Figure 11.38

Figure 11.38

You can probably guess how we can control the evolution during the t\ delay. We start this period with antiphase 13C magnetization, and we want to have 13C chemical-shift evolution during t1 without any /-coupling evolution. The solution is to convert the t1 delay into a spin-echo. We divide the t1 delay period into two delays of t1/2 each, with a 180° 1H pulse in the middle (Fig. 11.37). The /-coupling evolution "sees" the 180° 1H pulse in the middle and turns around (2SyIz — 2 [Sy] [—Iz]), but the 13C chemical shift continues because the Sx and Sy terms are unaffected by the 1H pulse. Now this sequence will do what our original design was supposed to do, even in the real world where peaks are not on-resonance.

One final refinement we might want to add: a refocusing delay of 1/(2/) to allow the antiphase 1H signals to come back together into in-phase signals. This makes all of our crosspeaks positive in the 2D spectrum. This is essential if we plan to use 13C decoupling, because the doublet collapses into a singlet that will have no intensity at all if the doublet is antiphase. Of course, we will need to use the spin echo 1/(2/) delay as we did at the beginning of the sequence (Fig. 11.38). We can call the first 1/(2/) period "defocusing" because the 1H SQC goes from in-phase to antiphase. Then we transfer from 1H SQC to 13C SQC and let the 13C SQC evolve under the influence of the 13C chemical shift. After transferring back to 1H SQC, we "refocus" for a period of 1/(2/) to bring the 1H SQC from antiphase back to in-phase. The arrows at the bottom of the diagram indicate the type of coherence (magnetization in the x'-y' plane) that we have at each stage of the pulse sequence. The pulse sequence uses single-quantum coherence (SQC) throughout, which is why it is called HSQC (heteronuclear single quantum correlation).

11.7.1 Product Operator Analysis of the HSQC Experiment

This is quite simple if we take into account only the type of evolution that is not refocused during each stage of the pulse sequence. Starting with 1H z magnetization:

Preparation: Iz — - Iy — ) 2IXSz y — 2[-Iz][-Sy] = 2SyIz Evolution: 2SyIz -> 2SyIzcos(^ch) -2SXIzsin(^ch)

90y 1H,90x 13C

-2SXIz sin(^ct1) — -2SXIX sin(^ct1) Detection: 2IXSzcos(^ct1) -> Iycos(^ct1) (observed in FID)

In the mixing step the cosine term is transferred back from 13C SQC to XH SQC, but the sine term is converted to a mixture of DQC and ZQC, which is not observable and can be ignored from here on. Refocusing of the cosine term gives in-phase 1H SQC modulated as a function of t1 and the 13 C shift because of the cos(^c t1) multiplier. During the recording of the FID we use 13C decoupling so the 1H SQC remains in-phase and simply rotates in the x-y plane at the rate in the rotating frame.

11.7.2 Cancelation of the 12C-H Signal

As already mentioned, the XH signal from the protons bound to carbon-12 is about 200 times as intense as the 13C-bound proton signals (satellites), so we need a way of removing this artifact. As always we have a choice of phase cycling or gradients (or both!) to remove the undesired signals. Phase cycling is a subtraction method, so the whole mess is recorded in the FID (12C-bound 1H and 13C-bound 1H signals) and by recording multiple FIDs (scans or transients) and subtracting them we remove the 12C-bound 1H signal. Gradients kill the undesired signal by "twisting" its coherence and leaving it twisted during the FID acquisition. The 12C-bound 1H signal never reaches the receiver so it is removed in a single scan.

The phase cycling method works like this: the phase of the second 90° 13C pulse is alternated between x (B1 field aligned along the x! axis) and —x (B1 field aligned along the —x' axis) with each signal-averaged acquisition. Because this pulse is essential for the transfer of magnetization (mixing) from 13C back to 1H, inverting its phase will have the effect of inverting the detected FID signal. In terms of product operators (I = 1H, S = 13C):

If we alternately add and subtract FID signals as the signal averaging progresses, these signals will reinforce and build up as we acquire a number of scans for each t1 value. The 12C-bound proton signal, however, is not affected by the 13 C pulses, and it gives rise to observable signals that do not alternate in sign:

As these signals are alternately added and subtracted into the summed FID, they cancel as long as we are careful to acquire an even number of scans for each t1 increment. This method depends for its success on precise subtraction of a very large signal, so it is sensitive to any instability (temperature change, vibration, variation in pulse widths, etc.) that occurs between one scan and the next.

To use the more formal analysis of phase cycling developed in Section 10.6, we first need to describe the coherence pathway in terms of spherical operators (I+, S—, etc). Starting at the end and working backward and using the convention of positive coherence order during

Figure 11.39

t1 and negative coherence order during t2 (Fig. 11.39), we have I- at the start of the FID (in-phase 1H SQC with p = -4) and I+ S° (= I+ Sz) before the refocusing period (antiphase 1H SQC with p = +4). The change in sign of coherence order is a result of the 1H 180° pulse in the center of the refocusing delay. The mixing step (simultaneous 1H and 13C 90° pulses) converts S+1° to I+S°, so we have S+1° throughout the evolution (t1) delay. The first coherence transfer step converts I+S° to S+1°, and so we start with I- just after the initial 90° pulse.

In the mixing step where we apply the phase cycle (13C SQC ^ 1H SQC), the desired coherence pathway is S+1° ^ I+S°. Considering the 90° 13C pulse, the effect it has on coherence order is Ap = —1 because the 13 C operator goes from S+ (p = 1) to S° (p = 0) as a result of the pulse. So if we alternate the phase of this pulse (AOp = 180°) we will have to alternate the phase of the receiver:

The 12C-bound 1H signal cannot be affected by the 13C 90° pulse, so Ap = 0 regardless of where it is (Iz, Iy, or Ix) when the pulse is executed. AOr = 0 for this signal, and thus it will be canceled if we alternate the receiver phase.

The same phase cycle can be used for the first coherence transfer step (1H ^ 13C) by alternating the phase of the first 90° 13C pulse. For example, we could use x, x, -x, -x (0 0 2 2) for the first 90° 13C pulse and x, -x, x, -x (0 2 0 2) for the second 90° 13C pulse in a four-step phase cycle. The receiver phase must follow the sum of the phase changes of the signal:

Or (1st pulse alone) : x, x, -x, -x (0022) A p = +1 Or(2nd pulse alone) : x, -x, x, -x (0202) A p = -1 Or (both pulses) : x, -x, -x, x (0220)

Of course, the experiment will take four times as long to acquire the same number of FIDs (the same number of t1 values) and this time is wasted if there is enough sample to get the desired signal-to-noise ratio with one scan per FID.

11.7.3 Gradient Coherence Pathway Selection

The disadvantage of using a phase cycle to cancel the 12C-bound 1H signal is that you have to do a minimum of two or four transients for each FID collected in the 2D experiment.

p = 0 -4 4 1 14 -4 I-I"-- I S0- S I0 S+I°-I+S°--1
0 0

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