Covariance spectroscopy

R. Bmschweiler, F. Zhang, Robust deconvolution of complex mixtures by covariance spectroscopy, Angew. Chem. Int. Ed. 46 (2007) 2639—2642. 

Y. Chen, F. Zhang, W. Bermel, R. Brueschweder, Enhanced covariance spectroscopy from minimal datasets, J. Am. Chem. Soc. 128 (2006) 15564. 

Y. Li, B. Hu, Q. Chen, Q. Wang, Z. Zhang, J. Yang, et al.. Comparison of various sampling schemes and accumulation profiles in covariance spectroscopy with exponentially decaying 2D signals. Analyst 138 (2013) 2411. 

E.C. Lin, S.J. OpeUa, Covariance spectroscopy in high-resolution multi-dimensional solid-state NMR, J. Magn. Reson. 239 (2014) 57. 

F. Zhang, N. Trbovic, J. Wang, R. Bmeschweiler, Double-quantum biased covariance spectroscopy application to the 2D INADEQUATE experiment, J. Magn. Reson. 174 (2005) 219. 

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 liquid solutions, nuclear spins are correlated through J-couplings, whereas in solids dipolar interactions come into play as well. The first report on the application of covariance to soHd-state NMR was published by Hu et al. in which an indirect covariance homonuclear correlation (HOMCOR) spectrum was obtained from a 2D-FT heteronuclear correlation (HETCOR) spectrum. The indirect covariance scheme, which will be discussed in Section 5.1, contrasts with the original direct covariance spectroscopy, where the covariance processing is performed over an array of one-dimensional spectra. 

Hu et al. also reported on the first appHcation of direct covariance spectroscopy to sohd-state NMR to reveal correlations in amino acids. 

The idea of NUS has found considerable interest and applications in the context of the conventional 2D-FT schemes. NUS is also compatible with the covariance spectroscopy. Lafon et al. reported on natural abundance deuterium NMR spectroscopy of 2-ethyloxirane (C4H8O) and methyl vemoleate (C19H34O3) dissolved in chiral polypeptide liquid crystals... 

Indirect covariance spectroscopy was proposed by Zhang and Briischweiler [85] soon after publication of their pioneering work on covariance spectroscopy [58]. Its apphcation to soHd-state NMR was reported a few years later by Hu et al. [86]. The procedure of the indirect covariance spectroscopy starts with a 2D Fourier-transformed FIETCOR spectrum. This is in contrast to the original direct covariance spectroscopy, in which covariance processing is appHed to an array of one-dimensional spectra so that Fourier transformation is performed only with respect to the direct dimension. From a single I—S 2D FiETCOR spectrum, a pair of HOMCOR spectra are... 

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... 

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