## Examples Of Jcoupling And Chemical Shift Evolution

Consider the example of a 13C-XH pair with J = 150 Hz and 13 C chemical shift of 51.5 ppm on a Bruker DRX-600 instrument (Fig. 6.13). We know that the 13C Larmor frequency is very close to one fourth of the 1H frequency (600 MHz), so the spectrometer frequency is 150 MHz (yClyH = 1/4) and 1 ppm is 150 MHz x 10-6 = 150 Hz. If the center of the 13 C spectral window is placed at 50 ppm, the rotating frame chemical shift for the doublet (Av) is 225 Hz (1.5 ppm downfield of the center, which is 0 Hz). The H = a line of the 13 C doublet (in the absence of XH decoupling) is at 225 + 75 = 300 Hz in the rotating frame, and the H = j line is at 225 - 75 = 150 Hz. Immediately after a 90° pulse on the y axis, both of the net magnetization vectors are on the x axis. After a delay of 0.8333 ms (833.3 ^s), which corresponds to 1/(8 J), we can calculate the amount of rotation each vector has experienced:

&(H = a) = 360° x 300 Hz x 0.0008333 s = 90°(counterclockwise)

©(H = j) = 360° x 150 Hz x 0.0008333 s = 45°(counterclockwise)

The angle between the two vectors is 45° and the center position (chemical shift position of the doublet) has rotated 67.5° (360° x 225 Hz x 0.0008333 s) to find itself exactly between the two vectors. We will represent this position with a dotted line (Fig. 6.13, t = 1l(8J)). Note that the H = a vector moves faster than the H = j vector because the NMR line that corresponds to it is farther from the center of the spectral window.

Both move counterclockwise, and they diverge from the center line even as the center line itself rotates counterclockwise at a rate of 225 Hz (the "chemical shift" of the doublet). After a total delay of 1.6667 ms (1/(47)), the H = a vector is on the — X axis and the H = 5 vector is on the / axis, with a 90o angle between them. After a total delay of 3.333 ms (the magic 1/(27) value), the H = a vector has rotated 360o back to the X axis and the H = 5 vector has rotated 180o to the — X axis. The pair is now in the antiphase relationship, and the chemical shift position (dotted line) is on the — y' axis, having rotated three fourths of a full rotation in the counterclockwise direction. The chemical shift position is not a magnetization vector, it is just a bookkeeping device to keep track of where the vectors would be if they had not undergone J-coupling evolution (i.e., if they had not diverged from each other during the delay). We can draw what the spectrum would look like at each stage of evolution if we started recording an FID at that moment. Typically, we choose the reference axis to be the one that would give positive absorptive peaks if there were no delay: in this case, the X axis. After a 1/(4J) delay, the H = a line is upside down (its vector is on the — X axis) and the H = 5 line is dispersive (its vector is on the y' axis). After a 1/(27) delay, the H = a peak is positive absorptive and the H = 5 peak is negative absorptive.

6.7.1 Experimental Example: 1H Observe with J-Coupling Evolution Only

The effect of J-coupling evolution can be observed directly using a sample of methyl iodide (CH3I) in CDCl3, which is enriched in 13C to the level of 60% (Fig. 6.14). Now we are looking at the 1H-13C one-bond coupling from the point of view of the three equivalent protons, rather than from the point of view of 13C. In the 1H spectrum, we see a singlet at the center for the 12CH3I peak (placed on-resonance, Av = 0, and representing 40% of peak intensity) and a doublet centered on the same chemical shift for the 13CH3I molecules (60% of the sample, each peak 30% of the total intensity). If we observe 13C, we would see only

the 13CH3I (60%) part of the sample, and the peak would appear as a quartet due to coupling to the three protons, but observing 1H we see a doublet because each of the three equivalent protons is coupled to only one 13C nucleus. If we insert a delay of duration t between the 90° 1H excitation pulse and the start of the FID, we will see /-coupling evolution for the 13CH3I protons but the 12CH3I protons will not evolve. Let us put the 1H 90° pulse on the y axis, so the two vectors representing 1H net magnetization (C = a and C = ft) will both be rotated by the pulse from the +z axis to the +X axis. We choose the +X axis as our reference axis, so the FID with no delay (t = 0, Fig. 6.14(a)) gives positive absorptive peaks for both components, at +//2 (C = a) and —//2 (C = ft) in the spectrum. The net 1H magnetization for 12CH3I is also rotated to the +X axis and gives a positive absorptive peak in the spectrum at the center of the spectral window (Av = 0). If we increase the delay from zero to 1/(4J), the C = a component rotates counterclockwise (toward the y' axis) by an angle rotation = Av x t = 1/(4/) x J/2 = 1/8 cycle = 45°

