Heteronuclear coherence order

The most important thing about the raising and lowering (or spherical ) operators is the way they react to gradients, which is to say their coherence order. The coherence order is no longer ambiguous. For the heteronuclear system... 

For heteronuclear systems, it is convenient to redefine the coherence order p so that it includes the relative magnetogyric ratio y/Yc (or y/ya in the general case) ... 

In addition to sensitivity-improved two-dimensional TOCSY experiments, PEP versions of two-dimensional HSQC-TOCSY experiments (Cavanagh et al., 1991) as well as three-dimensional HSQC-TOCSY and three-dimensional TOCSY-HMQC experiments (Palmer et al., 1992 Ranee, 1994 Krishnamurthy, 1995) have been reported. This enhancement scheme is also used in heteronuclear coherence-order-selective coherence transfer (COS-CT Schleucher et al., 1994 Sattler et al., 1995a). Because in... 

T. O. Reiss, N. Khaneja and S. J. Glaser, Time optimal coherence-order-selective transfer of in-phase coherence in heteronuclear IS spin systems. J. Magn. Reson., 2002, 154, 192-195. 

Thus, the first gradient of Fig. 6.9a acts when both proton and carbon have coherence order p = - -1 (heteronuclear double-quantum coherence), so the effect of the gradient is written Gi(yh -I- Yc)- For the second gradient this becomes G2(-Yh + Yc) and for the third Gsf-Yn)- To preserve this pathway, the overall phase induced by the gradients must be zero ... 

In heteronuclear systems it is sometimes useful to classify operators according to their coherence orders with respect to each spin. So, for example, 1Ilz[2y has p = 0 for spin 1 and p = 1 for spin 2. 

Note that separate coherence orders are assigned to the I and S spins. Observable signals on the I spin must have p = -1 and ps = 0 (any other value of ps would correspond to a heteronuclear multiple quantum coherence). Given this constraint, and the fact that the I spin 180° pulse simply inverts the sign of... 

The S spin coherence order only changes when pulses are applied to those spins. The first 90° S spin pulse generates ps = 1, just as before. As by this point pI = +1, the resulting coherences have ps = +1, pt = -1 (heteronuclear zero-quantum) and ps = +1, pj = +1 (heteronuclear double-quantum). The I spin... 

In a heteronuclear system a coherence order can be assigned to each spin... 

The processes that occur during the evolution period are probably the most important in describing the effect of the complete pulse sequence. During this period coherence can evolve, coherence can be selectively manipulated or coherence transfer can occur. Coherence manipulation can be the inversion of the coherence order (WATERGATE experiment) or in a l S spin system a phase shift depending upon signal multiplicity (APT or SEMUT experiment). In the case of heteronuclear IS spin systems the creation of antiphase coherence and subsequent polarization transfer using a INEPT or a DEPT unit can be used in multiplicity edited experiments or heteronuclear 2D correlation experiments. In transient NOE experiments such as ROE and TROESY, coherence... 

Recently a new type of proton assisted recoupling experiments has been developed for coherence transfer where rf irradiation is taking place on all involved rf channels. This embraces the homonuclear proton assisted recoupling (PAR) [45, 140, 141] and the later resonant second-order transfer (RESORT) [142] experiments, as well as the heteronuclear proton assisted insensitive nuclei (PAIN) cross polarization [44] experiments. In PAR and PAIN, spin-lock CW irradiation is applied on both passive ( H) and active spins (13C, 15N) without matching rotary resonance conditions. In RESORT a phase alternation irradiation scheme for the passive spins is used. 

Fig. 10.14. Gradient-enhanced HMQC pulse sequence described in 1991 by Hurd and John derived from the earlier non-gradient experiment of Bax and Subramanian. For 1H-13C heteronuclear shift correlation, the gradient ratio, G1 G2 G3 should be 2 2 1 or a comparable ratio. The pulses sequence creates heteronuclear multiple quantum of orders zero and two with the application of the 90° 13C pulse. The multiple quantum coherence evolves during the first half of ti. The 180° proton pulse midway through the evolution period decouples proton chemical shift evolution and interchanges the zero and double quantum coherence terms. Antiphase proton magnetization is created by the second 90° 13C pulse that is refocused during the interval A prior to detection and the application of broadband X-decoupling.

In the following, we will discuss heteronuclear polarization-transfer techniques in four different contexts. They can be used as a polarization-transfer method to increase the sensitivity of a nucleus and to shorten the recycle delay of an experiment as it is widely used in 1H-13C or 1H-15N cross polarization. Heteronuclear polarization-transfer methods can also be used as the correlation mechanism in a multi-dimensional NMR experiment where, for example, the chemical shifts of two different spins are correlated. The third application is in measuring dipolar coupling constants in order to obtain distance information between selected nuclei as is often done in the REDOR experiment. Finally, heteronuclear polarization transfer also plays a role in measuring dihedral angles by generating heteronuclear double-quantum coherences. 

In order to carry out complete structural elucidation of unknown compounds (especially for complex molecules), the RF probe should enable a variety of heteronuclear NMR techniques to be performed. In particular, inverse detection H-15N and 1H-13C experiments such as heteronuclear multiple quantum coherence (HMQC) [29,30] and heteronuclear single quantum coherence (HSQC) [31] find almost ubiquitous application in myriad research environments. Although the microliter-scale probes described above feature both heteronuclear and homonuclear capabilities, no commerical product is... 

Figure 12.12a gives a good illustration of the need for going to a third dimension to facilitate the interpretation of a crowded 2D spectrum. The NOESY spectrum of a uniformly 15N-enriched protein, staphylococcal nuclease, has so many cross peaks that interpretation is virtually impossible. However, it is possible to use, 5N chemical shifts to edit this spectrum, as indicated in Fig. 12.121) and c in a three-dimensional experiment. With the 15N enrichment, NOESY can be combined with a heteronuclear correlation experiment, in this case HMQC, but HSQC could also be used. A 3D pulse sequence can be obtained from two separate 2D experiments by deleting the detection period of one experiment and the preparation period of the other to obtain two evolution periods (q and t2) and one detection period (f3). In principle, the two 2D components can be placed in either order. For the NOESY-HMQC experiment, either order works well, but in some instances coherence transfer proceeds more efficiendy with a particular arrangement of the component experiments. We look first at the NOESY-HMQC sequence, for which a pulse sequence is given in Fig. 12.13. The three types of spins are designated I and S (as usual), both of which are H in the current example, and T, which is 15N in this case.

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... 

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. 

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