1. Applications of 1H-15N Long-Range Heteronuclear Shift Correlation and 15N NMR in Alkaloid ChemistryGary E. Martin and Antony J. Williams2. Solid-state Covariance NMR SpectroscopyKazuyuki Takeda3. Recent Advances in Chlorine, Bromine, and Iodine Solid-State NMR SpectroscopyPatrick M. J. Szell and David L. Bryce4. Recent Advances in Small Molecule NMR: Improved HSQC and HSQMBC Experiments Laura Castañar and Teodor Parella5. A Review of 91Zr Solid-State Nuclear Magnetic Resonance SpectroscopyBryan E.G. Lucier and Yining Huang
Chapter Two
Solid-State Covariance NMR Spectroscopy
Kazuyuki Takeda Division of Chemistry, Graduate School of Science, Kyoto University, Kyoto, Japan
Abstract
Covariance NMR spectroscopy allows acquisition of spin-spin correlation in a more efficient way compared to the traditional two-dimensional Fourier-transformation NMR spectroscopy, leading to reduction in the experimental time or increase in the sensitivity of the spectrum obtainable within a given experimental time. This chapter summarizes recent works on covariance NMR, focusing on its applications to solid-state NMR spectroscopy. In addition to a brief survey of the covariance spectroscopy, an open question of whether "inner-product" spectroscopy is more natural is posted. The usefulness of covariance NMR spectroscopy is presented by exploring its applications to solid-state systems of chemical/biological interest. A number of recent reports to further improve its efficiency or to extend the scope of its applicability are reviewed.
Keywords
Time-saving schemes
Covariance
Indirect covariance
Dual transformation
HETCOR
Phase covariance
1 Introduction
In NMR spectroscopy, the sensitivity has been the issue of general interest. The technological/methodological advances in sensitivity enhancement made so far had enabled one to reveal hitherto inaccessible structural information, strengthening NMR spectroscopy as a means for chemical analysis. Further progress in future is anticipated to push NMR spectroscopy, and thereby science, forward. That is why the sensitivity enhanced NMR continues and will continue to be an active research subject matter in the community.
The strategies toward sensitivity enhancement are diverse. One way is to increase nuclear spin polarization and thereby the macroscopic nuclear magnetization. This can be done straightforwardly either by increasing the static magnetic field or decreasing the sample temperature so as to raise the equilibrium Boltzmann population difference over the Zeeman levels. Recent remarkable magnet technology realized highly homogeneous fields of up to 23.48 T or above, corresponding to the proton resonance frequency that exceeds 1 GHz. Drastic signal enhancement is possible through nuclear hyperpolarization, which can be realized by dynamic nuclear polarization [1], optical pumping [2], and the Haupt effect [3-8].
The NMR sensitivity can also be enhanced by improving the efficiency of signal detection, instead of, or in combination with, nuclear-spin hyperpolarization. By cooling the NMR sample coil down to cryogenic temperatures, the coil resistance can be reduced. As a result, the Q-factor of the resonance circuit increases so that higher signal voltages can be extracted from the nuclear spin system. In addition, the thermal noise is expected to be suppressed as decreasing the temperature, and the overall effect is to enhance the signal-to-noise ratio. Thermal insulation between the coil and the sample was a technical challenge but had been overcome. In practice, it is necessary to cool the preamplifier as well as the sample coil, in order to gain satisfactory enhancement in the sensitivity. Probes incorporating such features are known as cryo probes [9-11] and nowadays commercially available for liquid-state NMR. Cryogenically cooled MRI probes [12, 13] and solid-state magic angle spinning (MAS) probes [14-16] have also been reported.
The detection sensitivity can be optimized by employing application-tailored experimental systems. For cases where NMR spectra of two separate spin species need to be measured one after another, an NMR system with parallel receivers [17, 18] could improve the throughput of research. When the sample of interest is unconventionally tiny, microcoil probes may be the choice [19-24]. For extremely small samples, force detection can be advantageous over the conventional Faraday detection [25-29].
