Inverse Heteronuclear 2d Experiments Hsqc Hmqc And Hmbc

This chapter examines three two-dimensional (2D) experiments that correlate 13 C nuclei with 1H nuclei within a molecule. Unlike the HETCOR experiment, in which 1H magnetization is indirectly detected (f 1) and converted to 13 C magnetization that is directly detected (F2), in these "inverse" experiments the F1 dimension is 13C and the F2 dimension is 1H. They are called "inverse" experiments because historically the 13C-detected experiments were done first and therefore were considered "normal." There are numerous advantages to these experiments over the traditional HETCOR experiment, including increased sensitivity (a 0.5-mg sample is sufficient) and the ability to see long-range (two and three bond) interactions between 13C and 1H. The combination of HSQC and HMBC constitutes the most powerful method available for tracing out the carbon skeleton of an organic compound.

HSQC stands for heteronuclear single quantum correlation, meaning that two different types of nuclei (usually 1H and 13 C) are correlated in a 2D experiment by the evolution and transfer of single-quantum (SQ) coherence, the simple magnetization that can be represented by vectors in the x'-y' plane. HMQC stands for heteronuclear multiple quantum correlation and does the same thing as HSQC except that it uses double-quantum (DQ) and zero-quantum (ZQ) coherence during the evolution (t1) period. These mysterious states involve the DQ (aa ^ PP) and ZQ (ap ^ pa) transitions that cannot be directly observed but evolve in the x'-y' plane during the t1 period and are then converted back to observable (SQ) coherence. HMQC and HSQC are equivalent in the appearance of the spectra and the processing of data. HMBC stands for heteronuclear multiple bond correlation, which is the same thing as HMQC except that the J value selected for coherence transfer is much smaller (10 Hz for HMBC versus 150 Hz for HMQC) so that the two- and three-bond relationships are detected (2'3JCH ~ 10 Hz) and the one-bond relationship is rejected (1JCH ~ 150 Hz).

NMR Spectroscopy Explained: Simplified Theory, Applications and Examples for Organic Chemistry and Structural Biology, by Neil E Jacobsen Copyright © 2007 John Wiley & Sons, Inc.

11.1 INVERSE EXPERIMENTS: JH OBSERVE WITH 13C DECOUPLING

Because heteronuclear NMR started with the observation of 13C and decoupling of XH, this is considered the "normal mode" for the two nuclei. Probes were originally designed with two concentric coils: an inner "observe" coil tuned to the 13C frequency and an outer "decouple" coil tuned to the 1H frequency (Chapter 4, Fig. 4.9). The inner coil was used for 13 C because 13 C is a far less sensitive nucleus to observe, so the coil needs to be as close as possible to the sample. The opposite experiment is called an "inverse" experiment for purely historical reasons: 1H is observed on the inner coil whereas 13C pulses and decoupling are applied to the outer (13C) coil. This arrangement is called an "inverse" probe. The obvious advantage of observing 1H rather than 13 C is sensitivity: Of the three "gammas" (Chapter 1, Section 1.4) that contribute to the amplitude of the NMR signal of a nucleus, two are involved in the observation of the FID: the strength of the nuclear magnet (y) and the rate at which it precesses in the x-y plane (y#o). These together determine the intensity of the FID signal induced in the probe coil. Because yh is four times larger than yC, this means that observation of 1H gives a signal 16 times larger than observation of 13C.

The other gamma comes from the population difference at equilibrium; we saw in Chapter 7 how 13 C can be observed using the population difference of 1H, so this disadvantage can be overcome by coherence transfer. This is the strategy used in the 2D HETCOR experiment (Chapter 9). The low natural abundance of 13C, 1.1%, is also irrelevant here— whether we observe 1H or 13 C in a 2D correlation experiment we are still dependent upon the number of 13C-1H pairs in the sample, and this is limited by the natural abundance of 13 C. In this analysis we have ignored the intensity of the noise; to describe the sensitivity of an NMR experiment we also have to consider the noise amplitude. It turns out that noise amplitude is roughly proportional to the square root of the frequency being detected (vo), so this reduces S/N by a factor of VyBo. So the advantage of inverse detection in a 1H-13C 2D experiment is actually a factor of 8 in signal-to-noise ratio (4 x 4/V4).

