## Info

1---------1---------1---------1---------1---------1---------1-----------------------------------------------------------1---------1---------1---------1---------1 ppm

42 40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 ^

### Figure 6.19

1---------1---------1---------1---------1---------1---------1-----------------------------------------------------------1---------1---------1---------1---------1 ppm

42 40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 ^

### Figure 6.19

not resolved in the APT spectrum because both lead to negative peaks. In all, there are 13 positive peaks and 14 negative peaks (counting as two the broad peak at 42.3 ppm) in the APT spectrum. This is consistent with the structure of cholesterol, which has 3 quaternary carbons and 11 CH2 carbons (14 negative peaks), and 8 CH carbons and 5 CH3 carbons (13 positive peaks).

You might wonder why anyone would do a simple 13 C spectrum when an APT spectrum gives the same information (chemical shifts and intensities) plus the added distinction of spectral editing (CH and CH3 opposite in phase to Cq and CH2). But the signal-to-noise ratio is 45.0 for the simple 13C spectrum and 16.1 for the APT with the same number of scans (Fig. 6.19); to get the same signal-to-noise ratio for the APT would require 2.5 times as long an acquisition. The reduced sensitivity for APT is the result of T2 relaxation during the long 2/J (13.33 ms) delay of the spin echo.

### 6.8.1 Understanding APT with the Vector Model

APT is a very simple and elegant method to distinguish the number of protons attached to a carbon atom. Recall that in the rotating frame of reference, the net magnetization vector stands still in the x'-y' plane for resonance frequencies exactly at the center of the spectral window ("on resonance"). Off-resonance lines give rise to magnetization vectors that rotate in the X-y' plane at an angular velocity Av, where Av is the frequency offset (in hertz) from the center of the spectral window. Peaks downfield of the center will rotate with a positive angular velocity (counterclockwise from X to /, — X, —yf, etc.) and peaks in the upfield half of the spectral window will rotate in the opposite direction (clockwise). In the APT experiment, 13 C magnetization is rotated into the x-y plane by a 90o 13 C pulse, and then allowed to precess (without 1H decoupling) for a short period of time equal to 1/J, where J is the one-bond 1H-13C coupling constant (~150 Hz). The effect of this precession period is shown in Figure 6.20 for a 13C nucleus with a single 1H attached, assuming that the 13C resonance frequency (center of the doublet) is exactly on-resonance (center of the spectral window). The 90o 13C pulse (on the yf axis) rotates the 13C z magnetization onto the X axis of the rotating frame of reference. The downfield component of the 13 C doublet, which arises from 13 C nuclei attached to 1H nuclei that are in the a state, begins to rotate in the X-y' plane counterclockwise (ccw) toward the y' axis with angular frequency J/2 in hertz. The upfield component of the 13 C doublet, which arises from 13 C attached to 1H nuclei

Figure 6.20

Figure 6.20

that are in the ft state, rotates in the opposite direction (cw) in the X-/ plane toward the —/ axis with angular frequency —J/2 in hertz. After a period of time t equal to 1/(2J), the H = a vector is on the y' axis and the H = ft vector is on the — y' axis; this is the antiphase state. After a period of time t equal to 1/J, both components have rotated exactly 360° x J/2 x 1/J = 180°, meeting at that moment on the —xX axis. If we begin acquisition at this point, the FID will be exactly 180° out of phase from a normal FID acquired without the 1/J time delay and will yield an upside-down doublet in frequency domain (reference axis = +X). If we apply XH decoupling during the acquisition of the FID, the two components (H = a and H = ft) now have the same resonant frequency and we observe a single upside-down peak at the center of the spectral window. A quaternary carbon (on-resonance) has a single magnetization vector that will not budge from the X axis during the whole 1/J delay period and will give a normal spectrum with a positive peak (Fig. 6.21). A 13CH2 group will give a triplet 13C spectrum (Fig. 6.22). With the central peak of the triplet on-resonance, the downfield component of the triplet (with attached XH nuclei Hi = a, H2 = a) rotates

with angular f requency J Hz (ccw) whereas the central peak (attached nuclei aft or fta) will remain on the yf axis (on-resonance) and the upfield component (!H nuclei ftft) will rotate with angular frequency —J Hz (cw). Note that each attached proton in the a state leads to an increase in the resonant frequency of the 13 C nucleus (downfield shift) of J/2 Hz, and each attached proton in the ft state leads to a decrease in resonant frequency (upfield shift) of J/2 Hz. We are assuming that the two protons are equivalent, so the effect of each proton is the same (13C-H1 coupling = 13C-H2 coupling) and they cancel out if one is a and the other is ft. After a period of time t equal to 1/(2J), the two outer peaks (aa vector and ftft vector) will have traveled 180° (J x 1/(2J) = 1/2 cycle) in opposite directions to meet on the — X axis, whereas the inner peak (aft/fta vector) remained stationary on the X axis. After a total delay of 1/J, both off-resonance components will have made a complete rotation (360° and —360°) back to the positive X axis, so that all three components of the triplet will give positive peaks after acquisition and Fourier transform. With 1H decoupling, the 13C triplet will "collapse" into a single on-resonance positive peak. Similar arguments can be used to show that a 13 C quartet (13CH3 group) will end up with all four components on the — X axis after a period of time 1/J (Fig. 6.23). The outer lines aaa (three times J/2 downfield shift) and ftftft (3J/2 upfield shift) rotate 270° (3J/2 x 1/(2J) = 3/4 cycle) in a delay of 1/(2J), with the aaa vector rotating ccw from +X to +yf, — x' and finally to — y'. The ftftft vector rotates cw at the same rate to — yf, — xf and ending at +yf. After another 1/(2J) period, the aaa and ftftft vectors rotate another 3/4 turn: aaa from — yf ccw to X, yf, and — X and ftftft from +y' to +X, — y', and — X. Thus, after a total delay of 1/J, both of the "outer line" vectors are on — X. The "inner line" vectors correspond to the line at +J/2, composed of all 13 C nuclei with two Hs in the a state and one in the ft state (aaft, afta, and ftaa), and the line at —J/2, composed of all 13C nuclei with one H in the a state and two Hs in the ft state (ftfta, ftaft, and aftft). In each case, the two opposing 1H spins cancel out and only the effect of the remaining one is observed, leading to a shift of J/2 Hz from the chemical shift position of 13C. The vector corresponding to the +J/2 line behaves just like the H = a vector in the CH case (Fig. 6.20) and moves to the +yr axis after t = 1/(2J) and to the — X axis after t = 1/J. The vector with frequency —J/2 moves to the — y' axis after t = 1/(2J) and to the — X axis after t = 1/J. Thus, at the end of the 1/J delay all four vectors are on the — X axis, leading to an upside-down quartet in the 13C spectrum. With 1H

decoupling, we have an upside-down (negative absorptive) singlet at the center of the spectral window.

With this simple process, we have encoded information about the number of attached protons into the phase of the 13 C peak. Proton decoupling during the acquisition period will give a spectrum with single peaks for each carbon resonance, pointing either up or down according to the number of attached protons.

Group

Pattern

Angular Frequency in hertz

Rotation in cycles after t = 1/J

Axis Phase

C (quaternary) Singlet

CH Doublet

CH2 Triplet

CH3 Quartet

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