Heteronuclear Hartmann-Hahn Sequences

Name Basic Composite Pulse Expansion f , (6 dB) by (6 dB) 6, (6 dB) References 

In heteronuclear triple-resonance experiments (TCP Majumdar and Zuiderweg, 1995), the spin system corresponds to an effective PPP coupling topology if planar effective coupling tensors are created. In an ISQ system, triple-resonance Hartmann-Hahn transfer from a spin / to a spin Q is only efficient if I//5I J,q (Glaser, 1993c Majumdar and 

Zuiderweg, 1995). In the case of a linear ISQ system, concatenated cross-polarization (CCP Majumdar and Zuiderweg, 1995) is more efficient than two sequential double-resonance (DCP) Hartmann-Hahn transfer steps. The CCP scheme is a combination of a DCP and TCP experiment with optimized mixing times Tj and Tj that depend on the magnitudes of and J Q (Majumdar and Zuiderweg, 1995). 

The first heteronuclear Hartmann-Hahn transfer in the liquid state preceded the homonuclear analogs of the experiment by about two decades. In their seminal paper on nuclear double resonance in the rotating frame, Hartmann and Hahn (1962) focused on heteronuclear polarization transfer in the solid state with the help of two matched CW rf fields with However, in the same paper, Hartmann and Hahn also discussed the coherent heteronuclear transfer of polarization for pairs of /-coupled heteronuclear spins in liquids and reported polarization-transfer experiments between H and P in hypophosphorous acid. Heteronuclear Hartmann-Hahn transfer in liquids with CW irradiation was applied by several groups (Maudsley et al., 1977 Muller and Ernst, 1979 Bertrand et al., 1978a, b Murphy et al., 1979 Chingas et al., 1979a, b, 1981). A detailed analysis of the experiment was presented by Muller and Ernst (1979) and by Chingas et al. (1981). Matched CW irradiation at the 

The MLEV-16 sequence, which contains rf pulses with orthogonal phases, has poor heteronuclear transfer characteristics. The effective coupling tensors are neither planar nor isotropic. For two spins on-resonance, the average coupling tensor has the form 

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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). 

Heteronuclear Hartmann-Hahn sequences also effect homonuclear Hartmann-Hahn transfer, resulting in (heteronuclear and homonuclear) total correlation spectroscopy (TOCSY Bearden and Brown, 1989 Zuiderweg, 1990 Brown and Sanctuary, 1991 Ernst et al., 1991). Simultaneous heteronuclear and homonuclear magnetization transfer can be beneficial in relayed transfer experiments (Gibbs and Morris, 1992 Tokles et al., 1992 Majumdar et al., 1993). However, as pointed out by Ernst et al. 

Lock on unprepared spins Heteronuclear Hartmann-Hahn sequences developed by M. G. Schwendinger Pulse sequenee and supercycle developed by M. Levitt... 

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 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... 

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 ... 

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). 

Homonudear Hartmann-Hahn sequences with delays were developed for clean TOCSY experiments (see Section X.B). Examples are delayed MLEV-17 (Griesinger et al., 1988), delayed DIPSI-2 (Cavanagh and Ranee, 1992), and clean CITY (computer-improved total-correlation spectroscopy Briand and Ernst, 1991). The MGS sequences (Schwendinger et al., 1994) are examples of broadband heteronuclear Hartmann-Hahn mbdng sequences with delays and variable rf amplitudes. 

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 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. 

The most important criteria for experimental Hartmann-Hahn mixing sequences are their coherence-transfer properties, which can be assessed based on the created effective Hamiltonians, propagators, and the evolution of the density operator. Additional criteria reflect the robustness with respect to experimental imperfections and experimental constraints, such as available rf amplitudes and the tolerable average rf power. For some spectrometers, simplicity of the sequence can be an additional criterion. Finally, for applications with short mixing periods, such as one-bond heteronuclear Hartmann-Hahn experiments, the duration Tj, of the basis sequence can be important. 

In the case of heteronuclear Hartmann-Hahn experiments, independent, uncorrelated rf-field distributions must be assumed for the different nuclear species if two separate rf coils are used (Ernst et al., 1991 Schwendinger et al., 1994 also see Section XI). Multiple-pulse sequences that are compensated for rf inhomogeneity are also relatively insensitive to a miscalibration of the experimental rf amplitude Quality factors for the sensitivity of Hartmann-Hahn transfer to other imperfections, such as... 