Another advantage of 1H observation is that a proton can only be attached to one 13 C. We saw in Chapter 7 the complexities of refocusing of 13 C antiphase coherence: different times are optimal for CH, CH2, and CH3 groups. A proton coupled to 13C will always be a doublet—never a triplet or quartet—and will evolve into antiphase or refocus from antiphase to in-phase in a time of exactly 1/(27).

There is one disadvantage to the observation of 1H. With the observation of 13 C, the 99% of carbon nuclei that are 12C are invisible in the NMR experiment and so they do not interfere in any way. In contrast, when we observe 1H we are trying to see the 1.1% of protons that are associated with 13C in the presence of the 98.9% of protons that are associated with 12C. Both will give a signal in the 1H FID unless we use special techniques to destroy the "12C artifact." In a 1D 1H spectrum, the peaks we normally see are due to the 12C-bound protons, which constitute the vast majority of protons (~99%, neglecting the protons bound to oxygen and nitrogen). The 13C-bound protons appear as tiny "satellites," which are very wide doublets (1JCH ~ 150 Hz or 0.5 ppm on a 300-MHz spectrometer) centered on the 12C-bound proton signal and 0.55% of its peak intensity (Fig. 11.1). In this chapter we will focus on these satellite peaks, around 150 Hz apart, and do our best to destroy the 100 times larger 12C-bound 1H signal in the center.

We saw in Chapter 2 (Fig. 2.18) that the intensities of these two peaks (singlet for 1H-12C and doublet for 1H-13C) are reversed for 13C-labeled compounds: The wide doublet dominates, and the residual 12C shows up as a tiny central singlet. Not only are the protons directly attached to 13 C "split" into doublets, but also those two or three bonds away (13C-CH and

Figure 11.1

13C-C-CH) are split by couplings to 13C similar in magnitude to the homonuclear 2JHH (geminal) and 3JHH (vicinal) couplings (Fig. 11.2). These "long range" (>1 bond) het-eronuclear couplings can be transmitted through oxygen and nitrogen as well as carbon: 13C-O-CH and 13C-N-CH. As long as the coupled proton is not exchanging too rapidly to be observed, it can even be bound to nitrogen or oxygen: 13C-C-OH or 13C-C-NH. The three-bond couplings even show a Karplus dependence (Chapter 2, Fig. 2.11) on dihedral angle very similar to the vicinal3 JHH coupling: Maximum 3 JCH coupling occurs in the anti configuration of 13C-X-Y-1H, with H and C opposite each other. All of these heteronuclear couplings are in addition to the homonuclear J couplings that determine the "multiplicity" of a 1H resonance: double doublet, ddd, dt, and so on. For example, a ddt 1H peak will have identical ddt peaks about 75 Hz upfield and downfield of the central 12C peak, 0.55% of the intensity of the central peak.

Figure 11.3 shows the downfield portion of the 1H spectrum of sucrose (g1 doublet, JHH = 3.8 Hz) with normal vertical scaling and with the vertical scale increased by a factor of 100 to show the 13C satellites. The satellites show the same doublet JHH coupling observed in the 12C-bound proton signal (J = 3.8 Hz), with an additional 169.6 Hz coupling to the 13C nucleus (1JCH). The peak height is roughly half (actually half of 1% because the vertical scale is 100 x) of the central peak because they are part of a doublet with concentration about 1% of the concentration of the 12C species. If you look closely you will see that the center of the 1H-13C double doublet is not exactly the same chemical shift as the center of the 1H-12C doublet. There is a small isotope effect on chemical shift, so we do not expect them to be exactly the same. Figure 11.4 (top) shows the 1H spectrum of

