Decoupling

For the remainder of this chapter we will be exploring the effects of continuous low-power irradiation of one nucleus on the spectrum of another. Two important phenomena occur as a result of low-power irradiation: decoupling, which reduces or eliminates the J-coupling (splitting) effect on the observed nucleus and the nuclear Overhauser effect (NOE), which enhances the population difference (and hence the signal intensity) of the observed nucleus. Decoupling is accomplished by continuous low-power irradiation during the acquisition of the FID, and the NOE develops during continuous irradiation at even lower power during the relaxation delay.

Decoupling is the process of removing specific kinds of J-coupling interactions in order to simplify a spectrum or to identify which pair of nuclei is involved in the J coupling. In order to understand how decoupling works, we should review what causes J coupling in the first place. As we saw in Section 1.1, a resonance is split into a doublet by a nearby spin-/ nucleus because the tiny magnetic field produced by that nucleus perturbs the Bo field experienced by the nucleus we are observing. If the perturbing nucleus is aligned with the Bo field (a state), we see a shift in the effective field Beff in one sense (increase by our convention), and if the nucleus is aligned against the Bo field (j state) we see a perturbation of Beff in the opposite sense (decrease). These changes in Beff lead to a shift in the Larmor frequency (vo = Y Beff/2n) by J/2 Hz downfield (perturbing nucleus in the a state) or by J/2 Hz upfield (perturbing nucleus in the j state). Because the perturbing nucleus has a 50% chance of being in the a state and a 50% chance of being in the j state (actually something like 50.0001 and 49.9999, respectively), we see a doublet with a 1:1 ratio, centered on the chemical shift position and separated by J Hz. It is important to recognize that the J-coupling effect is transmitted through bonds and not through space. A much larger effect occurs directly through space (with couplings in the order of kHz instead of Hz), but this effect (dipolar or direct coupling) depends on molecular orientation relative to Bo and is averaged exactly to zero by the rapid isotropic reorientation (tumbling) of molecules in solution. This dipolar interaction is important as a mechanism of relaxation in liquid state NMR, but it shows up as a splitting only in solid state NMR.

Figure 4.1

A methine carbon (CH) is split into a wide (1 Jch ~ 150 Hz) doublet, one line representing the population of molecules with 13 C in that position and the attached 1H in the a state and the other line representing the population of molecules with 13 C in that same position and the attached 1H in the ft state. The C is underlined in CH to indicate that we are observing and discussing the C resonance, not the H resonance. The H is included in the discussion only with respect to its effect on the C resonance.

Decoupling is accomplished by irradiating at the frequency of one nucleus (1H) with continuous low-power RF (Figure 4.1). This irradiation causes the 1H nucleus to "flip" from the lower energy (a or aligned) to the higher energy (ft or opposed) state and back again very rapidly. Because the NMR "timescale" or "shutter speed" is relatively slow (in this case on the order of 1/J = 1/150 = 6.67 ms), the other 13C sees only an average magnetic environment, which is not perturbed at all by the presence of the proton's magnetic field. The two components of the 13 C doublet are averaged to a single peak in the center as long as the 1H spins are "flipping" back and forth rapidly enough. If the RF power is not enough to create perfect averaging, the protons will flip back and forth more slowly and we will see a doublet for 13C with a reduced separation or J value. The RF irradiation must go on during the entire process of recording the FID (the acquisition time) in order to eliminate the coupling. If the frequency of the irradiation is not exactly at the resonant frequency of the CH proton, there will still be some decoupling, but it depends on the power of the RF signal and the frequency difference. The larger the frequency difference between the RF signal and the resonant frequency of the proton, the greater the power required to achieve decoupling. Another way of saying that is that a high-power RF signal will decouple a wider range or band of frequencies (chemical shifts) around the frequency of the RF signal. Most of the time this is desirable, but in some cases, where we want to irradiate a specific peak in the 1H spectrum and not any other peaks, higher power is undesirable because it reduces the selectivity of decoupling.

