Hartmann-Hahn limit

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). 

In the infinitely strong coupling limit Hartmann-Hahn limit r]2l -> 0) Eq. (30) may be simplified to... 

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... 

N, or 29Si. In CP, both nuclear spin species are spin locked and the rf amplitudes adjusted so that their Larmor precession frequencies in their respective rotating frames are equal the Hartmann-Hahn condition. The single-contact CP enhancement of the rare spins is given by yj/ys. Additional enhancement normally occurs because the CP experiment may be recycled at a rate limited by the usually much faster spin-lattice relaxation rate of protons rather than that of the rare spins. 

The value of COSY stems from its dependence on the presence of spin coupling between the nuclei involved in the correlation. As we have seen, such coupling for protons is usually limited to three or four chemical bonds, hence provides some specificity that is helpful for structure elucidation. On the other hand, useful complementary information can be obtained from longer range interactions among a set of coupled nuclei. The standard method for obtaining such information is described by two acronyms—TOCSY (for total correlated spectroscopy, which best describes the aim of the experiment) and HOHAHA (for fiomonu-clear Hartmann-Hahn, which better describes the mechanisms employed). 

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, ... 

Although the bandwidth (6 dB) of CW irradiation is very limited (see Table 2), efficient Hartmann-Hahn transfer between two spins with offsets V, and Vj is also possible outside of this bandwidth along the diagonal and near the antidiagonal of a two-dimensional spectrum, where... 

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...

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... 

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). 

Multiple-step homonuclear Hartmann-Hahn transfer is not limited to highly selective transfer steps. As suggested by Glaser and Drobny (1989), several consecutive, band-selective Hartmann-Hahn mixing steps can be used to transfer coherence selectively in coupling networks with selected ranges of chemical shifts and coupling constants. 

In multidimensional NMR experiments that contain several evolution and mixing periods, even more combinations are possible (Griesinger et al., 1987b). In these experiments, Hartmann-Hahn mixing periods with in-phase coherence transfer are of particular advantage, because the resolution is often limited in the indirectly detected frequency dimensions. 

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. 

Although polarization transfer techniques have been available for over a decade, they have not been widely used to obtain 29Si-NMR spectra. 7-cross polarization (7) (JCP), which evolved from methods used to enhance the solid state spectra of rare spin nuclei, (8) has been applied to 29Si-NMR spectroscopy (9). JCP suffers from several limitations the proton and 29Si pulses must be on resonance, and the Hartmann-Hahn condition (8) (yHHH = VsiHsi) must be established for full enhancement. Neither of these conditions is trivial to obtain, and the difficulty in establishing them has prohibited routine application of JCP methods to 29Si-NMR spectroscopy.3... 

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