Double-quantum spectra

Double quantum spectra give very similar information to that obtained from COSY i.e. the identification of coupled spins. Each method has particular advantages and disadvantages ... 

Figure 4 Covariance C double-quantum spectra of C-labeled tyrosine obtained from the same data source as that used to obtain the conventional double-quantum spectrum shown in Fig. 3. (A) was obtained from 125 data arrays. Even though the array length was intentionally reduced to only 25, the covariance spectrum shows little degradation, as demonstrated in (B). Reprinted with permission from Ref. [74]. Copyright 2008 American Institute of Physics.

Figure 2.10 (a) 2D H- N HETCOR correlation spectrum of fully N-labeled complex [(=SiO)2Ta(=NH) (NHj)] and [=Si- NH2] and comparison with 2D double quantum (b) and triple quantum (c) correlation spectra. An exponential line broadening of 100 Hz was applied to all the proton dimensions before Fourier transform. The dotted gray lines correspond to the resonances of the tantalum NH, NH2 and NH3 protons. The dotted circles underline the absence of auto-correlation peaks for the imido proton in the double quantum spectrum (b), and for the amido proton in the triple quantum, spectrum (c) (from Reference [9]). 

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.

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.

Peak three corresponds to the equivalent P atoms of the P2O7 unit, the other four peaks correspond to the two inequivalent PO4 units, each split by its proximity to two configurations of the P2O7 unit which differ in the position of the bridging oxygen. B. 2D double-quantum P spectrum demonstrating the connectivity between two equivalent coupled P nuclei (P2O7 unit) with the same chemical shift (— 18.6 ppm). The fl2 dimension is the 2D spectrum filtered by the double quantum, the fl] dimension is the double quantum spectrum. From Pichot et al. (2001) by permission of Elsevier Science. 

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].

We see that the single-quantum spectrum consists of three doublets of doublets, the double-quantum spectrum of three doublets and the triple-quantum spectrum of a single line. This illustrates the idea that as we move to higher orders of multiple quantum, the corresponding spectra become simpler. This feature has been used in the analysis of some complex spin systems. 

Double-quantum spectrum for a three-spin system... 

Schematic two-dimensional double quantum spectrum showing the multiplets arising from evolution of doublequantum coherence between spins 1 and 3. If has been assumed that J12 > J13 > J23.

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. 

In COSY the cross-peak multiplet is anti-phase in both dimensions, whereas in a double-quantum spectrum the multiplet is only anti-phase in F2. This may lead to stronger peaks in the double-quantum spectrum due to less cancellation. However, during the two delays A magnetization is lost by relaxation, resulting in reduced peak intensities in the double-quantum spectrum. 

There are no diagonal-peak multiplets in a double-quantum spectrum, so that correlations between spins with similar offsets are relatively easy to locate. In contrast, in a COSY the cross-peaks from such a pair of spins could be obscured by the diagonal. 

In more complex spin systems the interpretation of a COSY remains unambiguous, but the double-quantum spectrum may show a peak with F coordinate (f2 + 2b) and F2 co-ordinate f2 (or f2t.) even when spins A andB are not coupled. Such remote peaks, as they are called, appear when spins A and B are both coupled to a third spin. There are various tests that can differentiate these remote from the more useful direct peaks, but these require additional experiments. The form of these remote peaks in considered in the next section. 

As commented on above, in NOESY all that is required to change from cosine to sine modulation is to shift the phase of the first pulse by 90°. The general recipe is to shift the phase of all the pulses that precede tx by 90°/l/ 11, where pl is the coherence order present during tv So, for a double quantum spectrum, the phase shift needs to be 45°. The origin of this rule is that, taken together, the pulses which precede t] give rise to a pathway with Ap=pv... 

Two-dimensional multiple-quantum (2D2Q) C1 NMR spectra of systems exhibiting electric quadrupolar effects have been obtained. In such spectra the single quantum spectrum is displayed along one axis against the double quantum spectrum along the other. Such spectra give information about the quadrupolar interactions present in ordered systems. 

