Hartmann-Hahn Experiments

B. Band-Selective Heteronuclear Hartmann-Hahn Experiments... 

Hartmann-Hahn experiments rely on the resonant interaction of spins (see Section II). How is it possible to create energy-matched conditions in an external magnetic field for two spins that have different chemical shifts or even different gyromagnetic ratios ... 

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). 

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. 

Multiple-pulse sequences are indispensable tools for the practical implementation of Hartmann-Hahn experiments in liquid state NMR. They often consist of thousands of defined rf pulses with or without intermediate delays and allow one to create a desired form of the effective Hamiltonian for a given class of spin systems. In the field of high-resolu-tion NMR, multiple-pulse sequences are also used for broadband het-eronuclear decoupling (Levitt et al., 1983 Shaka and Keeler, 1986). Composite pulses (Levitt, 1986) and shaped pulses (Warren and Silver, 1988 Freeman, 1991 Kessler et al., 1991) may be considered as special classes of multiple-pulse sequences. 

Although in general, only one multiple-pulse sequence is applied to homonuclear spin systems, it can be useful to apply different multiple-pulse sequences to several nuclear species at the same time by using separate rf channels. In heteronuclear Hartmann-Hahn experiments, the same multiple-pulse sequence is usually applied simultaneously to two or more nuclear species. However, some selective homonuclear Hartmann-Hahn experiments are also based on the simultaneous irradiation of a multiple-pulse sequence at two or more different frequencies (see Section X). If only a single homonuclear rf channel is used, this can be achieved experimentally by adding an amplitude or phase modulation to the sequence, in order to create appropriate irradiation sidebands (Konrat... 

In heteronuclear Hartmann-Hahn experiments, a rf sequence is irradiated simultaneously at two frequencies vf and Vg. These experiments are conveniently analyzed in the corresponding doubly rotating frame (Ernst et al., 1987). In this frame, the free-evolution Hamiltonian contains offset terms and for / and 5 spins, isotropic homonuclear /-/ and 5-5 coupling terms and, and truncated heteronuclear coupling terms... 

For heteronuclear Hartmann-Hahn experiments, the rf amplitudes of the two rf fields must be matched... 

Whereas the term 0( > 3) can often be neglected in practice, the effective fields and the effective coupling tensors are decisive for the transfer of magnetization in Hartmann-Hahn experiments. If the basis sequence of duration is repeated n times, the propagator U nTff) is simply given by the nth power of... 

In heteronuclear Hartmann-Hahn experiments, where two (or more) nuclear species are irradiated simultaneously with the same multiple-pulse sequence, the heteronuclear coupling terms have the following form in the toggling frame ... 

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 ... 

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... 

Fig. 6. Classification schemes for Hartmann-Hahn experiments based on (A) the aggregation state of the sample, (B) nuclear species of the spins between which magnetization is transferred, (C) dynamics of magnetization transfer and its reach within a spin system, (D) isotropic or nonisotropic magnetization transfer, (E) magnitude of effective fields, (F) type of effective coupling tensors, (G) active bandwidth of the sequence, (H) type of multiple-pulse sequence, and (I) suppression of cross-relaxation.

More recently, a number of Hartmann-Hahn experiments were developed, which allow one to control the transfer of magnetization within an extended coupling network and to deliberately restrict coherence transfer to a defined subset of spins (see Section X.C). The first experiments of this class were called tailored TOCSY experiments (Glaser and Drobny, 1989),... 

Hartmann-Hahn experiments may be classified based on the isotropic or nonisotropic nature of magnetization transfer (see Fig. 6D). In the first case, all magnetization components (i.e., x, y, and z magnetization) are transferred identically, whereas in the second case only certain magnetization components have optimum coherence-transfer efficiency. 

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). 

With respect to the relative bandwidth, Hartmann-Hahn experiments may roughly be divided into broadband, band-selective, and (highly) selective experiments. 

For the practical implementation of Hartmann-Hahn experiments, the type of multiple-pulse sequence can be important (see Section III). Continuous wave (CW) irradiation represents the simplest homonuclear Hartmann-Hahn mixing sequence (Bax and Davis, 1985a). Simultaneous CW irradiation at the resonance frequencies of two heteronuclear spins is the simplest heteronuclear Hartmann-Hahn mixing sequence (Hartmann and Hahn, 1962). 

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... 

The following four characteristic zero-quantum coupling tensors between any pair of spins i and j constitute idealized limiting cases for experimentally relevant Hartmann-Hahn experiments. These characteristic zero-quantum coupling tensors are characterized by effective coupling constants which are related to the actual coupling constants /,y by the scaling factors 5, ... 

Isotropic effective /-coupling tensors (/) with a scaling factor s 1 are characteristic for ideal homonuclear Hartmann-Hahn experiments and, in particular, for homonuclear isotropic mixing experiments (see Section X). Isotropic effective /-coupling tensors can also be created between heteronuclear spins i and m (see Section XI) however, this results in a reduced effective coupling constant with a scaling factor i 1/3 [see Eq. (115)]. 

Sjj 1/2) are also characteristic for many selective homonuclear Hartmann-Hahn experiments based on doubly selective rf irradiation (see Section X.C). 

In Hartmann-Hahn experiments, the transfer functions T 5(t) and Tg (t) are often closely related. It is always possible to find a set of basis functions in which the matrix representation of a Hermittian Hamiltonian has only real-valued matrix elements this case, the matrix... 

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