Bounds on spin dynamics and the design of multiple-pulse NMR experiments

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Abstract
The “universal bound on spin dynamics’’ proposed by So/rensen is examined in detail and shown to be of great assistance in the design of novel multiple-pulse NMR experiments. The efficiency of coherence transfer between all possible states of a spin system, including populations, single-quantum coherences, and multiple-quantum coherences, is investigated. Examples are drawn from coherence transfer processes in quadrupolar coupled spin I=1 and 3/2 nuclei and weakly J coupled systems of two and three spin I=1/2 nuclei. It is found that many of the most commonly used NMR pulse sequences fail to achieve the maximum coherence transfer efficiency when applied to spin I=3/2 or to three spin I=1/2 nuclei. However, it is shown that, with knowledge of the universal bound, novel multiple-pulse NMR experiments that achieve optimal efficiency can be easily derived using computer optimization. The application of the universal bound to two-step coherence transfer experiments presents a number of conceptual difficulties. In particular, examples are presented where the product of the universal bounds on the two individual coherence transfer coefficients is larger than the universal bound on the overall transfer from the initial to the final state. These difficulties are resolved and explained in terms of the presence of a “residue’’ that is created together with the intermediate state. The universal bound is used to examine the conditions under which the effect of this residue can be suppressed and the constraints that this places on the design of optimal multi-step coherence transfer NMR experiments.