Indirect covariance homonuclear spectra

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. 

The resulting spectrum, Cindirect/ is a symmetric matrix whose axes are defined by the indirect dimension, F1. Applying indirect covariance processing to a non-symmetric data matrix such as heteronuclear 1H-13C HSQC-TOCSY spectrum affords a symmetric homonuclear 13C-13C TOCSY spectrum analogous to that described originally by Turner.22... 

Doubly indirect covariance (DIG) yields a symmetric correlation map [13]. It can further be considered as a bridge to the generalization of indirect covariance. It implies that correlation spectra, that are used for indirect covariance, themselves may be a creation of a previous covariance transformation. Scheme 5.1 serves as an example to elucidate this perspective. In Scheme 5.1A and B, indirect covariance generates homonuclear spectra. Part (C) leads to the creation of a heteronuclear correlation, which itself can be taken as component spectrum for transformation (A) or (B). It is apparent that Scheme 5.1 represents an oversimplification of the types of indirect covariance treatment. A wider variety of spectra that can be obtained by UIC processing is collected in Table 5.1. 

The direct covariance matrix multiplication of a homonuclear NMR spectrum yields a homonuclear covariance map whose square root is equivalent to the NMR spectrum obtained from Fourier transformation. As can be readily seen from Fig. 5.1 A, the higher resolution of the direct dimension is mapped onto the indirect dimension. Hence, a symmetric spectrum... 

---