Hartmann-Hahn transfer experiments

Polarization can be transferred simultaneously within several spin pairs without cross-talk if different rf amplitudes are used for each pair of spins in the multiply selective irradiation scheme. This principle has been used in Hartmann-Hahn Hadamard spectroscopy (HAHAHA), where a phaseencoding scheme is used to separate simultaneously acquired spectra that represent individual doubly selective Hartmann-Hahn transfer experiments (Kupce and Freeman, 1993e). 

Coherent transfer experiments can roughly be divided into two classes pulse-interrupted free-precession experiments and Hartmann-Hahn-type experiments (Ernst et al., 1987). Examples of homo- and heteronuclear pulse-interrupted free-precession coherence transfer are COSY (correlation spectroscopy Aue et al., 1976), RELAY (relayed correlation spectroscopy Wagner, 1983), and INEPT (insensitive nucleus enhancement by polarization transfer) transfer steps (Morris and Freeman, 1979 Burum... 

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). 

Various authors have used different names for Hartmann-Hahn-type experiments that emphasize distinct experimental or theoretical aspects. For example, heteronuclear Hartmann-Hahn transfer in liquids has been called coherence transfer in the rotating frame (Muller and Ernst, 1979), J cross-polarization (JCP Chingas et al., 1981), heteronuclear crosspolarization (Ernst et al., 1991), HEHAHA (heteronuclear Hartmann-Hahn transfer Morris and Gibbs, 1991), and hetero TOCSY (total correlation spectroscopy Brown and Sanctuary, 1991). Homonuclear Hartmann-Hahn transfer has been referred to as TOCSY (Braunschweiler... 

In this article, the basic principles of Hartmann-Hahn transfer in isotropic liquids will be revealed and the most important tricks of the trade will be disclosed. We hope that this will dispel the mystique surrounding Hartmann-Hahn experiments without reducing the fascination with this potent and multifaceted experimental technique. 

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... 

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... 

Hence, in the idealized zero-quantum coupling topologies that are characteristic for most Hartmann-Hahn-type experiments, the magnetization-transfer functions between two single spins 1/2 are independent of the direction of the transfer (Griesinger et al., 1987a). 

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). 

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. 

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... 

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. 

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... 

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 highly selective Hartmann-Hahn transfer between two spins i and j with offsets p, and Vj, Konrat et al. (1991) introduced an attractive alternative to CW irradiation. Their method, named doubly selective HOHAHA, is based on the use of two separate CW rf fields with identical amplitudes pf, which are irradiated at the resonance frequencies p, and Vj of the spins, between which polarization transfer is desired. In the limit I / I I. Vjl this experiment is the exact homonuclear analog of het-eronuclear Hartmann-Hahn transfer (Hartmann and Hahn, 1962), where matched rf fields are irradiated at the resonance frequencies of two different nuclear species (see Section XI). If the necessary hardware for pulse shaping is available, doubly selective homonuclear irradiation can be... 

In principle, this type of band-selective Hartmann-Hahn transfer can be used to restrict coherence transfer to spins with resonances in certain frequency ranges. However, in these experiments the effective coupling constant is reduced by a factor of 1/2, which requires longer mbdng times. However, in broadband homonuclear isotropic-mixing experiments as discussed in Section IV.C.2 coupling constants are scaled by a factor... 

If the coupling constants are known in advance, the total mixing time can be reduced in multiple-step selective coherence-transfer experiments by using the selective homonuclear analog of the optimized heteronuclear two-step Hartmann-Hahn transfer technique proposed by Majumdar and Zuiderweg (1995). In this technique [concatenated cross-polarization (CCP)] a doubly selective transfer step (DCP) is concatenated with a triple selective mking step (TCP). For the case of a linear three-spin system with effective planar coupling tensors, a CCP experiment yields complete polarization transfer between the first and the third spin and the total transfer... 

In heteronuclear triple-resonance experiments (TCP Majumdar and Zuiderweg, 1995), the spin system corresponds to an effective PPP coupling topology if planar effective coupling tensors are created. In an ISQ system, triple-resonance Hartmann-Hahn transfer from a spin / to a spin Q is only efficient if I//5I J,q (Glaser, 1993c Majumdar and... 

Zuiderweg, 1995). In the case of a linear ISQ system, concatenated cross-polarization (CCP Majumdar and Zuiderweg, 1995) is more efficient than two sequential double-resonance (DCP) Hartmann-Hahn transfer steps. The CCP scheme is a combination of a DCP and TCP experiment with optimized mixing times Tj and Tj that depend on the magnitudes of and J Q (Majumdar and Zuiderweg, 1995). 

The first heteronuclear Hartmann-Hahn transfer in the liquid state preceded the homonuclear analogs of the experiment by about two decades. In their seminal paper on nuclear double resonance in the rotating frame, Hartmann and Hahn (1962) focused on heteronuclear polarization transfer in the solid state with the help of two matched CW rf fields with However, in the same paper, Hartmann and Hahn also discussed the coherent heteronuclear transfer of polarization for pairs of /-coupled heteronuclear spins in liquids and reported polarization-transfer experiments between H and P in hypophosphorous acid. Heteronuclear Hartmann-Hahn transfer in liquids with CW irradiation was applied by several groups (Maudsley et al., 1977 Muller and Ernst, 1979 Bertrand et al., 1978a, b Murphy et al., 1979 Chingas et al., 1979a, b, 1981). A detailed analysis of the experiment was presented by Muller and Ernst (1979) and by Chingas et al. (1981). Matched CW irradiation at the... 

Fig. 35. Experimental HCCH-COSY spectra of the fully C-labeled protein rhodniin with two heteronuclear Hartmann-Hahn transfer steps. The spectra were acquired at a spectrometer frequency of 600 MHz employing DIPST2 with = 4.8 kHz (A) and MGS-2 with = 3.78 kHz (B). In the experiments the heteronuclear Hartmann-Hahn mixing periods had a duration of 6 ms. The same plot levels were used for both spectra. (Adapted from Schwendinger et al., 1994, courtesy of Academic Press.)...

Heteronuclear Hartmann-Hahn sequences also effect homonuclear Hartmann-Hahn transfer, resulting in (heteronuclear and homonuclear) total correlation spectroscopy (TOCSY Bearden and Brown, 1989 Zuiderweg, 1990 Brown and Sanctuary, 1991 Ernst et al., 1991). Simultaneous heteronuclear and homonuclear magnetization transfer can be beneficial in relayed transfer experiments (Gibbs and Morris, 1992 Tokles et al., 1992 Majumdar et al., 1993). However, as pointed out by Ernst et al. 

Broadband Hartmann-Hahn sequences, such as DIPSI-2 or WALTZ-16, can be made band-selective by reducing the rf amplitude of the sequences (Brown and Sanctuary, 1991). Richardson et al. (1993) used a low-amplitude WALTZ-17 sequence for band-selective heteronuclear Hartmann-Hahn transfer between N and in order to minimize simultaneous homonuclear Hartmann-Hahn transfer between and The DIPSI-2 sequence was successfully used by Gardner and Coleman (1994) for band-selective Hartmann-Hahn transfer between C d and H spins. So far, no crafted multiple-pulse sequences have been reported that were optimized specifically for band-selective heteronuclear Hartmann-Hahn transfer. Based on the results of Section X, it is expected that such sequences with well defined regions for coherence transfer and effective homonuclear decoupling will result in increased sensitivity of band-selective heteronuclear Hartmann-Hahn experiments. 

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