Multiple-pulse sequence homonuclear sequences

Since the first description of the Hartmann-Hahn transfer in liquids, spectroscopists have been fascinated by this technique. Many theoretical and practical aspects have been thoroughly investigated by several groups. With the development of robust multiple-pulse sequences, homonuclear and heteronuclear Hartmann-Hahn transfer has become one of the most useful experimental building blocks in high-resolution NMR. 

The influence of the homonuclear magnetic dipole-dipole interaction on can be reduced either by an increase of the sample spinning frequency, Vjot, (Eq. (20)) or by the application of a multiple-pulse sequence causing an additional averaging of this interaction (combined rotation and multiple-pulse spectroscopy, CRAMPS 19-21 ). With today s instruments, sample spinning frequencies of up to 40 kHz can be reached using MAS NMR rotors with an outer diameter of 2.0 mm. 

Undesired homonuclear spin interactions can be also suppressed using suitable multiple-pulse sequences while still exploiting the information content provided by interactions that are not affected. Using a combination of MAS and pulse decoupling it is even possible to reintroduce parts of an interaction that would be averaged out by one of the manipulation techniques alone ( recoupling ) [11]. This high flexibility of solid-state NMR enables one to fully exploit the rich information content provided by the spin interactions. It becomes particularly powerful if such experiments are combined to multidimensional NMR techniques as discussed in Section 14.3. 

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). 

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 general, the full isotropic coupling tensor between two homonuclear spins i and j can only be preserved by a multiple-pulse sequence if Ui (t) Uj U) [i.e., if fl j (t) = ap(t)] for 0 < / < Tj,. For multiple-pulse sequences with constant rf amplitude this is only possible for spin pairs with small offset differences p - Vj v, that is, for small angles 0-j. In general, the average coupling tensors are nonisotropic. Even if isotropic effective coupling tensors (with c J = c Jy = c 0 and c Jp = 0 for a = p)... 

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). 

Phase-modulated multiple-pulse sequences with constant rf amplitude form a large class of homonuclear and heteronuclear Hartmann-Hahn sequences. WALTZ-16 (Shaka et al., 1983b) and DIPSI-2 (Shaka et al., 1988) are examples of windowless, phase-alternating Hartmann-Hahn sequences (see Table II). 

Under the idealized zero-quantum coupling topologies (see Section V.B), the transfer of magnetization between two spins 1 /2 that are part of an arbitrary coupling network is identical in both directions (see Section VI). This symmetry with respect to the direction of the transfer is related to the symmetry of homonuclear, two-dimensional Hartmann-Hahn spectra with respect to the diagonal (Griesinger et al., 1987a). In Hartmann-Hahn experiments, the properties of the multiple-pulse sequence can induce additional symmetry constraints (Ernst et al., 1991). 

Homonuclear or heteronuclear Hartmann-Hahn mixing periods are versatile experimental building blocks that form the basis of a large number of combination experiments (see Section XIII). In practice, the actual multiple-pulse sequence that creates Hartmann-Hahn mixing conditions can usually be treated as a black box with characteristic properties. In this section, design principles and practical approaches for the development of Hartmann-Hahn mixing sequences are discussed. 

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). 

In the homonuclear case, the synchronous and matched irradiation at two frequencies and Vj can be implemented by placing the transmitter midway between the selected frequency ranges Rj and Rj and by modulating a band-selective multiple-pulse sequence with cos r(i, — Vj)/2]. This method can be regarded as an extension of the doubly selective HOHAHA experiment (Konrat et al., 1991), where a weak square pulse, rather than a multiple-pulse sequence, is amplitude-modulated. Implementations based on the principle of interleaved DANTE sequences (Morris and Freeman, 1978 Patt, 1992 Kupce and Freeman, 1992c) are also feasible. 

Only recently, new multiple-pulse sequences that were developed specifically for broadband heteronuclear Hartmann-Hahn experiments in liquids were reported. The SHR-1 sequence developed by Sunitha Bai et al. (1994) consists of a windowless phase-alternated composite pulse R, which is expanded according to the MLEV-8 supercycle. R was optimized based on a phase-distortionless single-spin 180° composite pulse and is related to the composite pulses used in DIPSI-1 (Shaka et al., 1988) and the composite pulses in the homonuclear IICT-1 sequence (Sunitha Bai and Ramachandran, 1993). The bandwidth of the SHR-1 sequence is comparable to the bandwidth of DIPSI-3, albeit with a slightly reduced transfer efficiency (Sunitha Bai et al., 1994 Fig. 33F). 

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. 

Homonuclear dipolar decoupling can be achieved by using so-called multiple pulse sequences (MPS). These are carefully tailored short and intense pulse cycles averaging the homonuclear dipolar interactions by reorientadon of the nuclear spins. 

In this section we list some of the homonuclear dipolar decoupling multiple-pulse sequences for high-resolution NMR in the solid-state which we will analyse... 

There are two requirements for the use of multiple-pulse sequences to speed up the spin-diffusion process First, the scaling factor of the homonu-clear dipolar coupling should be as large as possible and, second, the effective spin lock has to be larger than the homonuclear dipolar interactions between the S-spins [19] to prevent loss of sum magnetization into dipolar order [15]. 

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