Hahn sequence

Fig. 3. The basic Hahn sequence for the measurement of the transverse relaxation time T2. Any precession motion characterized by the frequency v in the rotating frame is refocused. This precession may arise either from chemical shift or from Bq inhomogeneity (symbolized by the shaded area, which has been strongly reduced for visualization purposes owing to the fast decay of the fid, it should in fact extend to the whole circle).

Extending the analysis of the Hahn sequence to the present experiment, we obtain the amplitude of the rath echo ... 

We note that for an evolution whose duration is identical to that of a Hahn sequence, the argument of the exponential relevant to diffusion has been divided by ra. Therefore, the remedy to make negligible translational diffusion effects consists simply of increasing ra, which amounts to bring the 71 pulses closer to each other. 

Fig. 4. The CPMG pulse sequence. An echo is formed halfway between two consecutive K pulses. The echo amplitude (or the Fourier transform of the half-echo) provides an evaluation of T2 less affected by translational diffusion than in the simple Hahn sequence. The phase change of k pulses with respect to the initial Jt/2 pulse cancels the effect of (re) pulse imperfections.

As stated in the introduction of this section, we use Hartmann-Hahn experiment as the generic term for transfer experiments that are based on the Hartmann-Hahn principle, that is, on matched effective fields. Because two vanishing effective fields are also matched, Hartmann-Hahn sequences need not have finite effective fields. Examples of Hartmann-Hahn sequences without effective spin-lock fields are MLEV-16 (Levitt et al, 1982), WALTZ-16 (Shaka et al., 1983b) and DIPSI-2 (Shaka et al., 1988). Note that the term Hartmann-Hahn sequence has also sometimes been used in the literature in a more restricted sense for experiments with matched but nonvanishing effective spin-lock fields (see, for example, Chandrakumar and Subramanian, 1985, and Griesinger and Ernst, 1988). 

Phase-modulated multiple-pulse sequences with constant rf amplitude form a large class of homonuclear and heteronuclear Hartmann-Hahn sequences. WALTZ-16 (Shaka et al., 1983b) and DIPSI-2 (Shaka et al., 1988) are examples of windowless, phase-alternating Hartmann-Hahn sequences (see Table II). 

Homonudear Hartmann-Hahn sequences with delays were developed for clean TOCSY experiments (see Section X.B). Examples are delayed MLEV-17 (Griesinger et al., 1988), delayed DIPSI-2 (Cavanagh and Ranee, 1992), and clean CITY (computer-improved total-correlation spectroscopy Briand and Ernst, 1991). The MGS sequences (Schwendinger et al., 1994) are examples of broadband heteronuclear Hartmann-Hahn mbdng sequences with delays and variable rf amplitudes. 

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. 

Local quality factors such as qfiv, Vj) provide a detailed view of the offset dependence of the efficiency of Hartmann-Hahn transfer. For the optimization of Hartmann-Hahn sequences, the offset-dependent local quality factors must be condensed into a single global quality factor. For example, for a constant rf amplitude, the global quality factor can be defined as the minimum of the local quality factor Vj) in a predefined offset range and (Glaser and... 

In this chapter multiple-pulse sequences for homonudear Hartmann-Hahn transfer are discussed. After a summary of broadband Hartmann-Hahn mixing sequences for total correlation spectroscopy (TOCSY), variants of these experiments that are compensated for crossrelaxation (clean TOCSY) are reviewed. Then, selective and semiselective homonudear Hartmann-Hahn sequences for tailored correlation spectroscopy (TACSY) are discussed. In contrast to TOCSY experiments, where Hartmann-Hahn transfer is allowed between all spins that are part of a coupling network, coherence transfer in TACSY experiments is restricted to selected subsets of spins. Finally, exclusive TACSY (E.TACSY) mixing sequences that not only restrict coherence transfer to a subset of spins, but also leave the polarization state of a second subset of spins untouched, are reviewed. 

In addition to multiple-pulse sequences that were derived from heteronuclear decoupling experiments, a number of rf sequences have been specifically developed for homonuclear Hartmann-Hahn transfer. A systematic search for phase-alternated composite 180° pulses R expanded in an MLEV-16 supercycle was reported by Glaser and Drobny (1990). Several clusters of good sequences were found for the transfer of magnetization in the offset range of 0.Av. However, substantially improved Hartmann-Hahn sequences were found after the condition that restricted R to be an exact composite 180° pulse on-resonance was lifted. For example, the GD-2 sequence is based on R = 290° 390° 290°, which is a composite 190° pulse on-resonance and is one of the best sequences based on composite pulses of the form R = (Glaser and Drobny, 1990). 

Even larger usable bandwidths can be obtained for a given average rf power if clean homonuclear Hartmann-Hahn sequences are optimized from scratch (Briand and Ernst, 1991 Quant, 1992 Kadkhodaei et al., 1993 Mayr et al., 1993), rather than modifying existing uncompensated TOCSY sequences. The clean CITY sequence (see Fig. 26C, Table 3), which was developed by Briand and Ernst (1991), is still one of the most efficient broadband Hartmann-Hahn sequences with cross-relaxation compensation. The sequence is constructed using Method C and is based on the computer-optimized symmetric composite pulse R = SS with S = 48° 138° (see Fig. 22F, sequence 5g). The TOWNY (TOCSY without... 

In general, a given pulse sequence can act as a TOCSY or as a TACSY mixing sequence, depending on the rf amplitude, the irradiation frequency, and the spin system to which is it applied. Therefore, it is important to consider the offset dependence of the coherence-transfer efficiency of a Hartmann-Hahn sequence. In this respect, a rough distinction between highly selective and band-selective Hartmann-Hahn experiments is useful. 

Both limitations can be avoided if tailor-made multiple-pulse sequences are used for band-selective Hartmann-Hahn transfer. The so-called tailored TOCSY sequences TT-1 and TT-2 (see Table 4) were the first crafted band-selective Hartmann-Hahn sequences to be reported in the literature (Glaser and Drobny, 1989). Both phase-alternated sequences do not use any supercycling scheme. The TT-1 sequence with vf = 10 kHz was developed for band-selective coherence transfer between the offset ranges R- (-2.5 kHz < < —1.5 kHz) and Rj (1.5 kHz < Vj < 2.5 kHz). 

Doubly Band-Selective Hartmann-Hahn Sequences... 

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