Figure 11.3

glucose labeled with 13C in the C-1 (anomeric) position. Glucose exists as an equilibrium mixture of a and i anomers (Chapter 1, Fig. 1.12) in slow exchange. The a anomer (H-1 equatorial) gives a wide, 170 Hz doublet for the H-1 proton, which is directly bonded to 13C. The smaller doublet coupling (3.8 Hz) is the homonuclear (3/hh) coupling to H-2, which is small because it is a gauche (equatorial-axial) relationship. This is just like the 13C satellites observed for H-g1 of sucrose (Fig. 11.3). The i anomer (H-1 axial) gives a 161 Hz doublet for the H-1 proton, with a homonuclear coupling of 7.7 Hz. This vicinal (H-H) coupling (7.7 Hz) is relatively large because H-1 in the i form has an axial-axial (anti) relationship to H-2. Anomeric protons (protons on doubly oxygenated sp3 carbons) give larger 1/CH couplings (160-170 Hz) than protons on singly oxygenated carbons (140-150 Hz). In addition, in six-membered ring sugars the a anomer tends toward the upper end of this range (~170 Hz) and the i anomer tends toward the lower end (~160 Hz). These one-bond C-H coupling constants can be useful in structure analysis in other ways as well, and we will see how they can be obtained from 2D HSQC (or HMQC) spectra.

11.1.1 Isotope Filtering: Fun With BIRDs

We saw in Chapter 9 how the BIRD building block (Fig. 9.11) can be used as a selective 180° pulse that affects only the 12C-bound protons and has no effect on the 13C-bound protons. We can change the selectivity by changing the phase of the central 180° XH pulse from y to —x (Fig. 11.5). For a 12C-bound proton, there is no net evolution during the two delays, so we can see it as three rotations about the X axis: 90°, —180°, and 90°, adding up to zero. For a 13C-bound proton, if we start with Iz the first 90° pulse rotates to —Iy, and the spin-echo results in /-coupling evolution from —Iy to 2IX Sz and on to Iy, with the central 180° pulse on — x changing this to —Iy. The final 90° pulse rotates —Iy to —Iz, so overall we have an inversion (180° pulse).

We saw in Chapter 8 how a selective 180° pulse can be placed between two gradients of the same sign and duration to give a pulsed field gradient spin echo (PFGSE) that not only selects the desired coherence but also destroys any other coherences. First, we use a hard 90° pulse to create coherence on all spins, and then the first gradient twists the coherence into a helix (Fig. 8.21). The selective 180° pulse reverses the direction of twist in

the helix for the selected spins only, and then the second gradient "untwists" the helix for the selected spins and doubles the twist for all other spins. We can put our selective 180° pulse (BIRD: 13C-bound 1H only) between two gradients and get the same effect: all 12C-bound 1H coherence is "double-twisted" and all 13C-bound 1H coherence is "rescued" by the second gradient (Fig. 11.5). The sequence is repeated to give a double PFGSE (DPFGSE) with a 180° XH pulse in the center to reverse J coupling evolution that happens during the gradients: XH 90°-G1-BIRD-G1-1H 180°-G2-BIRD-G2-FID. This overall sequence is called "G-BIRD." After the first gradient, we have magnetization in the x'-y' plane in all directions, depending on the position along the z axis in the NMR tube. The effect of the BIRD element on the 12C-bound coherence is as follows:

The effect on the 13C-bound proton coherence in the x-y plane is:

I 1H90° I r—180—r _I 1H90° __. Ix ^ Ix ^ Ix ^ Ix

In the case of Ix, the central spin echo (r-180-r) leads to 1JCH evolution for a total time of 1/J, which moves Ix to 2Iy Sz and on to —Ix. The central 180° pulse on 1H must be taken into account, but we consider it as if it happened at the beginning of the evolution, when we have Ix, so it has no effect. Thus, the overall effect of the BIRD element is exactly the same as a 180° pulse on the y' axis for the 13 C-bound protons, and it has no effect on the 12C-bound protons. This will reverse the sense of the coherence helix in the NMR tube for the 13C-bound protons only, allowing the second gradient to "straighten them out" while it further scrambles the 12C-bound protons.