4.4 HETERONUCLEAR DECOUPLING: XH DECOUPLED 13C SPECTRA 4.4.1 Why Decouple?

There are two main reasons to decouple. The first is to identify which pair of nuclei is involved in the J coupling, and the second is to simplify 13 C spectra by removing the

1H-13C couplings. The latter application is so routine that most users forget that these large couplings (J up to 180 Hz) even exist. In fact, without 1H decoupling all13 C spectra would show very wide quartets for CH3 carbons, triplets for CH2 carbons, and doublets for CH carbons. This can be useful information, but for molecules of any size and complexity it leads to a tangled forest of multiplets and a costly reduction in signal-to-noise ratio. 1H decoupling gives 13 C spectra in which there is only one (singlet) peak for each unique carbon in the molecule. For example, the 13C spectrum of phenetole (ethoxybenzene) is shown with 1H decoupling in Figure 4.2 (top). In the aromatic region we see two large peaks (two carbons each, ortho and meta to the ethoxy group), one smaller (para) and the other quite small quaternary peak (ipso, or at the point of attachment of the ethoxy group). In the upfield region of the spectrum we see two peaks (one singly oxygenated sp3 carbon and one carbon without oxygen). In the 13C spectrum without 1H decoupling (Fig. 4.2, bottom), only the ipso aromatic carbon (quaternary) is a singlet. The other aromatic carbons are doublets (CH), and the ethoxy group gives rise to a triplet (CH2) and a quartet (CH3). In Figure 4.3 we see the 13C spectrum of sucrose with and without 1H decoupling. The CH2OH region (60-63 ppm) is particularly crowded with overlapping triplets in the absence of 1H decoupling.

4.4.2 Continuous-Wave Heteronuclear Decoupling

Low-power irradiation at a single frequency tends to excite only a very narrow range of frequencies because a rectangular pulse of duration tp seconds excites a bandwidth of roughly 1/tp Hz. For a typical13 C acquisition time of 1.0 s, irradiation of protons during the entire acquisition period would correspond to an excitation bandwidth of 1.0 Hz (1/1.0 s) in the proton spectrum. A more precise treatment describes the reduction of the "undecoupled" coupling constant Jo to the observed (reduced) coupling constant JR, by a continuous 1H irradiation at decoupler field strength B2 with frequency offset Av away from the frequency of the proton being decoupled (Fig. 4.4):

The left-hand side of the equation can be regarded as the decoupler field strength in units of hertz. This is the same as describing the main magnetic field, Bo, as yHBo/2n in hertz. For

example, you might say "we have a 300 MHz instrument," which means that you have a magnetic field strength Bo that gives a resonance frequency of 300 MHz for protons. To be precise, it means that yHBo/2n is 300 MHz, where yH is the magnetogyric ratio for protons. Likewise, if you say "we have a decoupler field strength of 10 kHz," this means that in the rotating frame of reference the proton magnetization precesses at 10 kHz around the B2

field vector, which is in the X-y' plane. More precisely, it means that YHB2/2n is 10 kHz, where we use the proton magnetogyric ratio yH. We use B2 to refer to the decoupler and B1 for the transmitter, but they represent the same thing: the magnetic field due to the radio frequency signal applied to the probe coil, which is a stationary vector in the X-y' plane when viewed in the rotating frame of reference.

The right-hand side of the equation represents the amount by which the proton frequency is off-resonance (Av) and the factor by which the apparent 13C-1H coupling constant is reduced. For nice, sharp 13C singlets we would like to have the apparent J value, JR, be less than the natural 13C linewidth so that it does not even broaden the singlet carbon peak. The equation makes more sense in rearranged form:

This says that the residual coupling, JR, is larger if the proton resonance is farther away from the decoupler frequency (larger Av) and smaller if we use more decoupler power (larger YHB2/2n). Figure 4.4 shows that peaks near the decoupler frequency in the 1H spectrum (top) have small JR values (1H-13C splittings) in the 13 C spectrum (bottom), and protons that are far away from the decoupler position have wide multiplets in the 13C spectrum for the corresponding 13C directly bound to that 1H. Equation (4.1) can actually be used to calibrate the decoupler field strength B2 by observing the effect of off-resonance decoupling on the observed J value of a 13C multiplet.

