Hartmann-Hahn polarization transfer

Historically, Hartmann-Hahn polarization transfer was first applied to systems in the solid state (Slichter, 1978 Ernst et al., 1987), even though, in their seminal paper, Hartmann and Hahn (1962) reported applications to liquid samples. In general, Hartmann-Hahn experiments in the solid and liquid states differ with regard to the coupling mechanism (dipolar or indirect electron-mediated J coupling), the magnitude of the coupling... 

Isotropic mixing [29] known also as Hartmann-Hahn polarization transfer [30,31] is a unique and very efficient method of coherence transfer between spins. Non-selective isotropic mixing is widely used in different types of correlation experiments. Selective Hartmann-Hahn transfer has been introduced quite recently [32-37] and provides the means for multiplet-selective [33-37] or band-selective [32] correlation experiments. 

Fig. 11.3 Schematic pulse sequence of Hartmann-Hahn cross polarization to transfer polarization from the / spins to the S spins by matching the rf-field amplitudes such that the condition co ( = coiS is fulfilled.

Hartmann-Hahn cross polarization between two low-y nuclei has been successfully used to record chemical-shift correlation spectra between 13C and 15 N nuclei. Cross polarization between two low-y nuclei suffers from a high sensitivity to the exact matching condition at one of the side bands of the Hartmann-Hahn condition [101]. Adiabatic methods (APHH-CP) can eliminate most of this sensitivity and lead to high transfer efficiencies [34, 62, 90]. 

These intermolecular correlation peaks mean that intermolecular cross polarization (CP) occurs between the carbon and proton of intermolecular -interacting polypeptides in blend. There may be two pathways for the observed intermolecular CP. One is that a direct transfer from proton to carbon exists, and another is that a change in the magnetization by spin diffusion (homonuclear Hartmann Hahn transfer) exists. It is thought that the former is much more efficient than the latter because the former comes from only one magnetization transfer process, but the latter comes from two... 

Switching on the 13C RF transmitter is represented by opening the valve between the reservoirs H and 13C. The relative powers of the proton and 13C RF transmitters are adjusted to maximize interactions between the two types of precessing nuclei. Polarization can then be transferred between neighboring nuclei through spin flip-flop processes. Optimization is achieved when the Hartmann-Hahn condition is met, i.e., the H and 13C RF field strengths are in a ratio set close to 1 4 (Pines et al. 1973). Magnetization is then transferred with a time constant TCH-... 

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 the limit of infinitely strong coupling Hartmann-Hahn limit), only the terms and I yl2x hxhy) are created from o-(O) = (see Fig. 1C). The most remarkable property of this limit is that the transfer of polarization between the two coupled spins iscomplete. In the simulation of Fig. 1C a coupling constant 7,2 = 10 Hz was assumed. In this case, the initial polarization of the first spin is completely transformed into polarization Ilx of the second spin after 50 ms, which is equal to l/fZ/jj). 

However, for efficient polarization transfer, the two frequencies Vj and P2 need not be exactly identical and it is sufficient if the spin system is in the Hartmann-Hahn limit, where... 

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. 

Here the generic term Hartmann-Hahn experiment is used for polarization- or coherence-transfer experiments that are based on the Hartmann-Hahn principle (see Section II), that is, on matched effective fields that are created by a rf irradiation scheme. These experiments may be classified according to the following practical and theoretical aspects (see Fig. 6) that are related to properties of samples, spin systems, coherent magnetization transfer, effective Hamiltonians, multiple-pulse sequences, and incoherent magnetization transfer ... 

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). 

Homonuclear Hartmann-Hahn transfer functions for off-resonant CW irradiation have been derived for two coupled spins 1 /2 (Bazzo and Boyd, 1987 Bothner-By and Shukla, 1988 Elbayed and Canet, 1990) and for the AX 2 spin system (Chandrakumar et al., 1990). In the multitilted frame, Hartmann-Hahn transfer functions under mismatched effective fields are related to polarization- and coherence-transfer functions in strongly coupled spin systems (Kay and McClung, 1988 McClung and Nakashima, 1988 Nakai and McDowell, 1993). Numerical simulations of homonuclear... 

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. 

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. 

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