Hartmann-Hahn transfer sequence

As demonstrated by Hartmann and Hahn (1962), energy-matched conditions can be created with the help of rf irradiation that generates matched effective fields (see Section IV). Although Hartmann and Hahn focused on applications in the solid state in their seminal paper, they also reported the first heteronuclear polarization-transfer experiments in the liquid state that were based on matched rf fields. A detailed analysis of heteronuclear Hartmann-Hahn transfer between scalar coupled spins was given by Muller and Ernst (1979) and by Chingas et al. (1981). Homonuclear Hartmann-Hahn transfer in liquids was first demonstrated by Braunschweiler and Ernst (1983). However, Hartmann-Hahn-type polarization-transfer experiments only found widespread application when robust multiple-pulse sequences for homonuclear and heteronuclear Hartmann-Hahn experiments became available (Bax and Davis, 1985b Shaka et al., 1988 Glaser and Drobny, 1990 Brown and Sanctuary, 1991 Ernst et al., 1991 Kadkhodaei et al., 1991) also see Sections X and XI). 

Schleucher et al., 1995b, 1996). This relation has important consequences for the suppression of Hartmann-Hahn transfer in ROESY experiments. The relationship shows that the suppression of Hartmann-Hahn transfer ( A = max ) and the suppression of longitudinal cross relaxation (Ih / I = min ) are in fact conflicting goals. The best a sequence can do is... 

A large number of polarization-transfer experiments already exist that are based on the Hartmann-Hahn principle, and the number of Hartmann-Hahn mixing sequences is still rapidly growing. Therefore, it is important to have classification schemes that allow one to disentangle the plethora of known (and potential) mixing sequences. In the NMR literature, a number of different classification schemes have been used for Hartmann-Hahn experiments. However, the nomenclature of different authors is not always uniform (and in some cases it is even contradictory). In this section, existing classification schemes are reviewed and discussed. This discussion also defines the nomenclature that is used in this review. 

Even in the absence of relaxation, Hartmann-Hahn transfer depends on a large number of parameters pulse sequence parameters (multiple-pulse sequence, irradiation frequency, average rf power, etc.) and spin system parameters (size of the spin system, chemical shifts, /-coupling constants). For most multiple-pulse sequences, these parameters may be destilled into effective coupling tensors, which completely determine the transfer of polarization and coherence in the spin system. This provides a general classification scheme for homo- and heteronuclear Hartmann-Hahn experiments and allows one to characterize the transfer properties of related... 

A number of theoretical transfer functions have been reported for specific experiments. However, analytical expressions were derived only for the simplest Hartmann-Hahn experiments. For heteronuclear Hartmann-Hahn transfer based on two CW spin-lock fields on resonance, Maudsley et al. (1977) derived magnetization-transfer functions for two coupled spins 1/2 for matched and mismatched rf fields [see Eq. (30)]. In IS, I2S, and I S systems, all coherence transfer functions were derived for on-resonance irradiation including mismatched rf fields. More general magnetization-transfer functions for off-resonance irradiation and Hartmann-Hahn mismatch were derived for Ij S systems with N < 6 (Muller and Ernst, 1979 Chingas et al., 1981 Levitt et al., 1986). Analytical expressions of heteronuclear Hartmann-Hahn transfer functions under the average Hamiltonian, created by the WALTZ-16, DIPSI-2, and MLEV-16 sequences (see Section XI), have been presented by Ernst et al. (1991) for on-resonant irradiation with matched rf fields. Numerical simulations of heteronuclear polarization-transfer functions for the WALTZ-16 and WALTZ-17 sequence have also been reported for various frequency offsets (Ernst et al., 1991). 

Hartmann-Hahn transfer functions for specific multiple-pulse sequences have been used to study the effects of offset and experimental errors (Remerowski et al., 1989 Eaton et al., 1990 Listerud et al., 1993). Hartmann-Hahn transfer in ROE experiments was simulated numerically by Bazzo et al. (1990a). 

Independent of the experimental implementation, idealized Hartmann-Hahn transfer functions can be calculated for characteristic zero-quantum coupling topologies (see Section V.B). Except for simple two-spin systems, transfer functions are markedly different for different zero-quantum coupling tensor types (see Fig. 10). This difference results from different commutator sequences that occur in the Magnus expansion of the density operator zero-quantum coupling topologies are shown schematically in Fig. 11. 

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. 

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... 

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. 

With vf = 10 kHz, these sequences create only a small effective field that is on the order of a few hertz in the offset range between 11.5 kHz (MLEV-16) and between 9 kHz (DIPSI-2), respectively. Spins in this range of offsets have approximately matched effective fields Iv Kv,) and efficient Hartmann-Hahn transfer is possible,... 

The most direct assessment of Hartmann-Hahn mixing sequences is based on the efficiency of polarization or coherence transfer. Fortunately, the transfer efficiency between two coupled spins is usually sufficient to characterize the transfer properties in extended coupling networks. Several offset-dependent quality factors have been proposed that are based on magnetization-transfer functions T r) (see Section VI) between two spins i and j with offsets v, and Vj. 

In the case of heteronuclear Hartmann-Hahn experiments, independent, uncorrelated rf-field distributions must be assumed for the different nuclear species if two separate rf coils are used (Ernst et al., 1991 Schwendinger et al., 1994 also see Section XI). Multiple-pulse sequences that are compensated for rf inhomogeneity are also relatively insensitive to a miscalibration of the experimental rf amplitude Quality factors for the sensitivity of Hartmann-Hahn transfer to other imperfections, such as... 

