Hartmann-Hahn matching experiment

Fourier transformation over an incremented Hartmann-Hahn evolution period yields the eigenfrequencies of the (effective) Hartmann-Hahn Hamiltonian. In solid samples with resolved heteronuclear dipolar couplings (Muller et al., 1974), this approach yields heteronuclear dipolar oscillation spectra (Hester et al., 1975) if the heteronuclear spins are Hartmann-Hahn matched during the evolution period of the experiment. In liquid state NMR, Fourier transformation over incremented homonu-clear Hartmann-Hahn transfer periods yields so-called coherence-transfer... 

An essentially identical experiment has also been referred to as Homonuclear Hartmann-Hahn spectroscopy [50,51] or HOHAHA (the two differ only in some technical details in the originally published sequences). This name arises from its similarity with methods used in solid-state NMR spectroscopy for the transfer of polarisation from proton to carbon nuclei (so-called crosspolarisation), which are based on the Hartmann-Hahn match described below. For the same reason, the transfer of magnetisation during the TOCSY sequence is sometimes referred to as homonuclear cross-polarisation. Throughout this text the original TOCSY terminology is used, although TOCSY and HOHAHA are now used synonymously in the chemical literature. 

The requirement for nuclei to experience identical local fields during the mixing time for transfer to occur between them is also referred to as the Hartmann-Hahn match. More formally and more generally, this may be... 

Although in principle the simple scheme presented in Fig. 5.59 should provide TOCSY spectra, its suitability for practical use is limited by the effective bandwidth of the continuous-wave spin-lock. Spins which are off-resonance from the applied low-power pulse experience a reduced rf field causing the Hartmann-Hahn match to breakdown and transfer to cease. This is analogous to the poor performance of an off-resonance 180° pulse (Section 3.2.1). The solution to these problems is to replace the continuous-wave spin-lock with an extended sequence of composite 180 pulses which extend the effective bandwidth without excessive power requirements. Composite pulses themselves are described in Chapter 9 alongside the common mixing schemes employed in TOCSY, so shall not be discussed here. Suffice it to say at this point that these composite pulses act as more efficient broadband 180 pulses within the general scheme of Fig. 5.60. 

The first of these arises when the long spin-lock pulse acts in an analogous fashion to the last 90" pulse of the COSY experiment so causing coherence transfer between J-coupled spins. The resulting peaks display the usual antiphase COSY peak stmcture and tend to be weak so are of least concern. A far greater problem arises from TOCSY transfers which arise because the spin-lock period in ROESY is similar to that used in the TOCSY experiment (Section 5.7). This may, therefore, also induce coherent transfers between J-coupled spins when these experience similar rf fields, that is, when the Hartmann-Hahn matching condition is satisfied. Since the ROESY spin-lock is not modulated (i.e. not a composite pulse sequence), this match is restricted to mutually coupled spins with similar chemical shift offsets or to those with equal but opposite... 

Hartmann and Hahn [39] showed that CP can be achieved when two rf fields Bin and B c = 4Bih are simultaneously applied. Jn/jc = 4, so, when B c = 4Bm energy is transferred between them, or they are cross-polarized, because Tc ic = Th ih (which is called the Hartmann-Hahn match of heteronuclear rotating-frame frequencies). In the CP experiment C nuclei obtain their spin polarization from H nuclei, so, not only do the shorter proton spin-lattice relaxation times determine the repetition rate of... 

H O CP experiments are not routine. One problematic issue is the orientation dependency of the quadrupolar interaction. As a result, only a fraction of the nuclear spins in a powder satisfies the Hartmann—Hahn matching condition, leading to distorted lineshapes. Ando and co-workers [14,16,17] recorded a series of H—CP static spectra of polypeptides. The resultant spectra exhibit clear lineshape distortions, as a result of the combination of the CP experiment and low magnetic field detections. Witterbort and co-workers [28,52,97] successfully apphed a modified H—CP sequence in single-crystal experiments of bio- and organic molecules to regain sensitivity. 

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). 

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

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 ... 

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). 

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). 

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... 

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