## Intermediate States In Coherence Transfer

In the INEPT experiment, the final step of coherence transfer is the simultaneous 90o pulses on 13C and 1H:

1H and 13C90o pulses on y'

Again, reversing the roles of 1H and 13C operators requires the additional factor of four because our point of comparison is now 13C equilibrium net magnetization. We do not actually need to do the two 90o pulses simultaneously—we can do them in sequence with a small delay in between. First, let's try doing the 90o pulse on 1H, followed by a short delay and a 90o pulse on 13 C:

1H90o pulse on y'

We can consider the state — 2Iz Sz as an intermediate state in coherence transfer, just as we did in the analysis of populations (SPT) above. Often in INEPT-based experiments, this intermediate state is used as a way of "cleaning up" other coherences that are not desired. A pulsed field gradient (PFG, Chapter 8) is a way of temporarily messing up the shims, and this will destroy any magnetization that is in the x-y plane. The intermediate state — 2Iz Sz is not affected, however, because there is no net magnetization in the x-y plane. After the "spoiler" gradient, we can complete the coherence transfer (with the 13C 90° pulse). The field gradient ("temporary bad shimming") can be regarded as a filter that lets only z magnetization and more complicated spin states involving z magnetization get through.

Something even more interesting happens if we reverse the order of the two 90° pulses, starting with the 13 C 90° pulse:

13C90°pulse ony' 1H90°pulse ony'

Now in the intermediate state 2Ix Sx, we have both operators in the x-y plane. An operator in the x-y plane corresponds to observable coherence, corresponding to a transition between two energy states in which only one spin changes state (a to j or j to a). This is called a single-quantum (SQ) transition. For example, the aHaC i jHaC transition is an SQ transition because only the 1H changes its spin state. The corresponding coherence could be represented as Ix or Iy, for example. But what happens if two of these x-y plane operators are multiplied together? The product corresponds to transitions in which both spins change their spin state: for example, aHaC i jH jC. In this case, because both spins jump up simultaneously from a to j, we call this a double-quantum (DQ) transition. The transition aH jjC i jHaC is called a "zero-quantum" (ZQ) transition because one spin (1H) jumps up and one (13C) falls down, leading to a net change of zero in the total spin quantum number. At this point, all we can say about the product operator 2Ix Sx is that it represents a mixture of double-quantum coherence (DQC) and zero-quantum coherence (ZQC). We can call it "DQC/ZQC" or simply "MQC" for multiple-quantum coherence. This may seem pretty vague, but we will see later that ZQC and DQC can be very precisely defined and they undergo precession (evolution) and respond to RF pulses in completely predictable ways. Unlike 2Iz Sz, we cannot even draw a vector diagram of the spin state 2Ix Sx, so you can see we have finally left the vector model behind completely. Furthermore, if we turn on the ADC and record an FID at this point in the pulse sequence, starting with 2Ix Sx, we will see nothing at all: no FID and no spectrum. Double-quantum and zero-quantum coherences are not observable. From the point of view of quantum mechanics, there is a "selection rule" that states that observable transitions can only have a change in the total spin quantum number of +1 or -1 (1/2 to -1/2 or -1/2 to 1/2). Double-quantum transitions involve a change of +2 or -2, and zero-quantum transitions involve a change of zero. These violate the selection rule and therefore they are not observable in the FID. This "stuff" called DQC/ZQC is looking pretty mysterious: you can't draw a picture of it or see it. Does it really exist? It does because you can change it into observable single-quantum coherence (SQC) by applying an RF pulse:

Not only does this make it observable, but whatever changes might happen to 2Ix Sx during a delay (evolution, due to chemical shifts or J couplings) will change the observable outcome of the RF pulse, so we can infer changes that happen during the invisible MQC state. This is similar to z magnetization, which changes during the recovery period of an inversion-recovery experiment. We cannot observe z magnetization because it does not undergo precession in the magnetic field, but we can convert it into observable magnetization by "flipping" it into the x-y plane with a 90° pulse. What we observe in the FID after the 90° pulse is affected by what happened to the z magnetization (i.e., relaxation) during the recovery delay.

The MQC intermediate state in coherence ("INEPT") transfer can also be used to "clean up" the spectrum. In this case, we can apply a double-quantum filter (using either gradients or a phase cycle) to kill all coherences at the intermediate step that are not DQC. We will see the usefulness of this technique in the DQF (double-quantum filtered) COSY experiment (Chapter 10). As with the "spoiler" gradient applied to the 2Iz Sz intermediate state, a doublequantum filter destroys any unwanted magnetization, leaving only DQC that can then be carried on to observable antiphase magnetization in the second step of INEPT transfer.

In either case, whether we do the 1H 90o pulse first or the 13 C 90o pulse first, we are simply choosing the order of the two processes (Fig. 7.27): the 1H operator (Ix) in the product moves from the x-y plane to the z axis (1H 90o pulse) and the 13 C operator (Sz) in the product moves from the z axis to the x-y plane (13C 90o pulse). We can "bump up" the 1H operator to the z axis first, resulting in both operators on the z axis, and then "knock down" the 13C operator to the x-y plane. Alternatively, we can first "knock down" the 13 C operator from the z axis to the x-y plane, resulting in both operators in the product in the x-y plane (MQC), and then "bump up" the 1H operator from the x-y plane to the z axis.

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