2IZSZ

We can consider the state — 2IZSZ 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 —2IZSZ is not affected, however, because there is no net magnetization in the x-y plane. After... 

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 2IZSZ 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. 

Any coherences that did not make it to the 2IZSZ state will be killed by the gradient. 

For heteronuclear experiments, changing the phase of a pulse will only affect that part of the coherence that is sensitive to the pulse. For example, in the stepwise INEPT with 2IZSZ as in intermediate step in coherence transfer... 

The final two product operators are the longitudinal spin order operator (2IZSZ) and the identity operator (1) ... 

Ix cos2 + 2IySz(2 sin cos) - Ixsin2 -------I cos2 + 2IzSz(2sin cos) - lx sin2... 

A third combination of populations will be needed, which is represented by the operator 2IZSZ... 

Comparing this with Eq. [9] reveals that 2IZSZ represents the difference in population differences across the two I-spin transitions likewise, comparison with Eq. [10] shows that the same operator also represents the difference in population differences across the two S-spin transitions. 

What the Solomon equations predict is, for example, that the rate of change of Iz depends not only on 7Z - 7°, but also on Sz - Sz and 2IZSZ. In other words the way in which the magnetization on the I spin varies with time depends on what is happening to the S spin - the two magnetizations are connected. This phenomena, by which the magnetizations of the two different spins are connected, is called cross relaxation. 

According to the final Solomon equation, the operator 2IZSZ shows self relaxation with a rate constant... 

Iz cos(pJtl) cos(witl) + 2IxSz sin(pJtl) cos(witl) +Ix cos(pJtl) sin(witl) + 2IzSz sin(pJtl) sin(witl)... 

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