Vj, effective coherence transfer is possible (Davis and Bax, 1985 Bax et al., 1985). This sequence (DB-1) is the analog of square-wave heteronuclear decoupling (Grutzner and Santini, 1975 Dykstra, 1982). For heteronuclear Hartmann-Hahn experiments, a similar sequence [mismatch-optimized IS transfer (MOIST)] was introduced by Levitt et al. (1986) (see Section XII). In order to allow Hartmann-Hahn transfer of only a single magnetization component, the total duration during which the rf field is applied along the... 

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). 

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). 

A markedly increased bandwidth of heteronuclear Hartmann-Hahn transfer for a given average rf power can be achieved with the MGS-1 and MGS-2 sequences developed by Schwendinger et al. (1994) (see Fig. 33G and H). The sequences are MLEV-4 and MLEV-8 expansions of new composite pulses R, which consist of square pulses with rf phases of 0 or 180° and different rf amplitudes that are separated by delays (see Fig. 34). Figure 35 shows HCCH-COSY spectra of a fully C-labeled protein using DIPSI-2 and MGS-2 for the initial polarization transfer from H to (prepolarization) as well as for back-transfer from to H (Majumdar et al., 1993). Note that the absolute bandwidth of MGS-2 is markedly increased compared to DIPSI-2, even though the average power... 

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. 

Sample heating by extended periods of rf irradiation can cause a number of undesired effects, which in fact helped drive the development of efficient broadband homonuclear and heteronuclear Hartmann-Hahn mixing sequences (see Sections X and XI). 

FySy), where = E", (Schleucher et al., 1994). This Hamiltonian can be implemented using a heteronuclear Hartmann-Hahn mixing sequence that creates an effective Hamiltonian = 2TrJ f (FySy + F S ) that is embedded between two 9(f I,S)y pulses. A heteronuclear isotropic Hartmann-Hahn (HIHAHA) transfer step (Quant et al., 1995a Quant, 1996) can be used for in-phase COS-CT, for example, from S to F (Sattler et al., 1995a). CQS-CT mixing steps yield sensitivity-improved experiments and are especially useful for experiments that are based on gradient echoes. 

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. 

General symmetry principles for rotor-synchronized pulse sequences in MAS solid-state NMR have been presented. The synunetry theory has been extended to the case of generalized Hartmann-Hahn sequences, in which rotor-synchronized r.f. irradiation is applied simultaneously to two isotopic spin species. The symmetry theory has been used to design pulse sequences which implement heteronuclear dipolar recoupling at the same time as decoupling homonuclear spin-spin interactions, and which also suppress CSAs. Experimental demonstrations of heteronuclear 2D correlation spectroscopy, heteronuclear MQ spectroscopy, and the estimation of intemuclear dipolar couplings have been given. 

Important guidelines for the construction of a multiple-pulse sequence with desired properties are provided by average Hamiltonian theory (see Section IV). The effective Hamiltonian created by the sequence must meet a number of criteria (see Section IX). Most importantly, spins with different resonance frequencies, that is, with different offsets and Vj from a given carrier frequency, must effectively be energy matched in order to allow Hartmann-Hahn transfer. This can be achieved if the derivative of the effective field with respect to offset vanishes, which is identical to the Waugh criterion for efficient heteronuclear decoupling... 

Bax and co-workers demonstrated that a homonuclear Hartmann-Hahn transfer of net magnetization can be obtained by the application of a spin-lock field, using CW irradiation (Bax and Davis, 1985a Davis and Bax, 1985) or by the DB-1 sequence that consists of a series of phase-alternated spin-lock pulses (Davis and Bax, 1985). The homonuclear Hartmann-Hahn effect caused by CW irradiation was discovered when artifacts in ROESY experiments were analyzed (Bax and Davis, 1985a). CW irradiation can be regarded as a homonuclear analog of spin-lock experiments for heteronuclear cross-polarization (Hartmann and Hahn,... 

Heteronuclear Isotropic Hartmann-Hahn Mixing Sequences"... 

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