In addition to such physical ways toward sensitivity enhancement, development of acquisition/data-processing methods is also an important trend. The latter has been motivated by the necessity of extracting information of chemical interest within a limited experimental time and with a reasonable cost. So far, a number of approaches have been proposed to reconstruct one-dimensional or multidimensional spectrum from a smaller number of data sets than the previous schemes require. The first example of such time-saving protocols is the maximum entropy method (MEM), which was originally developed in astrophysics [30]. Its application to NMR spectroscopy was first reported by Sibisi and coworkers [31, 32]. MEM soon found wide applications [33-37] and was combined with nonuniform sampling (NUS) scheme [38, 39]. Since then, NUS has attracted considerable interest and has been incorporated into various protocols. Other noteworthy schemes include the Hadamard spectroscopy [40-44], reduced dimensionality [45-50], single scan two-dimensional spectroscopy or ultrafast two-dimensional spectroscopy [51-54], GFT NMR [55-57], covariance spectroscopy [58, 59], recursive multidimensional decomposition [60], compressed sensing [61-66], radial sampling [67], noise and artifact suppression using resampling [68], and so on.
Even though these methods make full use of mathematics and may look formidable to NMR researchers majoring in chemistry, they are all valuable in the sense that they lifted up the limitation of NMR spectroscopy, enabling us to gain such chemical information that has not been accessible so far. In particular, the idea of covariance NMR, put forth by Brüschweiler and Zhang in solution NMR [58], has lead to a number of recent applications. The purpose of this review is to summarize recent works on covariance NMR, focusing on its applications to solid-state NMR spectroscopy. In Section 2, we overview the concept of covariance NMR, leaving at the end of the section an open question on what the author call "inner-product" NMR spectroscopy. Section 3 introduces applications of covariance NMR to solid-state systems of chemical/biological interest. In Section 4, we review sampling schemes that make the time-saving covariance NMR spectroscopy further time saving. Section 5 is devoted to describe various variants of covariance NMR spectroscopy.
2 Overview of Covariance NMR Spectroscopy
In this section, we take a brief look at what the covariance NMR spectroscopy is. For more detailed and complete description, the reader may refer to the pioneering paper published by Brüschweiler [59].
The main arena in which covariance NMR is used is two-dimensional (2D) correlation spectroscopy [69]. For a simple example, let us consider a three-spin system consisting of spins A, B, and C, as schematically depicted in Fig. 1A, and suppose that spins A and B are relatively close to each other, whereas spin C is at a distance so that J/dipolar interactions are effective only between A and B. One can employ the conventional 2D Fourier transform (2D-FT) NMR to obtain a 2D spectrum that looks like the one in Fig. 1B, where the cross-peak tells the existence of the correlation, and thereby the spatial proximity, between the relevant spins. Such information is very useful, as it provides structure constraint that can be used for studies of higher-order structure of biomolecules.
Figure 1 (A) A schematic drawing of a system of three spins labeled 1, 2, and 3. When spin 1 and spin 2 have correlation while spin 3 is isolated, the cross-peak between 1 and 2 appears, as depicted in (B).
One possible and frequent problem with 2D-FT is that relatively a large number of data arrays need to be acquired, since the spectral resolution along the indirect dimension is determined by the number of the data arrays. In particular, when the signal-to-noise ratio of the individual free induction decays (FIDs) is low, as is often the case, signal averaging over many times is necessary for each evolution time, making the overall experimental time even longer. It is not unusual for one to spend several days or more just to obtain a single 2D-FT spectrum. However, in order to improve the throughput of research, it is highly desirable to employ more efficient ways that can be used to extract the necessary information sooner.
In covariance NMR spectroscopy, pulse sequences to be used are the same as those in 2D-FT, but much fewer amounts of data sets along the indirect dimension suffice to produce a 2D spectrum similar to that obtained with 2D-FT.
Covariance is a concept in statistics, giving a measure of how much a pair of variables change in a correlated way. To explain the idea proposed by Brüschweiler of applying the covariance processing to NMR, let us suppose that we have an array of one-dimensional spectra obtained with incremented evolution time, as schematically described in Fig. 2. In this example, we have a homonuclear system of three spins, labeled with i, j, and k. For peak i and peak j, the ways that the peak amplitudes change with the...
