Supercycled homonuclear dipolar decoupling sequences in solid-state NMR

doi:10.1016/j.jmr.2008.11.011

Journal of Magnetic Resonance

Volume 197, Issue 1, March 2009, Pages 14-19

https://doi.org/10.1016/j.jmr.2008.11.011 Get rights and content

Abstract

We compare the performance of the windowed phase-modulated Lee–Goldburg (wPMLG) and the windowed decoupling using mind boggling optimisation (wDUMBO) sequences at various magic-angle spinning rates and nutation frequencies of the pulses. Additionally, we introduce a supercycled version of wDUMBO and compare its efficiency with that of the non-supercycled implementation of wDUMBO. The efficiency of the supercycled version of wPMLG, denoted wPMLG-S2, is compared with a new supercycled version of wPMLG that we notate as wPMLG-S3. The interaction between the supercycled homonuclear dipolar decoupling sequences and the sample rotation is analysed using symmetry-based selection rules.

Introduction

High-resolution proton nuclear magnetic resonance (NMR) spectroscopy is possible in the solid-state, due to the development of combined magic-angle spinning and multiple-pulse techniques, that average out the strong homonuclear dipolar couplings [1], [2]. Among the various multiple-pulse schemes that are normally employed, those that have been shown to perform well at MAS frequencies of 10–25 kHz are the frequency-switched Lee–Goldburg (FSLG) [3], [4], the phase-modulated Lee–Goldburg (PMLG) [5], [6], and the decoupling using mind boggling optimisation (DUMBO) [7] sequences. FSLG and PMLG are the sequences of choice in most two-dimensional (2D) experiments requiring high-resolution ¹H spectra, for example, in 2D heterocorrelation spectroscopy [8], [9], [10], [11], [12] and 2D double quantum–single quantum correlation spectroscopy [13]. Both double-quantum and triple-quantum ¹H spectroscopy have also been reported with the use of DUMBO [14], [15], [16]. wPMLG has been widely used to obtain high-resolution ¹H spectra in one-dimensional (1D) experiments. A detailed report on the various experimental aspects, such as optimisation protocols of FSLG, PMLG, and wPMLG, has recently been published [17].

The windowed 1D version of PMLG, the wPMLG sequence [18], has evolved in last 10 years in its experimental implementation and theoretical understanding, which is based on bimodal Floquet theory [2]. A supercycled version of the wPMLG scheme was recently implemented, notated as $w {PMLG}_{mm}^{x \bar{x}}$ [19], [20]. This supercycled version of wPMLG generates an effective z-rotation for the transverse magnetisation, resulting in good spectra at a wider range of resonance offsets, a more robust scaling factor, and relatively good performance at moderately high MAS frequencies. However, the realisation of this experiment at high MAS frequencies such as 25–30 kHz requires high RF power (nutation frequencies around 150–180 kHz) as discussed below.

In this article the notation wPMLG5-S(P) refers to a supercycle constructed by P wPMLG5 elements with overall phases incremented by $2 π / P$ . A single wPMLG5 element consists of 10 pulses followed by an observation window, where the pulse phases and timings are specified explicitly in Refs. [2], [20]. The sequence denoted as $w {PMLG}_{mm}^{x \bar{x}}$ in Refs. [19], [20] is henceforth referred to as wPMLG-S2.

The 1D version of the DUMBO scheme with windows (wDUMBO) has also been shown to work well up to a MAS frequency of ca. 25 kHz [21]. A detailed theoretical study of wDUMBO has never been attempted, although most of the modifications suggested to improve the wPMLG scheme can be extended to wDUMBO without any loss of generality.

Here we introduce a supercycled version of wDUMBO, denoted wDUMBO-S2, which uses a supercycling scheme similar to wPMLG-S2, to enable its implementation at high MAS frequencies of 30 kHz. We compare the performance of wDUMBO and wDUMBO-S2, wPMLG-S2, and wDUMBO-S2 at various spinning frequencies. The performance of wPMLG-S2 is then compared with another supercycled version of wPMLG called wPMLG-S3 which allows the implementation of wPMLG in regimes where wPMLG-S2 is not very effective. We use a symmetry-based average Hamiltonian analysis to predict the conditions under which particular supercycles are most appropriate.

Section snippets

Experimental

The experiments comparing wDUMBO and wDUMBO-S2, and wPMLG5-S2 and wDUMBO-S2 (Fig. 2, Fig. 3, Fig. 4) were performed on a sample of glycine in a Bruker AVIII 700 MHz spectrometer with a narrow-bore magnet (bore size 54 mm) using a 2.5 mm double-resonance probe. All the other experiments on glycine (Fig. 5, Fig. 7) and l-histidine · HCl · H₂O (Fig. 6) were performed on a Bruker AVI 500 MHz spectrometer with a wide-bore magnet (bore size 89 mm) using a 4 mm triple-resonance probe. In all cases the rotor was

Methods

The pulse sequences implemented in this article are depicted in Fig. 1. Fig. 1a illustrates a supercycled homonuclear dipolar decoupling sequence with $P = 2$ in which A can either be the PMLG or the DUMBO scheme. Each wPMLG or wDUMBO block (consisting of a single homonuclear decoupling sequence followed by an observation window) is considered to be a cyclic element with total duration denoted $τ_{C}$ . A data point (denoted by the asterisk) is acquired during each acquisition window. The basic pulse

Results and discussion

Fig. 2 compares the performance of the wDUMBO-S2 scheme and the non-supercycled version of wDUMBO for a sample of glycine at MAS frequencies of 10 kHz and 25 kHz. The quality of the spectrum improves with supercycling of wDUMBO especially at the higher MAS frequency of 25 kHz as reported for wPMLG-S2 [19]. The supercycling in wDUMBO-S2 removes the criterion of off-resonant irradiation, which is normally required for homonuclear decoupling under the DUMBO scheme. The effective z-rotation of the

Conclusions

We have introduced a supercycled version of wDUMBO, denoted by wDUMBO-S2, with an improved performance. We have compared wPMLG-S2 and wDUMBO-S2 schemes and observed that the performance efficiency of both are nearly the same except that wDUMBO-S2 requires a slightly higher RF power level than wPMLG-S2 for a given spinning speed. In all cases, rotary-resonance conditions occur at certain ratios of spinning frequency and cycle frequency and must be avoided if the best resolution is desired. It is

Acknowledgments

We thank the financial support by the Royal Society (UK) and the British Council of India, EPSRC (UK), the use of National Facility for High-Field NMR, TIFR, for the use of the Bruker AV500 spectrometer, and M.V. Naik for technical assistance.

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Supercycled homonuclear dipolar decoupling sequences in solid-state NMR

Abstract

Introduction

Section snippets

Experimental

Methods

Results and discussion

Conclusions

Acknowledgments

Solid State NMR

Chem. Phys. Lett.

Chem. Phys. Lett.

J. Magn. Reson.

J. Magn. Reson.

Chem. Phys. Lett.

J. Magn. Reson.

Chem. Phys. Lett.

Chem. Phys. Lett.

J. Magn. Reson.

Chem. Phys. Lett.

Utility of pulse nuclear magnetic resonance in studying protons in coals

J. Phys. Chem.

Strategies for high-resolution proton spectroscopy in solid-state NMR

Top. Curr. Chem.

Magic-angle NMR experiments in solids

Phys. Rev.

Phase modulated Lee–Goldburg magic angle spinning proton nuclear magnetic resonance experiments in the solid state: a bimodal Floquet theoretical treatment

J. Chem. Phys.