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Figure 2.20

Figure 2.20

ABC System: Ja Figure 2.21

the center proton being the most downfield (Fig. 2.22). If the center proton (Hb) has the same coupling constant to Ha and Hc (i.e., if Jab = Jbc), it will appear as a triplet, leaning toward the chemical shift positions of Ha and Hc. Ha and Hc will appear as doublets, each leaning toward the Hb triplet. In reality, there is a smaller long-range coupling (4 JHH) between Ha and Hc (the "meta" coupling), and we would see the Ha and Hc patterns further split by the smaller coupling. The distortion of this smaller coupling "points" to the right-hand side in the Hc pattern and to the left-hand side in the Ha pattern. It is important to keep in mind that these patterns can be considerably more complicated, but the "leaning" principle can often be recognized and used to interpret coupling patterns even when they are more complex.

Let's look at the simple AB system in more detail. Consider that the J coupling is held constant and the chemical shift difference Av is gradually reduced (Fig. 2.23). We

Figure 2.23

can do this by simply reducing the Bo field strength, so that the chemical shift difference (which is constant in units of parts per million) is reduced in units of hertz, while the J coupling is constant because it is independent of Bo. When the shift difference is very large (Av » J), we see little or no "leaning" of the two doublets. As the shift difference gets smaller, the inner peaks grow and the outer peaks shrink. Another important point is that the chemical shift position is no longer halfway between the two lines of the doublet: it is now the weighted average of the two line positions, weighted by the peak intensities:

where 81 and 82 are the two line positions and I1 and I2 are the two line heights. You can get the exact line positions from a peak list and the line heights by measuring in millimeters with a ruler. Another way to say this is that as the two chemical shift positions, 8a and 8b, are brought closer together, the outer lines get shorter and farther away from the chemical shift positions and the inner lines get taller and closer to the chemical shift positions. The distance between the two lines of each doublet does not change, however. It is always equal to the coupling constant Jab.

There is a point in this process where the distance between the inner lines is exactly Jab so that the patterns look very much like a quartet, the 1:3:3:1 pattern resulting from a single resonance split by three equivalent protons (Fig. 2.23, Av = 17.32 Hz). In this case Av/J = 1.732 and the ratio of peaks in the AB system is exactly 1:3:3:1, because the outer lines have been reduced by 50% and the inner lines have been increased in intensity by 50%. Some people report this AB pattern as an "AB quartet," but this terminology is misleading and should not be used. The AB system always has two different chemical shifts coming from two distinct proton resonances, unlike a true quartet that comes from a single resonance. There is no way to distinguish a true quartet from an AB system with this coincidental spacing; you have to consider both possibilities and use the context of what you already know about the molecule to decide.

As we continue to reduce the Bo field, moving the 8a position even closer to the 8b position, the two inner lines become very close to each other, but they never meet or cross. The outer lines become so weak that they may appear as tiny bumps, or they may disappear into the noise, depending on the signal-to-noise ratio of the spectrum. At this point of near-equivalence of chemical shifts, the pattern looks very much like a doublet with a small coupling constant, especially if you do not notice the weak outer lines. This can be very confusing if you do not consider the possibility of a "tight AB" (Av < J) system. The separation between the two inner peaks is not a J-coupling at all—it is a complex function of Av and Jab. In the weak coupling limit, this distance is close to Av — J, but in the strong coupling limit, it becomes close to Av because the inner lines are just inside the two chemical shift positions. If you cannot find the outer lines, there is really no way to determine 5a, 5b, and Jab.

Finally, when the two chemical shifts are exactly equal (Av = 0), the two inner lines become one and the two outer lines have zero intensity. The two protons Ha and Hb are chemically equivalent, that is, they have the same chemical shift, and we see no splitting at all. This explains, in a way, why equivalent protons do not split each other: they do split each other but the inner lines coincide and the outer lines have zero intensity. Theoretically, the pattern still has four lines, but we only observe one: a singlet. The same applies to any number of chemically equivalent protons, for example, a methyl group (CH3). All three protons have the same chemical shift, and in the absence of any other coupling (e.g., CH3O or CH3Cq, where Cq is a quaternary carbon), we will see a singlet with area proportional to three.