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... 

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... 

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. 

Since the seminal paper of Braunschweiler and Ernst (1983), many experimental mixing schemes have been proposed for broadband homonuclear Hartmann-Hahn transfer. The most important mixing sequences are summarized in alphabetical order in Table 2. The listed names of the sequences are either acronyms that were proposed in the literature or acronyms composed from the initials of the authors who introduced them. For each sequence, the expansion scheme that is applied to the basic (composite) pulse R is indicated. For symmetric composite pulses R that can be decomposed into a composite pulse 5 and its time-reversed variant 5, only S is specified in Table 2 for simplicity and classification. For example, the composite 180° pulse R = 90 180 90 (Levitt and Freeman, 1979), which forms the basis of the MLEV-16 sequence, consists... 

Bax and co-workers demonstrated that a homonuclear Hartmann-Hahn transfer of net magnetization can be obtained by the application of a spin-lock field, using CW irradiation (Bax and Davis, 1985a Davis and Bax, 1985) or by the DB-1 sequence that consists of a series of phase-alternated spin-lock pulses (Davis and Bax, 1985). The homonuclear Hartmann-Hahn effect caused by CW irradiation was discovered when artifacts in ROESY experiments were analyzed (Bax and Davis, 1985a). CW irradiation can be regarded as a homonuclear analog of spin-lock experiments for heteronuclear cross-polarization (Hartmann and Hahn,... 

Vj, effective coherence transfer is possible (Davis and Bax, 1985 Bax et al., 1985). This sequence (DB-1) is the analog of square-wave heteronuclear decoupling (Grutzner and Santini, 1975 Dykstra, 1982). For heteronuclear Hartmann-Hahn experiments, a similar sequence [mismatch-optimized IS transfer (MOIST)] was introduced by Levitt et al. (1986) (see Section XII). In order to allow Hartmann-Hahn transfer of only a single magnetization component, the total duration during which the rf field is applied along the... 

Figure 24A -D shows the offset dependence of the corresponding MLEV-16 and MLEV-17 sequences. The reduction of the active bandwidth, which is induced by the additional pulse, can be limited by reducing the flip angle B of this pulse (Sklenaf and Bax, 1987 Bax, 1988a see Fig. 24B and C). For example, for a MLEV-17 sequence with pf = Pj = 10 kHz and B = 180° (Bax and Davis, 1985b), the effective fields for two spins i and j with offsets p, = 0 kHz and Vj = 3 kHz are mismatched by about 13 Hz [psl(f,) = 303 Hz and Psl(f,) 316 Hz], which significantly reduces the efficiency of Hartmann-Hahn transfer for coupling...

Generalized MLEV-16 sequences that consist of symmetric composite pulses R = l yO x have been investigated by Glaser and Drobny (1990). A systematic variation of the flip angles a and j8 provided a map of this sequence space. This map showed that the composite pulse R = 90° 180° 90° is by no means unique. In fact, in the offset range of +0.4i f, Hartmann-Hahn transfer is much more efficient for R = 90° 240° 90° (Levitt et al., 1983 Fujiwara and Nagayama, 1989). However, for 0° < a 360° and 0° < 13 < 360°, the best transfer properties were found for the GD-1 sequence (Table 2) with R = 260° 80° 260°. 

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). 

For an evaluation of these methods, it is important to analyze the effects of the delays on cross-relaxation and on the efficiency of Hartmann-Hahn transfer. In order to avoid spin diffusion effects, the effective crossrelaxation rate should be averaged to zero on a time scale that is short compared to the inverse cross-relaxation rates. In practice, this implies that the delays must be separated by less than about 10 ms (Bearden et al., 1988). This condition is excellently fulfilled by Methods C and D, and can also be fulfilled by Method B if the delays are introduced after only a few repetitions of the basis sequence. However, in most cases spin diffusion effects cannot be suppressed using Method A. 

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. 

Because every broadband Hartmann-Hahn mixing sequence has only a finite bandwidth, it can, in principle, be turned into a band-selective Hartmann-Hahn mixing sequence by scaling down the rf amplitude of the sequence. Then coherence transfer is restricted to the scaled active bandwidth and coherence transfer to spins that are well outside of this... 

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). 

Based on the correspondence between rf pulses in the usual rotating frame and Hartmann-Hahn transfer in the zero-quantum frame (see Sections II and VIII.C), Mohebbi and Shaka (1991b) introduced an alternative approach for the construction of (band-) selective Hartmann-Hahn transfer. In direct analogy to DANTE sequences (Bodenhausen et al., 1976 Morris and Freeman, 1978) and binomial solvent suppression... 

With this approach, any broadband Hartmann-Hahn mixing sequence can be converted into a sequence that is selective for chemical shift differences. In complete analogy to the selectivity of binomial (Plateau and Gueron, 1982 Sklenaf and Starcuk, 1982 Hore, 1983) or DANTE-type sequences (Bodenhausen et al., 1976 Morris and Freeman, 1978), the selectivity of the corresponding zero-quantum sequences depends on the duration and number of delays A. In Fig. 28B, the two-dimensional offset dependence of the polarization-transfer efficiency is shown for the zero-quantum analog of a 1-2-1 sequence. 

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