Multiple-pulse sequence optimization

For a given set of spin systems with known (or estimated) coupling constants, chemical shifts, and relaxation rates, the following questions must be addressed What is the optimal effective mixing Hamiltonian (see Sections IV and V) How can the optimal mixing time be determined (see Section VI) How can the ideal mbdng Hamiltonian be implemented in practice with the help of a multiple-pulse sequence (see Sections VIII-XI) ... 

This approach for the development of multiple-pulse sequences is only practical if a large number of sequences can be assessed in a short period of time. The final assessment of the quality of a multiple-pulse sequence must always be based on experiments. However, for the optimization of multiple-pulse sequences, experimental approaches are, in general, too slow and too expensive (instrument time ). An attractive alternative to experiments at the spectrometer is formed by numerical simulations, that is, experiments in the computer. In simulations it is also possible to take relaxation and experimental imperfections such as phase errors or rf inhomogeneity into account. In addition to the direct translation of a laboratory experiment into a computer experiment, it is possible to numerically assess the properties of a multiple-pulse sequence on several abstract levels, for example, based on the created effective Hamiltonian. If simple necessary conditions can be defined for a multiple-pulse sequence with the... 

The choice of an appropriate class of multiple-pulse sequences and its parametrization is critical for the success of the screening and optimization process. In particular, the number of variable parameters that determine the dimensionality of the parameter space must be carefully chosen. In general, the flexibility and potential performance of a multiple-pulse sequence increases with the number of parameters. However, if the size of the parameter space is too large, it cannot be screened efficiently and it can be impossible to find good sequences in a reasonable amount of time. For many applications, powerful Hartmann-Hahn mixing sequences can be developed with a minimum number of variable parameters if supercycling schemes are used to expand a basic composite pulse and if the symmetry properties of composite pulses are taken into account (Levitt, 1982 Murdoch et al., 1987 Ngo and Morris, 1987 Shaka and Pines, 1987 Lee and Warren, 1989 Lee et al., 1990 Simbrunner and Zieger, 1995). 

In Section VIII, optimization strategies for the development of Hartmann-Hahn mixing sequences were discussed. These approaches rely on the quantitative assessment of a given sequence with the help of so-called quality factors. The assessment of multiple-pulse sequences is also important for the choice of practical mixing sequences (see Sections X and XI). In this Section, approaches for the assessment of a Hartmann-Hahn mixing sequence are summarized. In addition, scaling... 

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. 

If more sophisticated experiments are aimed, such as those involving multiple pulse sequences, spin echo detection, rotor synchronization, or 2D methods, additional calibration steps, trial tests, and optimization procedures are required. The reader is referred to the specific literature dealing with each particular method for a proper description of the experimental setup. A general account of these methods can also be found in the monographs by MacKenzie and Smith [4] and Duer [15]. 

Fig. 1. Pulse sequences modified for multiple selective excitation. I ID TOCSY, II het-eronuclear ID NOE, III ID INADEQUATE, IVa heteronuclear ID COSY (optimized to detect Jch), IVb heteronuclear ID COSY (optimized to detect "Jch), V 2D TOCSY-COSY, Via 2D HMBC (designed to detect heteronuclear long-range couplings "Jch only), VIh 2D HMBC (extended pulse sequence to detect both heteronuclear long-range "Jch and...

The excitation schemes, or pulse sequences, that optimize the SNR depend on the relaxation times and frequencies inherent to the quadrupolar nuclei under observation and on the characteristics of the excitation/detection hardware. Focusing first on relaxation times, we define two broad categories (i) 7 , 1 and (ii) 7 2 Tl. Most materials fall in the former category, and the pulse sequences discussed in Sector 4.1.1. all involve the creation and detection of multiple spin echoes, which generally requires that r2e be at least several tens of milliseconds. The most notable exception is RDX, which is in the second category under ambient conditions. For materials with very short 7 ,s such as RDX at elevated temperatures, a single echo pulse sequence, or even a single-pulse FID acquisition, may be required. 

Modified binomial sequences in which a binomial sequence is inserted between a -tt and a +tt pulse have been developed that significantly reduce the phase shift. The phase behaviour of the binomial sequences can also be improved using true binomials with a total flip angle of Morris et al considered computer optimization to improve the amplitude response of binomial sequences. More complex hard pulse sequences have also been developed such as NERO and others. However, as these sequences become more complicated so does their experimental setup, for example the accurate determination of the pulse lengths required by these sequences which are generally not multiples of ttI2. 

The other common inverse-detection method, heteronuclear multiple quan-turn coherence (HMQC) relies on multiple-quantum coherence transitions during the pulse sequence. Due to the multiple-quantum coherence transitions it is more laborious to theoretically follow the course of magnetization, and the cross peak will be broader in the Fi dimension due to the /hh evolution. Unlike HSQC, HMQC can also be optimized for Jch couplings. This heteronuclear multiple bond correlation experiment, or HMBC, ° ° has lower sensitivity than HMQC/HSQC experiments, and the Jch correlations can appear as artefacts in the spectrum. However, the cross peak volume should follow the concentration of analyte, so with proper method validation HMQC and HMBC should also be applicable for quantification. 

Calibrations and tolerance Now we add one more level of complication. Not only will the sequence need the characteristics described above (i.e. powerful, selective, quick, and clean), but we also seek methods that are easy to use and tolerant of mistakes. All NMR users, regardless of experience, would imdoubt-edly appreciate a pulse sequence that is easy to conceptualize, requires the least number of experimental parameters to be optimized, and yields simple reproducible results for efficient optimization. If a pulse sequence takes hours to optimize (e.g. full equilibrium must be reached between transients) with multiple interdependent parameters and must subsequently be re-optimized for each sample, then the sequence will need exceptional performance in every other aspect of evaluation to be adopted. Alternatively, a pulse sequence that gives only average suppression but requires little or no optimization will likely receive enthusiastic usage even though the overall performance may not meet that of other suppression choices. While neither extreme is likely we are often faced with several comparable choices and must evaluate the experimental needs and the robustness of the chosen suppression method(s). 

Most of the sequences performed well even on this short and moderately shimmed sample. Despite not optimizing the shims, almost every sequence was able to suppress sufficiently to acquire useful spectra with minimal baseline distortions even close to the solvent. The exception occurred for the WET style sequences. The WET family did not suppress nearly as well and required the gain to be reduced by 6 dB (vertical scale in the figure was increased to compensate) to prevent a receiver overflow and ADC error. However, WET and SWET are very easy to include in pulse sequences (e.g. during the recycle delay or mixing periods) and allow simple suppression of multiple frequencies using composite shaped pulses. The poor results may come from several sources (e.g. coding error, optimization error, etc.) and therefore may not represent a limitation of the pulse sequences. Alternatively, as a real world example, some sequences simply perform better on some spectrometers and users must be prepared to adapt when necessary. We have t)q)ically found WET to be extremely reliable and robust, but certainly not on this particular sample. 

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