Development of Hartmann-Hahn Mixing Sequences

Development of Hartmann-Hahn Mixing Sequences 

Homonuclear or heteronuclear Hartmann-Hahn mixing periods are versatile experimental building blocks that form the basis of a large number of combination experiments (see Section XIII). In practice, the actual multiple-pulse sequence that creates Hartmann-Hahn mixing conditions can usually be treated as a black box with characteristic properties. In this section, design principles and practical approaches for the development of Hartmann-Hahn mixing sequences are discussed. 

Important guidelines for the construction of a multiple-pulse sequence with desired properties are provided by average Hamiltonian theory (see Section IV). The effective Hamiltonian created by the sequence must meet a number of criteria (see Section IX). Most importantly, spins with different resonance frequencies, that is, with different offsets and Vj from a given carrier frequency, must effectively be energy matched in order to allow Hartmann-Hahn transfer. This can be achieved if the derivative of the effective field with respect to offset vanishes, which is identical to the Waugh criterion for efficient heteronuclear decoupling 

In Section IV it was noted that for a given spin system with Hamiltonian and a given multiple-pulse sequence with. f(t), it is always possible to calculate the total propagator U r ), a corresponding effective Hamiltonian and the evolution of the density operator ait) (see Fig. 5). However, because the relationship between t) + [ t) and U(t ) 

This approach for the development of multiple-pulse sequences is only practical if a large number of sequences can be assessed in a short period of time. The final assessment of the quality of a multiple-pulse sequence must always be based on experiments. However, for the optimization of multiple-pulse sequences, experimental approaches are, in general, too slow and too expensive (instrument time ). An attractive alternative to experiments at the spectrometer is formed by numerical simulations, that is, experiments in the computer. In simulations it is also possible to take relaxation and experimental imperfections such as phase errors or rf inhomogeneity into account. In addition to the direct translation of a laboratory experiment into a computer experiment, it is possible to numerically assess the properties of a multiple-pulse sequence on several abstract levels, for example, based on the created effective Hamiltonian. If simple necessary conditions can be defined for a multiple-pulse sequence with the 

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VIII. Development of Hartmann-Hahn Mixing 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... 

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