Figure 11.4 (center) shows the result of the G-BIRD sequence on 1-13C glucose with the spin-echo delay (1/(2J)) set to 2.94 ms (i.e., for 1JCH = 170 Hz). The HOD peak is gone, as are all of the glucose peaks that are not due to the H-1 position, the position that is labeled with 13C. We only see the 13C-bound protons. This is an example of isotope filtering, a class of NMR experiments in which only those protons that are bound to 13 C (or 15N) show up in the experiment. Filtering can work either way: We can also set it up to see only the protons not bound to 13 C (or 15N). This is a very powerful and sophisticated tool for biological NMR. For example, an unlabeled small molecule can be bound to a 13C-labeled protein and only those NOE interactions between a 13 C-bound proton and a 12C-bound proton pass through the isotope filter. This allows observing only the interactions between the protein and the ligand, without interference from the intramolecular NOEs.

We can change the delay time of the G-BIRD to "tune" the isotope filter to different 1JCH values. The crucial J-coupling evolution for the time 1/J must give an inversion (180° rotation in the x'-y' plane from in-phase to antiphase and back to in-phase) in order for the coherence to survive the G-BIRD gradients. What happens to 13C-bound 1H coherence if the delay is not exactly tuned to the JCH coupling? We can use product operators to predict the result:

^90° T 1H180-X Ix ^ Ix ^ cos(nJr) + 2IySz sin(nJr) -x Ixcos(n/r) + 2IySz sin(nJr)

13C180°

^ Ix cos2 + 2IySz(2 sin cos) — Ixsin2 -> Ixcos2 + 2IzSz(2sin cos) — Ix sin2

The first term is just like 12C-bound 1H coherence: It has not experienced a 180° pulse, and it will be destroyed by the second gradient. Only the last term will survive because it has experienced the equivalent of a 180°), pulse. In the complete G-BIRD there are two PFGSE elements, so the term becomes sin4(n/r). In the example of Figure 11.4 (center), t was set to 2.94 ms, so the effect on various 1JCH values can be predicted, as well as on long-range 2J and3 J values:

J: 170 160 142 125 250 8

The filter is fairly tolerant of the range of 1JCH values normally encountered (142 is a typical singly oxygenated carbon, 125 is a saturated hydrocarbon environment, 250 is a terminal alkyne, and 8 is the maximum for long-range 2'3JCH couplings). This is the assumption built into all of the heteronuclear coherence transfer experiments, from DEPT to HETCOR to the inverse experiments HSQC and HMQC: that the one-bond CH coupling is around 150 Hz and the range of variation is not that large.

Figure 11.4 (bottom) shows the result of the G-BIRD experiment with the t delay set to 62.5 ms (1/(2J) for J = 8 Hz). We see many signals now in the 12C-bound XH region of the spectrum because many of these have long-range couplings to C-1. We expect a 2JCH coupling from C-1 to H-2 in both forms and a3 JCH coupling from C-1 to H-3 and H-5. The most prominent peak is the ^-glucose H-2 peak at 3.1 ppm (compare the lactose ^-glu-2 peak in Fig. 10.10). We still see the H-1 peaks because these are spinning around in the x'-y' plane many, many times during the long 62.5 ms t delay and where they land is more or less random. For example, H-1 of a-glucose has a J coupling of 170 Hz to C-1 and moves from Ix to 2Iy Sz by J coupling evolution (1/(2J)) in 2.94 ms, so in 62.5 ms it has made 5.3 complete cycles from Ix to 2Iy Sz to —Ix to —2Iy Sz and back to Ix. The term sin4(nJT) is 0.73 for 170 Hz, but it is zero if Jt is an integer; that is, if J is any multiple of 16 Hz (1/t). A JCH value of 128, 144, 160, or 176 Hz would give a null whereas J values of 136, 152, 168, or 184 would give a maximum signal. We will see how this long evolution delay leads to the same effects in the HMBC experiment.

