TrendsThe WURST kind of pulses in solid-state NMR
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Introduction
WURST pulses (wideband, uniform rate, smooth truncation) were first introduced in 1995 by Kupče and Freeman [1], [2]. Their name was chosen to reflect their broad excitation/inversion capabilities, the linear sweep rate of their effective frequency, and the rounded-off shape of their amplitude profile. Initially developed as adiabatic inversion pulses for the purpose of broadband heteronuclear decoupling in solution NMR [3], they have more recently found an impressively diverse variety of applications in the solid state. This article provides a broad overview of these applications, highlighting the most significant publications and providing practical advice on how to implement the pulses where appropriate. Section 2 introduces the theory behind WURST pulses, including the simple mathematical formulae defining their characteristic amplitude and phase modulations, as well as brief descriptions of how they function in the adiabatic and non-adiabatic regimes. Subsequent sections review the various ways in which they have been applied in solid-state NMR over the past decade or so. It is hoped that this article will encourage further explorations into the properties and potential uses of these versatile pulse shapes.
Section snippets
Amplitude and phase modulation
In their original publication, Kupče and Freeman acknowledged that the acronym WURST was inspired by the sausage-like shape of the radiofrequency (RF) amplitude profile [1]. In fact, the shape of these pulses can vary significantly according to a user-specified parameter N, and various examples of WURST-N shapes are shown in Fig. 1a. A general expression describing this time-dependent amplitude ω1(t) iswhere ωmax is the maximum RF amplitude and τw is the pulse
Broadband decoupling
Although generally more useful for solution-state NMR, a brief discussion of the application of WURST pulses to broadband decoupling is included here since this was Kupče and Freeman's original intended application for these pulses [1].
As NMR spectroscopy is carried out at higher magnetic fields, broader decoupling bandwidths are required to cover the full chemical shift range of nuclei such as 13C. WURST pulses can be used to decouple 13C nuclei in solution-state 1H NMR experiments by
Frequency dispersed echoes
In the solid state, anisotropic interactions such as chemical shielding or quadrupolar coupling can broaden the NMR signal over extremely wide frequency ranges, and powder patterns with widths measured in MHz are not uncommon. Patterns widths in excess of 250 kHz are beyond the excitation bandwidth of standard RF pulses and require specialised “ultra-wideline” approaches to observe [13]. Such spectra are generally extremely sensitive to subtle changes in the surrounding electronic structure,
Broadband cross polarisation
Cross polarisation (CP) is commonly used in solid-state NMR to boost the signal from insensitive X nuclei such as 13C by transferring the larger polarisation across from a higher frequency nucleus (typically 1H). Conventionally, this transfer is achieved during a contact period by spin locking the transverse 1H magnetisation and irradiating the X nucleus at the Hartman–Hahn match condition, ν1(1H)=ν1(X). This is a robust approach, and 13C CPMAS combined with decoupling of the 1H nuclei during
Half-integer spin quadrupolar nuclei
The concept of enhancing the NMR signal from the central transition (CT) of a half-integer quadrupolar nucleus by irradiating the satellite transitions (STs) prior to the excitation pulse is now well-established in solid-state NMR. By either saturating or inverting the STs, the population difference across the CT can be increased by a factor of S+½ or 2S respectively, where S is the nuclear spin number. This is illustrated in Fig. 15. Note that for half-integer quadrupoles with spin numbers of
Spectral editing
Grandinetti and co-workers exploited the ability of a WURST pulse to selectively invert a single set of ST spinning sidebands to carry out spectral editing experiments [46]. They looked at a mixture of Rb2SO4 and RbClO4, for which the 87Rb ST signals from the three different rubidium sites are better resolved under MAS than the CT signals due to the smaller second-order quadrupolar broadening. Their experiment consisted of three pulses, (π/2)CT–(WURST π)ST–(π/2)CT. The CT signal from all sites
Direct and indirect 14N overtone NMR
While WCPMG can be used to acquire ultra-wideline 14N NMR spectra as discussed above, the resulting powder patterns are without exception very strongly overlapped and the resolution is therefore low, restricting the utility of this approach to samples with a small number of distinct nitrogen sites. This overlap is due to the very large first-order quadrupolar broadening, which vastly exceeds the chemical shift range of nitrogen. Overtone NMR spectroscopy provides a potential way around this
Symmetry-based recoupling under MAS
The J coupling interaction can be exploited in NMR spectroscopy to observe through-bond correlations between nuclei. In the solid state, magic angle spinning is used to achieve a high resolution by averaging a variety of anisotropic interactions, and the J coupling (or other interactions) can then be selectively re-introduced using tailored RF pulse sequences synchronised with the sample rotation. Meier and co-workers have used WURST pulses as a building block for symmetry-based J recoupling in
Summary and outlook
This article has provided an overview of WURST pulses and their applications in solid-state NMR spectroscopy. Despite being developed by Kupče and Freeman with a specific solution-state application in mind, they have proven to be extremely useful in a very broad range of solid-state experiments. As adiabatic inversion pulses they can be employed for more efficient broadband cross polarisation, signal enhancement, spectral editing and symmetry-based recoupling. As non-adiabatic excitation and
Acknowledgments
I thank the numerous authors whose contributions are highlighted in this article. In particular, Kupče and Freeman are acknowledged for obvious reasons, as are Bhattacharyya and Frydman, whose 2007 paper [4] kick-started my interest in WURST pulses. I am grateful to Prof Robert Schurko, Dr Christopher Ratcliffe and Prof Maria Forsyth for providing me with the opportunity to pursue this interest over the past six years.
Luke A. O'Dell is a Senior Lecturer in the Institute for Frontier Materials at Deakin University (Australia). He obtained his PhD at the University of Warwick (UK) in 2007, and carried out post-doctoral research in solid-state NMR with Prof Mark Smith (Warwick) and Prof Robert Schurko (University of Windsor, Canada). He has also worked as a Research Associate at Canada's National Research Council. His research interests focus on the development of new solid-state NMR techniques for insensitive
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Luke A. O'Dell is a Senior Lecturer in the Institute for Frontier Materials at Deakin University (Australia). He obtained his PhD at the University of Warwick (UK) in 2007, and carried out post-doctoral research in solid-state NMR with Prof Mark Smith (Warwick) and Prof Robert Schurko (University of Windsor, Canada). He has also worked as a Research Associate at Canada's National Research Council. His research interests focus on the development of new solid-state NMR techniques for insensitive quadrupolar nuclei, with a particular emphasis on nitrogen-14, as well as applications to study structure and dynamics in functional materials.
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