Multiple-pulse sequence transfer efficiency

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... 

Figure 22 illustrates how relatively simple global quality factors can be used as filters in the search for optimum solutions in the parameter space that defines multiple-pulse sequences. Suppose for typical coupling constants = 10 Hz a multiple-pulse sequence with a constant rf amplitude = 10 kHz is desired that effects efficient Hartmann-Hahn transfer in the offset range of +4 kHz. Here, the simple two-dimensional parameter... 

Only recently, new multiple-pulse sequences that were developed specifically for broadband heteronuclear Hartmann-Hahn experiments in liquids were reported. The SHR-1 sequence developed by Sunitha Bai et al. (1994) consists of a windowless phase-alternated composite pulse R, which is expanded according to the MLEV-8 supercycle. R was optimized based on a phase-distortionless single-spin 180° composite pulse and is related to the composite pulses used in DIPSI-1 (Shaka et al., 1988) and the composite pulses in the homonuclear IICT-1 sequence (Sunitha Bai and Ramachandran, 1993). The bandwidth of the SHR-1 sequence is comparable to the bandwidth of DIPSI-3, albeit with a slightly reduced transfer efficiency (Sunitha Bai et al., 1994 Fig. 33F). 

In practice, HNCO is now carried out by a somewhat more complex pulse sequence than that given in Fig. 12.16 in order to improve its efficiency. Pulsed field gradients are added to aid coherence pathway selection an INEPT transfer from N to K replaces the multiple quantum coherence step and the N evolution is carried out with a constant time experiment. 

In order to assess magnetization transfer in a multiple-spin system, it is necessary to define a measure that reflects the efficiency of the transfer between two spins i and j. This parameter should reflect the amplitude of the ideal polarization transfer as well as the duration of the mixing process, because, in practice, Hartmann-Hahn transfer competes with relaxation. Relaxation effects result in a damping of the ideal polarization-transfer functions 7j . The damping due to relaxation depends not only on the structure and dynamics of the molecule that hosts the spin system of interest, but also on the actual trajectories of polarizations and coherences under a specific multiple-pulse Hartmann-Hahn mixing sequence (see Section IV.D). For specific sample conditions and a specific experiment, the coherence-transfer efficiency can be defined as the maximum of the damped magnetization-transfer function. 

The main difference between approaches that use delays during the basis sequence (Methods C and D) or after completed basis sequences (Methods A and B) is the efficiency of Hartmann-Hahn transfer. In Methods A and B, no Hartmann-Hahn transfer occurs during the compensating delays. If Methods A or B are used, the total mixing time (including the compensating delays) must be increased by 50% compared to a partially compensated multiple-pulse TOCSY sequence with roe/4> in order to obtain the same Hartmann-Hahn transfer. 

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