The distance between the first and second line of the AB system, and between the third and fourth line, is always exactly equal to Jab, even though the chemical shift positions are not exactly in the middle of these pairs. Here are some exact values for the intensities, the error in chemical shift (in hertz) if you just calculate the simple average of line positions for each doublet, and the hertz spacing of the two inner lines:

Av/J /(outer) (%) I(inner) (%) v error/J inner spacing/J

20 95 105 0.01 19.02

For a J coupling of 10 Hz, the Av/J = 1.732 case above (1:3:3:1 ratio) would be observed when Av = 17.32 Hz, which is 0.29 ppm on a 60 MHz instrument, 0.058 ppm on a 300 MHz instrument, and 0.029 ppm on a 600 MHz instrument. Clearly, a much closer similarity of chemical shifts in parts per million is required to see strong coupling on high-field instruments. This is one reason to pay the big money for higher field—to simplify spectra and see mostly first-order splitting patterns. The chemical shift error due to simply averaging the line positions of each doublet of the AB pattern would be 1.3 Hz, which on a 60 MHz instrument is 0.022 ppm (a significant error) and on a 600 MHz instrument it is only 0.002 ppm.

In general, if we define Av' = [J2 + Av2]1/2, then relative to the center of the overall pattern the inner lines are (Av' - J)/2 away and the outer lines are (Av' + J)/2 away, with intensities of 1 + J/Av' (inner) and 1 - J/Av' (outer).

The AB system is a basic building block that can be expanded to a more complex system with additional weak couplings by simply building the splitting diagram (Fig. 2.24). Start with the distorted AB system and then diagram in the additional coupling by moving J/2

Figure 2.24

to one side and J/2 to the other side of each line in the AB system. This is called an ABX system: The X is chosen far away in the alphabet to indicate that its chemical shift is far away (weak coupling) from the Ha and Hb resonances, which are close together relative to Jab. There are two additional coupling constants: Jax and Jbx, and generally they will not be the same. Simply split the A half of the AB pattern with the Jax coupling and split the B half of the pattern with the Jbx coupling. Because it is a weak coupling, the additional splittings result in precise 50:50 intensity ratios, but they retain the distorted intensities of the parent lines. This is an extremely common system; for example, the CH-CH2 fragment in a chiral molecule will lead to an ABX system if it is isolated from any other couplings: CHx-CHaHb. A classic example of this occurs in the amino acid unit of peptides and proteins: in D2O the NH proton exchanges with D from solvent, so we have ND-CH-CH2-X for many of the amino acids: Asp, Asn, Cys, Ser, His, Phe, Trp, and Tyr. These systems are also referred sometimes as AMX systems, implying that the A and M chemical shifts are farther apart than in an ABX system. Because amino acids are chiral, the two protons of the CH2 group are nearly always nonequivalent and the CH (alpha proton) is usually considerably downfield of the pair due to the bond to electronegative nitrogen. If Ha and Hb are geminal protons on a saturated carbon, they will have a large coupling Jab (2-bond coupling 16-18 Hz) and the vicinal couplings Jax and Jbx will likely be smaller: for amino acids, 8-10 Hz for anti, 3-6 Hz for gauche, and 6-7.5 Hz for averaged conformations. The X position (Hx) should appear as a double doublet: 8x split by Jax and then by Jbx. If 8a and db get very close (Avab < Jab), it is possible that new lines will appear in the Hx pattern, making it more complex than a simple double doublet.

Another example that illustrates both the consequences of asymmetry and the use of the AB pattern as a building block is shown in Figure 2.25. The dihydropyridine has a mirror plane perpendicular to the plane of the double bonds, passing through the nitrogen and the CH-CH3 group. This makes the two ethyl groups chemically equivalent, and we can label the methylene (CH2) protons coming out of the paper Ha and the ones pointing back into the paper Hb. But we cannot say that Ha is equivalent to Hb because there is no

Figure 2.25

plane of symmetry in the plane of the double bonds (the plane of the paper)—such a plane would reflect the H into the CH3 at the 4-position of the dihydropyridine ring. This is an interesting case because the molecule as a whole is not chiral, as it possesses a mirror plane perpendicular to the plane of the double bonds. Because there is no mirror plane between the geminal pairs of the CH2 groups, these pairs represent two equivalent AB systems, each with two distinct chemical shifts. This makes sense because Ha is on the side of the CH3 group at C-4 and Hb is on the side of the H atom at C-4: two different chemical environments. We can predict the spectrum by first constructing an AB pattern (Jab = 16 for geminal protons on an sp3 carbon) from the two chemical shift values, 5a and 5b, and then building a 1:3:3:1 quartet (J = 6 Hz) from each line of the AB pattern, to generate the AB part of an ABX3 system. In this case the outer lines are one fourth of the height of the inner lines, so the two outer quartets have intensities 1:3:3:1 whereas the two inner quartets have intensity ratio 4:12:12:4. This is a surprisingly complex pattern for a pair of equivalent ethyl esters, for which we expect a simple quartet (CH2) and triplet (CH3) pattern.

