Assessment of Multiple-Pulse Sequences

In Section VIII, optimization strategies for the development of Hartmann-Hahn mixing sequences were discussed. These approaches rely on the quantitative assessment of a given sequence with the help of so-called quality factors. The assessment of multiple-pulse sequences is also important for the choice of practical mixing sequences (see Sections X and XI). In this Section, approaches for the assessment of a Hartmann-Hahn mixing sequence are summarized. In addition, scaling 

The most important criteria for experimental Hartmann-Hahn mixing sequences are their coherence-transfer properties, which can be assessed based on the created effective Hamiltonians, propagators, and the evolution of the density operator. Additional criteria reflect the robustness with respect to experimental imperfections and experimental constraints, such as available rf amplitudes and the tolerable average rf power. For some spectrometers, simplicity of the sequence can be an additional criterion. Finally, for applications with short mixing periods, such as one-bond heteronuclear Hartmann-Hahn experiments, the duration Tj, of the basis sequence can be important. 

For a specific spin system with given offsets and coupling constants /, it is always possible to simulate all possible polarization- or coherence-transfer functions under the action of a particular multiple-pulse sequence in the presence of relaxation and experimental imperfections. Multiple-pulse sequences can then be compared based on visual inspection of these transfer functions. However, this approach becomes impractical if the sequence is supposed to effect coherence transfer for a large number of spin systems that consist of different numbers of spins with varying coupling constants and a large range of possible offsets. Fortunately, it is possible to assess most Hartmann-Hahn sequences based on their effects on isolated spins or coupled spin pairs. 

Quality Factors Based on the Effective Hamiltonian 1. Offset Dependence of the Effective Field 

For spins i with offsets v, the effective fields correspond to the linear terms in the effective Hamiltonian [see Eqs. (62)-(65)]. As discussed in Section IV, the effective fields can be approximated by a single function 

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