4.4.3 Selective Decoupling

Another reason for decoupling is to identify the coupling "partner" of a particular peak in the spectrum. Irradiation of that peak at its exact frequency using low-power (for selectivity) continuous RF during the acquisition time will "collapse" to a singlet any multiplet patterns that result from the protons in the irradiated peak. For example, you might irradiate a 1H multiplet at 4.68 ppm and find that a *H double doublet (J = 12.2, 5.6 Hz) at 3.24 ppm "collapses" to a doublet (J = 12.2 Hz). This means that the multiplet at 4.68 ppm was the source of the 5.6 Hz coupling in the double doublet at 3.24 ppm, the coupling that "disappeared." This is an example of selective homonuclear decoupling: the nucleus we are irradiating is of the same type (XH) as the nucleus we are observing. This selective technique can also be used for heteronuclear couplings, so that irradiating a particular proton resonance results in the collapse of a 13 C multiplet to a sharp singlet in the13 C spectrum. This is called selective heteronuclear decoupling to distinguish it from the broadband nonselective XH decoupling that is normally used during the acquisition of 13 C spectra. As we saw above, not only will we collapse the 13 C multiplet corresponding to the carbon directly bound to the proton we are irradiating (Av = 0), but other 13C multiplets will be narrowed (JR < Jo) depending on the frequency difference (Av) between the irradiated proton and the other 13C multiplet's proton, and on the decoupler field strength. Figure 4.5 shows the 13C spectrum of phenetole with selective continuous-wave irradiation of the methyl protons (bottom) and the methylene protons (center). In the bottom spectrum, with irradiation of the CH3 proton peak at 1.37 ppm, the CH3 carbon peak is a clean singlet, and the CH2 carbon is a distorted triplet with a reduced coupling JR = 109 Hz (vs. Jo = 140). In the middle spectrum, with irradiation of the CH2 proton peak at 3.96 ppm, the CH2 carbon peak is a clean singlet, and the CH3 carbon is a distorted quartet with a reduced coupling JR = 96 Hz (vs. Jo = 131).

Figure 4.5

The aromatic CH 13C peaks in the bottom spectrum are little affected and show nearly the full coupling (148 vs. 160 Hz) because the aromatic CH protons are far from the CH3 protons in the proton spectrum (large Av). Selective heteronuclear decoupling is rarely used because the two-dimensional (2D) HETCOR and related inverse 2D experiments (HMQC, HSQC, and HMBC) give the same information with far less ambiguity (Chapter 11). In fact, selective homonuclear decoupling has all been replaced by 2D-COSY and related variants such as DQF-COSY and COSY-35 (Chapter 9). There are instances, however, where only one or two couplings are ambiguous and a 1D selective decoupling experiment can sort it out quickly.

4.4.4 Broadband Heteronuclear Decoupling

Normally in13 C spectra we want to decouple all of the protons from their attached13 C atoms. This means that we cannot irradiate exactly at the frequency of each proton simultaneously. We need "broadband" decoupling that will "cover" the entire range of 1H chemical shifts, which typically range from 0 ppm to 10 ppm, a width of 3000 Hz on a 300 MHz instrument. Because the decoupler frequency cannot be on-resonance for all of the protons in the sample at the same time, it is usually set in the center of the expected range of 1H frequencies. The problem then becomes how to "cover" the entire range of proton chemical shifts with effective decoupling. If we place the1H decoupler frequency at the center of the1H spectrum, the worst case would be trying to decouple a 1H signal at the upfield or downfield extremes of the 1H chemical shift range, which could be as much as 5 ppm (1500 Hz on a 300 MHz spectrometer) away from the center. According to equation (4.1), reduction of the observed J value from 150 to 1 Hz with Av = 1500 Hz would require a decoupler field strength

(YHB2/2n) of 225 kHz. This is an RF field strength corresponding to a 1.1 ^s 90° pulse because one cycle of rotation of the sample 1H magnetization takes 1/225,000 s or 4.4 ^s. This is ten times the amplitude of a high-power excitation (BO pulse, corresponding to 100 times the power: a power level that cannot be achieved without frying the sample and vaporizing the probe coil and the RF amplifiers!

