Covariance NMR spectroscopy

Zhang EL, Bruschweiler-Li L, Bruschweiler R (2010) Simultaneous de novo identification of molecules in chemical mixtures by doubly indirect covariance NMR spectroscopy. J Am Chem Soc 132(47) 16922-16927... 

An aspect, which has not been very intensively exploited in covariance NMR spectroscopy, is contained in Eq. (5.5). While the real part of a... 

N. Trbovic, S. Smirnov, F. Zhang, R. Brueschweiler, Covariance NMR spectroscopy by singular value decomposition, J. Magn. Reson. 171 (2004) 277. 

B. Hu, J.-P. Amoureux, J. Trebosc, Indirect covariance NMR spectroscopy of through-bond homo-nuclear correlations for quadmpolar nuclei in solids imder high-resolution, Solid State Nucl. Magn. Reson. 31 (2007) 163. 

Two-dimensional covariance NMR spectroscopy, which was originally established to extract homonuclear correlations (HOMCOR), has been extended to include heteronuclear correlations (HETCOR) by Takeda et al. In a 2D chemical shift correlation experiment, and N... 

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. 

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 pubhshed by Briischweiler [59]. 

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. 

To put the idea of covariance NMR spectroscopy using mathematical, thus unambiguous, expressions, let us consider a pair of vectors X =... 

Until recently, the scope of covariance NMR spectroscopy had been limited to HOMCORs. (Note that, in indirect covariance spectroscopy, HETCORs are used to obtain HOMCORs.) Extension of covariance spectroscopy to include HETCORs was reported by Takeda et al, who showed that the covariance processing can be used to obtain HETCORs together with HOMCORs in H- H dipolar coupling-mediated chemical... 

Even though the same data set can be used to obtain a pair of the conventional 2D-FT spectra (Figs. 23A and 25C and D), the covariance-processed HOMCOR/HETCOR spectrum retain the merits that have already been confirmed for the original covariance NMR spectroscopy the spectral resolution along the indirect dimension is determined by that... 

Even though phase covariance shares the term with covariance NMR spectroscopy, they are distinct from each other the former deals with correlation between the phase of the rf pulse and that of the resonance line of a one-dimensional spectrum, while the latter concerns exchange of magnetizations between nuclear spins. For simpHcity, we consider a single-pulse sequence with the phase of the rf pulse

dimensional spectra are obtained with consecutively incremented

correlation between the spectral phase and rf-pulse phase results in diagonal distribution, as shown in Fig. 26c. 

In this chapter, we have reviewed the covariance approach—one promising strategy toward efficient acquisition of information from a limited number of data sets. We have seen the fruitful outcomes of covariance NMR spectroscopy, including its applications to soHd-state NMR studies of chemically or biologically important systems, its improvements to enhance the efficiency further, and its modifications to accommodate various needs of structural analysis. In addition, the question regarding the inner-product spectroscopy, to be answered in future studies, has been posted. At the moment of writing this review, covariance NMR spectroscopy is rather young and the number of relevant papers is not many. From... 

I am grateful to Yuichi Masuda, Tatsuya Yatagawa, Yasushi Kusakabe, Yasuto Noda, Masashi Fukuchi, K. Takegoshi, Olivier Lafon, JuHen Trebosc, and Jean-Paul Amoureux for giving me opportunities to enjoy exploring solid-state covariance NMR spectroscopy. I thank Yasushi Kusakabe for his comments and su estions. 

---