracting out any signals that come from nonselected spins, either from recovery or from NOE. The nonselected spins behave the same either way (half are inverted and half are unaffected), so any signals they give directly will subtract out. Thus, the only signals we see will be NOE signals deriving from the selected spin. Are we fibbing then when we say it is not a difference experiment? Technically, yes, but the signals we are subtracting out are of similar magnitude (actually smaller) than the ones we end up with, so the errors of subtraction are negligibly small. There are a lot of details involved in optimizing this experiment, but the results are absolutely stunning in terms of clarity and lack of artifacts. This is important as NOEs are generally weak and can be ambiguous if the experiment is not really clean. Anyone still doing the old steady-state difference NOE experiment is living in the dark ages!

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