There are many computer programs available for calculating spectra from the chemical shifts and J coupling values. NMR is unique in that all line positions and intensities are easily calculated as long as the NMR parameters-chemical shifts and J values-are known. There are programs that will simulate the spectrum and compare it to a real spectrum, incrementing the NMR parameters in an iterative process until the greatest possible similarity is obtained between calculated and observed spectra. In this way all of the shifts and couplings can be determined even in systems that are too complex to analyze directly by diagraming and measuring peak separations.

2.8.1 Virtual Coupling

A common phenomenon occurs at lower magnetic fields when one nucleus (Ha) is coupled to another (Hm) that is far away from it in chemical shift but coupled to a third spin, Hn, that is very close to Hm in chemical shift:

We say that Hm and Hn are strongly coupled, which will distort the multiplet patterns of these two spins. We expect a simple doublet for Ha (weak coupling to Hm only), but instead

0.95 0.90 Figure 2.26

the Ha resonance is a more complex multiplet, as if it were coupled to Hn as well as to Hm. This is called "virtual coupling" because the Ha nucleus, which has no J coupling to Hn, appears to be coupled to it because of the strong coupling between Hm and Hn. It is like a very tight social group: If you get to know one of them, you end up knowing all of them. A general way of stating this is that any nucleus that is coupled to one member of a strongly coupled group of nuclei will behave as if it is J coupled to all of the members of the group. This phenomenon can lead to some very baffling results if you do not take it into account. Consider, for example, the straight-chain alcohols CH3-(CH2)n- CH2OH (Fig. 2.26). For n-propanol (n = 1), the CH3 resonance (0.94 ppm) is well separated from the neighboring CH2 resonance (1.59 ppm), which in turn is well separated from the CH2OH resonance (3.57 ppm). Both vicinal couplings (Jab ~ 7 Hz, Jbc ~ 7 Hz) can be described as weak couplings because the chemical shift differences are fairly large (vb — va = (1.59 — 0.94) x 250 = 163 Hz; Vc — Vb = (3.57 — 1.59) x 250 = 495 Hz). A nearly perfect triplet (Ha), sextet (Hb), and triplet (Hc) are observed with only slight "leaning." The OH resonance (d) does not show J coupling due to rapid exchange. For n-butanol (n = 2), the CH2 group next to the CH3 is farther from the electronegative oxygen, so it resonates farther upfield (1.38 ppm), closer to the "generic" hydrocarbon CH2 chemical shift of around 1.3 ppm. Still, the chemical shift difference (va — vb = (1.38 — 0.94) x 250 = 110 Hz) is significantly larger than the J value, and we can describe the Ha-Hb coupling as "weak." The next CH2 resonance (Hc), however, is still somewhat distant from the oxygen and resonates at 1.55 ppm. The Hb-Hc coupling (~7 Hz) is not ideally weak because the chemical shift separation is only (1.55 — 1.38) x 250 = 42.5 Hz, so that Av/J = 6. Some distortion of the Hb sextet and the Hc quintet can be seen in the spectrum (Fig. 2.26, right).

The spectrum of n-octanol (n = 6, Figure 2.26, bottom) is dramatically different. The first five CH2 groups after the CH3 group all resonate at nearly the same generic hydrocarbon shift, at 1.32 ppm (peak b). The CH3 peak falls at 0.83 ppm, essentially the generic hydrocarbon value for a methyl group. Only the difference in substitution (CH3 vs. CH2) provides a chemical shift difference between the a and b resonances because the OH group is far away and has no effect. Still, this difference is fairly large relative to

J: Av = (1.32 - 0.83) x 250 = 122.5 Hz = 17.5 J. The CH3 to CH2 coupling is a weak coupling. But the CH3 triplet is broadened and highly distorted, in contrast to the clean, sharp triplets observed for n-propanol and n-butanol. The reason is that the CH3 resonance (C8) is coupled to a CH2 group (C7) that is very strongly coupled to the next CH2 resonance in the chain (C6), leading the CH3 resonance to show "virtual coupling" to the protons on C6. In fact, the protons on C2-C6 (five CH2 groups) all have nearly the same chemical shift (1.32 ppm) and each vicinal relationship has a J coupling of around 7 Hz. This makes the CH2 resonance next to the CH3 group part of an extremely strongly coupled family of 10 protons, and coupling to two of these (the CH2 next to the CH3) is like coupling a little bit to all of them. This explains the very broad components of the CH3 triplet. This phenomenon is seen in all long, straight hydrocarbon chains: a very broad and distorted CH3 resonance around 0.83 ppm and a very tall and broad peak for all of the "hydrocarbon" CH2 protons around 1.3 ppm. Even at higher field (e.g., 600 MHz), the "pack" of CH2 groups is very strongly coupled and the "ugly" CH3 resonance is not improved.

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