Finally, if we observe XH we will have to consider how to remove the 13 C coupling during the recording of the FID; otherwise, we will have these very wide (150 Hz) doublets centered on the XH chemical shift. 13C decoupling requires more power because of the much larger range of chemicals shifts (~ 200 ppm 13 C on a 600-MHz instrument is 200 x 150 = 30,000 Hz, whereas ~ 10 ppm *H corresponds to 10 x 600 = 6000 Hz) that must be "covered" by a broadband decoupling scheme. In addition, the B\ field strength (or B2 as it is called for decoupling) needs to be four times greater (16 times greater power) to achieve the same rate of rotation (yB2/2n) of the sample's 13C magnetization because y is only one fourth as large for 13 C. These problems have been solved by new, more efficient composite pulse decoupling sequences and by limiting the "duty cycle" (percent time the decoupler is on during the pulse sequence) to avoid heating the sample and overtaxing the amplifiers.

13C decoupling was not a standard feature on spectrometers until the mid-1990s, so many of the inverse experiments (HSQC and HMQC) were done without 13C decoupling, simply living with the wide doublets due to 1JCH. Now this technique is routine on modern spectrometers. Computer optimization of the WALTZ-16 decoupling sequence (Chapter 4, Section 4.4) led to the GARP sequence, which uses seemingly arbitrary pulse widths: 30.5°, 55.2°, 257.8°, 268.3°, 69.3°, 62.2°, 85.0°, 91.8°, 134.5°, 256.1°, 66.4°,45.9°, 25.5°, 72.7°, 119.5°, 138.2°, 258.4°, 64.9°, 70.9°, 77.2°, 98.2°, 133.6°, 255.9°, 65.5°, and 53.4°, with phase alternating x, -x, x, -x, and so on. This sequence of 25 pulses is executed four times with the phases reversed (— x, x, —x, x, etc.) in cycles three and four. The 100-pulse supercycle is repeated throughout the acquisition of the 1H FID. Figure 11.6 (top) shows the results of a 13C decoupling test on the ^-anomeric proton (^-glu-1) of 1-13C-glucose using GARP decoupling at a power level corresponding to yCB2/2n = 5320 Hz (1/(4 x 47 |xs)). The decoupler offset is started at the 13C resonance of C-1 of ^-glucose and then moved 10 ppm farther off-resonance each time the experiment is repeated. This is exactly the reverse of the WALTZ-16 decoupler test (13C observe, 1H decouple) shown in Figure 4.7. Excellent decoupling is obtained for offsets up to 80 ppm on either side of the on-resonance 13 C frequency, representing a bandwidth of 160 ppm. This is adequate to "cover" all protonated carbons (0-150 ppm) except the carbonyl carbon of an aldehyde (~200 ppm). At 90 ppm off-resonance, we see the doublet (3Jhh = 7.7 Hz) split into two doublets due to the 1JCH coupling that is not completely removed. In Chapter 8 (Section 8.10) we briefly touched on the use of a moving spin lock as an efficient broadband method for inversion ("adiabatic inversion") using a shaped pulse. The frequency of the spin lock is "swept" from far upfield to far downfield, which has the effect of starting the spin-lock axis on the +z axis and slowly (i.e., on a timescale of ms) tilting it down to the x!-y' plane and on down to the — z axis, maintaining the sample magnetization spin

H-l of p -1-13C- glucose 'H = 600 MHz 13C decoupling test

H-l of p -1-13C- glucose 'H = 600 MHz 13C decoupling test

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