Double quantum coherence spectrum

As an example of the measurement of cross-correlated relaxation between CSA and dipolar couplings, we choose the J-resolved constant time experiment [30] (Fig. 7.26 a) that measures the cross-correlated relaxation of 1H,13C-dipolar coupling and 31P-chemical shift anisotropy to determine the phosphodiester backbone angles a and in RNA. Since 31P is not bound to NMR-active nuclei, NOE information for the backbone of RNA is sparse, and vicinal scalar coupling constants cannot be exploited. The cross-correlated relaxation rates can be obtained from the relative scaling (shown schematically in Fig. 7.19d) of the two submultiplet intensities derived from an H-coupled constant time spectrum of 13C,31P double- and zero-quantum coherence [DQC (double-quantum coherence) and ZQC (zero-quantum coherence), respectively]. These traces are shown in Fig. 7.26c. The desired cross-correlated relaxation rate can be extracted from the intensities of the cross peaks according to ... 

Fig. 14. The pulse sequence for recording the double-quantum 2H experiment.37 The entire experiment is conducted under magic-angle spinning. This two-dimensional experiment separates 2H spinning sideband patterns (or alternatively, static-like 2H quadrupole powder patterns) according to the 2H double-quantum chemical shift, so improving the resolution over a single-quantum experiment. In addition, the doublequantum transition frequency has no contribution from quadrupole coupling (to first order) so, the double-quantum spectrum is not complicated by spinning sidebands. Details of molecular motion are then extracted from the separated 2H spinning sideband patterns by simulation.37 All pulses in the sequence are 90° pulses with the phases shown (the first two pulses are phase cycled to select double-quantum coherence in q). The r delay is of the order 10 gs. The q period is usually rotor-synchronized.

Multiple-quantum ESR recently developed for measuring distances between spins (r) longer than 12 A is based upon double quantum coherence (DQC) pulsed ESR methods (Freed, 2000 Borbat and Freed, 2000). Introducing an extensive cycling of four-pulse sequence allowed the selection of the only coherence pathway related to dipole-dipole splitting in the homogeneous ESR spectrum. The latter is directly connected to the r value... 

The simulated double-quantum coherence 2D INADEQUATE spectrum of 2-chlorobutane is shown in Figure 13.18. The normal 13C spectrum is plotted along the top. Only the cross peaks appear in the contour plot, and each cross peak appears as a doublet (a pair of dots) at this level of resolution. The separation between these dots, about 35 Hz in this case, is /Cc- Each pair of correlated (by one-bond coupling) cross peaks is indicated by a separate dotted horizontal line, with the midpoint of each line on the diagonal. The F axis is the double-quantum frequency, essentially the sum of the 8v values of the two coupled nuclei. 

Figure 7.21. A. P MAS NMR spectrum of Cd3(P04)2 showing the six resolved P resonances corresponding to the six independent structural sites. B. Two-dimensional P double-quantum spectrum of Cd3(P04)2 correlated to the single-quantum dimension indicating the double-quantum coherences between the six different P resonances. The strongest correlation is between A and B, indicating that A/B is associated with the shortest P-P distance. Similar considerations allow the other resonances to be assigned to the other crystallographic sites on the basis of their X-ray P-P distances. From Dollase et al. (1997) by permission of the American Chemical Society.

Fig. 6.1.6. Two-dimensional time-incremented double quantum experiment on polycarbonate recorded using a single cycle of multiple quantum excitation, and a spinning speed of 14.8 kHz. The f evolution was restricted to double quantum coherences by phase suitable cycling. The oji dimension is, therefore, a double quantum spectrum. The u>2 dimension is a single quantum spectrum [21].

The double-quantum spectrum shows the relationship between the frequencies of the lines in the double quantum spectrum and those in the (conventional) single-quantum spectrum. If two two-dimensional multiplets appear at (h, F2) = (Aa + Qb, Qa) and (QA + Qn, Qy>) the implication is that the two spins A and B are coupled, as it is only if there is a coupling present that double-quantum coherence between the two spins can be generated (e.g. in the previous section, if J13 = 0 the term Bu, goes to zero). The fact that the two two-dimensional multiplets share a common F1 frequency and that this frequency is the sum of the two F2 frequencies constitute a double check as to whether or not the peaks indicate that the spins are coupled. 

The peaks in the 2D DQ spectrum correspond to double-quantum coherences between two spins which must be relatively close neighbors in space in order to contribute significantly to the peak intensity as follows from the strong distance sensitivity of the dipolar coupling. From the existence of the corresponding peaks therefore through space dipolar connectivities can be easily established. 

Zero-quantum coherence has also been recently used as an alternative to double-quantum coherence for establishing carbon-carbon connectivities. This is shown for the C-NMR spectrum of n-butanol in Figure 5.67C. The diagonal lines establish the connectivities between coupled carbons. An advantage of the zero-quantum coherence spectra, which resemble the SECSY spectra in appearance, is that in the latter, one usually encounters a large ridge of unresolved peaks near Fj = 0, but this is largely suppressed in zero-quantum spectra. 

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