4.4.5 Composite-Pulse Decoupling: Waltz-16

What we need is a method to achieve "broadband" decoupling of protons over the entire chemical shift range (e.g., 0-10 ppm) of the protons, in a very efficient way that uses the lowest possible yHB2/2n value (i.e., the lowest possible decoupler power). An early solution to this problem was to vary (modulate) the decoupling frequency over a wide range of 1H chemical shifts either by sweeping it back and forth or by random (noise modulated) variation. The currently accepted method to achieve wide decoupling bandwidths at low power levels is to employ repeated pulses of different phase and duration at a single frequency: "composite pulse decoupling." A "composite pulse" is a sandwich of several pulses designed to give an overall rotation that is less dependent on the resonance offset than a single pulse. Later we will see (Chapter 8, Figs. 8.5 and 8.6) that a "sandwich" of 90°x-180°-x-270°x (written as 123 in multiples of 90°, with bold italics indicating a phase of -x) gives efficient inversion (overall 180° pulse) over a wide range of chemical shifts ("broadband inversion"). A rapid-fire sequence of repeating 180o pulses would give good decoupling because the spins are inverted (a ^ f, f ^ a) over and over again very rapidly, averaging the /-coupling effect to zero. By using sandwich pulses in place of simple 180° pulses, the decoupling performance is good over a wide range of chemical shifts around the pulse frequency vr. To eliminate the accumulation of pulse calibration errors, the pulse phase is reversed (from x to -x) at regular intervals in the sequence: using R = 123, we have RRRR for 123123123123. Moving the beginning "1" (90°x) to the end gives 231231231231 or (combining 90° and 270° rotations of the same phase, 31 = 4 and 31 = 4) 2423124231. Repeat this with all phases reversed and you have: 24231 24231 24231 24231. Finally, if we move the ending 1 to the beginning and combine (12 = 3, 12 = 3) we have 342312423 342312423 (Fig. 4.6). This can be represented as R'R', which when repeated with opposite phase (R'R'R'R') gives a "supercycle" called "waltz-16": "waltz" because of the 123 building block and 16 because it contains 16 of the original 123 sandwiches. The 36 pulse block is repeated as many times as necessary to cover the entire time of acquiring the FID (Bruker aq, Varian at). From a hardware perspective, waltz-16 only involves changing the phase of the RF (x or -x) at specific times while keeping the amplitude constant (Fig. 4.6). The only parameters you need to set are the RF amplitude (Varian dpwr, Bruker DP or pl17) and the duration of the 90o pulse at that power level (Varian dmf = 1/t90, Bruker pcpd2).

With this method we can achieve decoupling of the full 1H chemical shift range with a decoupler power level (yHB2/2n) of less than 2500 Hz, or about one tenth of the amplitude (one percent of the power) used for single-pulse excitation of protons (e.g., yB1/2n = 25,000 Hz for a 10 ^s 90° 1H pulse). This decoupling power level corresponds to a 90° 1H pulse width of 1/(4 x 2500 Hz) = 100 ^s, and a reduction in power of 10 log [power ratio] = 10 log [(25,000/2500 Hz)2] = 10 log [(100/10 ^s)2] = 10 log [100] = 20 dB. The decoupler field strength, expressed in units of Hz, is proportional to the B1 amplitude, so the relation dB = 20 log [amplitude ratio] = 20 log [90° pulse width ratio] = 10 log [power ratio] can be applied. As power is the square of amplitude, we can also say that the power

Composite pulse decoupling "Waltz-16"

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Figure 4.6

Figure 4.6

level required for decoupling is 100 times (102) less than that of hard pulses (typically 0.5 watts for decoupling instead of 50 watts for hard pulses).

Figure 4.7 shows a series of 13C spectra of dioxane (four chemically equivalent CH2 groups) with waltz-16 decoupling, setting the proton decoupler frequency 12 ppm downfield of the1H peak of dioxane and then repeating the experiment, each time moving the decoupler 1H frequency upfield by 2 ppm (600 Hz on a Varian Unity-300). We see excellent decoupling over a range of 16 ppm, more than sufficient for "covering" the normal range of 1H chemical shifts. At the edges the peak height falls off drastically as the reduced coupling, JR, begins to show up enough to broaden the singlet line. A lower decoupler power setting would result in a narrower pattern, and higher power a larger range of 1H offsets (Av) that still give good decoupling. We try to minimize decoupler power because at high-power sample, heating will degrade the field homogeneity by setting up a radial temperature gradient in the sample.

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