The C = ft vector rotates clockwise (toward the —y axis) by the same amount. The two vectors have diverged (/-coupling evolution) to an angle of 90° between them but the center position between them has not moved (no chemical shift evolution: the chemical shift is on-resonance). The net magnetization for 12CH3I has not moved because it has a single peak which is on-resonance. We see a positive absorptive peak at the center and the outer peaks show some dispersive character, in opposite directions (Fig. 6.14(b)). Repeating the experiment with a longer delay, t = 1/(2/), the C = a vector has now rotated by 90° and is in the y axis, whereas the C = ft vector has rotated 90° in the opposite direction and is on the — y' axis. As the reference axis is +X, both peaks are completely dispersive, but in the opposite sense. The 12CH3I vector remains on the +X axis and still gives a positive absorptive peak at the center (Fig. 6.14(c)). This is the antiphase state, which we always reach from the in-phase state after /-coupling evolution for a period of time equal to 1/(2/). The two vectors (C = a and C = ft) have diverged to the maximum angle (180°) and are opposite to each other on the y axis. Increasing the delay to 3/(4/), we have a rotation of 135° for each vector, and they have diverged to an angle of 270° between them. The C = a vector is halfway between the +y and — X axes and the C = ft vector is halfway between the — y' and —X axes. In the spectrum, both are nearly upside down, with some dispersive character in the opposite sense (Fig. 6.14(d)). Finally, after a delay of t = 1//, each vector has rotated 180° in opposite directions, meeting each other on the —X axis. The doublet is in-phase on the — X axis, which is opposite to the reference axis (+x/), so the peaks are negative absorptive. The 12CH3I peak is still positive absorptive at the center of the spectrum (Fig. 6.14(e)). The 1// delay has turned the 13CH3I doublet upside down without changing the 12CH3I singlet. We will see that this reversal of sign for a doublet after a 1// delay is the basis of the attached proton test (APT).

The antiphase doublet (Fig. 6.14(c)) is dispersive because /-coupling evolution to the antiphase state moves the vectors by 90°, from the +X axis to the +y' and — y' axes. This dispersive antiphase doublet can be phase corrected by moving the reference axis from the +X axis to the +y' axis (90° zero-order phase correction). Now the C = a peak is positive absorptive and the C = ft peak is negative absorptive (Fig. 6.15) and the central 12CH3I peak is pure dispersive because the vector is on the +X axis and the reference axis is now +y (90° phase error).

Figure 6.15

We usually ignore relaxation during short delays (e.g., 1/(27) is usually milliseconds or tens of milliseconds) and consider it only when relaxation is essential to the experiment (e.g., inversion-recovery or nuclear Overhauser effect (NOE) experiments, typically hundreds of milliseconds or seconds for small molecules). Pulses are very short (tens of microseconds), so we do not usually worry about either evolution or relaxation during pulses. Although pulses may look "fat" in pulse sequence diagrams, they are really much shorter than most delays and their duration is not important in terms of evolution. Pulses lead to rotation of the net magnetization vector around the B1 axis, always in the counterclockwise direction.

### 6.7.2 Summary of Evolution

In the rotating frame of reference, the X and y' axes are rotating at the frequency of the pulse relative to the laboratory frame of reference. If the pulse frequency is not exactly equal to the Larmor frequency ("off-resonance pulse"), then the sample magnetization vector will not be stationary in the X-y' plane after a 90° pulse. The pulse frequency corresponds to the center of the spectral window, so any peak that is not exactly in the center of the spectral window will lead to a magnetization vector that rotates in the X-y1 plane at a rate that is equal to the distance (in hertz) between the peak and the center of the spectral window. A peak in the upfield half of the spectral window will give rise to a magnetization vector that rotates clockwise (negative frequency) in the X-y' plane, and a peak in the downfield half of the spectral window will give rise to a magnetization vector that rotates counterclockwise (positive frequency) in the X-y1 plane. A peak that is on-resonance (exactly at the center of the spectral window) will give rise to a stationary magnetization vector in the X-y1 plane. The motion of the magnetization vector in the rotating frame is called evolution.

220 THE SPIN ECHO AND THE ATTACHED PROTON TEST (APT) 6.8 THE ATTACHED PROTON TEST (APT)

APT is a technique for ^-decoupled 13C spectra, which uses the phase (normal or upside down) of the 13C peaks as a way to encode information about the number of protons attached to a carbon: Cq (quaternary carbon, no protons), CH (methine, one proton), CH2 (methylene, two), or CH3 (methyl, three). These spectra are called "edited" because the phase (positive absorptive or negative absorptive) is modified relative to a normal 13C spectrum in order to encode additional information. APT gives all of the information of a normal carbon spectrum with somewhat reduced sensitivity, and it tells you whether the number of attached protons is odd (CH3 or CH) or even (CH2 or quaternary).

To illustrate the concept, Figure 6.16 shows the expected results of a normal 13 C spectrum and an APT spectrum of 4-hydroxy-3-methyl-2-butanone. The APT spectrum shows all carbons including the quaternary C=O and solvent carbons, and sorts the carbons into categories of CH and CH3 ("up" peaks) and quaternary and CH2 ("down" peaks). Note that sometimes APT spectra are presented "upside down" with CH and CH3 peaks "down" and quaternary and CH2 peaks "up", but the deuterated solvent peak (no attached protons) tells us how to interpret it.

The APT spectrum of sucrose in D2O is shown in Figure 6.17. The quaternary carbon (fructose C2) is upside down, as are the three CH2OH carbons (fructose C1 and C6 and glucose C6). The remaining carbons are all CHOH carbons, with positive absorptive phase. From the chemical shifts we can assign glucose C1 as the most downfield of the CH carbons (anomeric carbon—two oxygens attached) and we can easily distinguish fructose C2 (anomeric and quaternary) from the CH2OH carbons (typical region 60-70 ppm). Figure 6.18 shows the downfield region of the APT spectrum of cholesterol in CDCl3, aligned with the 13C spectrum acquired with the same number of scans for comparison. The CDCl3 solvent peak (1:1:1 "triplet") is upside down at 77.0 ppm (technically, it is a quaternary carbon because it has no attached protons), as is the quaternary olefinic carbon

4-Hydroxv-3- methyl-2- butanoiie

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