Figm 53 The 500-MHz 2D-NMR spectra of PVC (a) H double quantum spectrum (INADEQUATE), and (b) relayed-COSY relay spectrum. Reprinted with permission from Mirau, P. A. Bovey. E. A. Macmmoleculesi9i6. 19, 210. Copyright 1986 American Chemical Society. 

Figure 5.37 (a) Conventional phase-sensitive COSY spectrum of basic pancreatic trypsin inhibitor, (b) Double-quantum filtered (DQF) phase-sensitive COSY spectrum of the same trypsin inhibitor, in which singlet resonances and solvent signal are largely suppressed. Notice how clean the spectrum is, especially in the region near the diagonal line. (Reprinted from Biochem. Biophys. Res. Comm. 117, M. Ranee, et al., 479, copyright (1983) with permission from Academic Press, Inc.)... 

The DQF (double-quantum filtered)-COSY spectrum of an isoprenyl coumarin along with H-NMR data are shown. Determine the H/ H homonuclear interactions in the DQF-COSY spectrum. 

Figure 7.25 Homoniiclear double-quantum filtered COSY spectrum (400 MHz) of 8-mMangiotensin II in H,0 recorded without phase cycling. Magnetic field gradient pulses have been used to select coherence transfer pathways. (Reprinted from J. Mag. Reson. 87, R. Hurd, 422, copyright (1990), with permission from Academic Press, Inc.)...

Figure 12 Expansion of the positive double quantum frequency range of the n,l-ADEQUATE spectrum shown in Figure 1. The correlation responses for the three possible carbon-carbon correlations from C14 are shown (see also Table 4 and 39,40, and 41). The very weak 2JCH correlation from H13 to C14 at the C14 + C21 DQ frequency is shown in the inset.

Fig. 2 (a) DRAMA pulse sequence (using % = t/2 = rr/4 in the text) and a representative calculated dipolar recoupled frequency domain spectrum (reproduced from [23] with permission), (b) RFDR pulse sequence inserted as mixing block in a 2D 13C-13C chemical shift correlation experiment, along with an experimental spectrum of 13C-labeled alanine (reproduced from [24] with permission), (c) Rotational resonance inversion sequence along with an n = 3 rotational resonance differential dephasing curve for 13C-labeled alanine (reproduced from [21] with permission), (d) Double-quantum HORROR experiment along with a 2D HORROR nutation spectrum of 13C2-2,3-L-alanine (reproduced from [26] with permission)... 

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 ... 

Table 25 summarizes the XH and 13C NMR spectra of 75. The proton resonances were analyzed by double quantum filtered H—H shift-correlated COSY spectrum and... 

Mono(hydride) zirconium species grafted on a silica surface show a high reactivity toward alkanes. This system has been studied using modern 2D NMR techniques, such as double quantum (DQ) rotor synchronized 2D H MAS and C- H HETCOR, to investigate the mechanism of formation of a zirconium bis(hydride) species and the simultaneous generation of silicon mono- and bis(hydride) species [111]. Figure 11.4 shows the H MAS NMR spectrum and DQ rotor-synchronized... 

The double quantum filter eliminates or at least suppresses the strong signals from protons that do not experience J-coupling, e.g. the solvent signal, which would otherwise dominate the spectrum and possibly be a source of troublesome tl noise. Compared to a phase-sensitive but non-DQ-filtered COSY with pure absorption lineshapes for the cross peaks but mixed lineshapes for the diagonal peaks, the phase-sensitive, DQ-filtered COSY has pure absoiption lineshapes throughout. 

H/ H-double quantum filtered COSY Note that with this experiment both the diagonal and the cross peaks may be phased to pure absorption. Therefore it is best to select diagonal peaks at the extremes and in the center of the spectrum for phase adjustment. The cros.s peaks when correctly phased consist of positive and negative peaks, which are anti-phase with respect to the active, and are in-phase with respect to the passive coupling(s). 

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