Double quantum frequency

Thus, if the vertical axis representing the double-quantum frequencies is defined by v, and the horizontal axis representing the chemical shifts of the two carbons A and X is defined by V2, then both pairs of C satellites of nuclei A and X will lie on the same row (at + Vx), equidistant from the diagonal. This greatly facilitates identification. The advantage is that no overlap can occur, even when fir.c values are identical, since each pair of coupled C nuclei appear on different horizontal rows. 

TABLE 1 Chemical shifts, offsets relative to the transmitter, calculated and observed double quantum frequencies for selected 13C resonances of strychnine (1)... 

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.

Artifactual peaks are even more dangerous than noise since they may not always be immediately recognized and may lead to erroneous assignments. An important source of artifacts is instability in the steady-state condition, e.g. if the relaxation delay is set too short. A commonly encountered example is presented by peaks which occur at the double quantum frequencies in DQF-COSY spectra. For detailed treatments of aspects of noise and artifacts see [4, 5]. 

The AB and AX systems of all 13C —13C bonds appear in one spectrum when the INADEQUATE pulse sequence (Fig. 2.48) is applied. Complete interpretation usually becomes difficult in practice due to signal overlapping, isotope shifts and AB effects (Section 2.9.4). A separation of the individual 13C— 13C two-spin systems by means of a second dimension would be desirable. It is the frequency of the double quantum transfer (d e) in Fig. 2.48 which introduces a second dimension to the INADEQUATE experiment. This double quantum frequency vDQ characterizes each 13CA — I3CX bond, as it depends on the sum of the individual carbon shieldings vA and vx in addition to the frequency v0 of the transmitter pulse located in the center of the spectrum if quadrature detection is applied [69c, 71] ... 

To conclude, the second dimension is introduced if the switching time ti (Fig. 2.48) is incremented in a series of single experiments so as to reach all possible double quantum frequencies vDQ within a sample molecule by the reciprocals l/t1. Again, the acquired FID signals will depend on two variable times t1 and t2, respectively. A first Fourier transformation in the t2 domain generates 13C — 13C satellite spectra. The corresponding AB or AX type doublet pairs, however, are modulated by the individual double quantum frequencies which characterize each AB or AX pair. The second Fourier transformation in the tl domain liberates the double quantum frequency as the second dimension Maximum AB or AX 13C—13C subspectra are observed at the corresponding double quantum frequencies, so that each doublet appears with unique coordinates,... 

In this arrangement the typical easy-to-analyse INADEQUATE appearance is lost. The 2D plot would contain 29Si double-quantum frequencies (i.e. sum of the chemical shifts of the two coupled silicon nuclei) along axis FI and XH frequencies along the F2 axis. A pair of cross-peaks at the same 29Si double-quantum frequency would indicate a Si—Si fragment two cross-peaks with the same XH frequency indicate a Si—Si H fragment. 

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. 

From Eqs. 6.29 and 6.34 we know that the frequencies of the single quantum transitions include both the chemical shift difference and the coupling constant, and we saw in Eq. 11.54 that the single quantum coherence terms evolve at those frequencies. From Eq. 6.29 we can see that the expression for the double quantum frequency E4 — E, would not depend on J, and the difference 3 — E2 likewise does not depend on J for weakly coupled spins. Thus zero quantum and double quantum coherences evolve as though there were no spin coupling. 

The period t is used to encode the double quantum frequency domain. The resulting 2D display contains a horizontal axis in V2 (the normal frequencies) and a vertical axis that is a double quantum domain represented by the sum of the frequencies of coupled nuclei ( U2 )- The latter frequencies are referenced to a transmitter frequency at zero. 

The one-dimensional variations of the INADEQUATE experiment suppress the intense C- C main signal, so that both AX and AB systems appear for all C— C bonds in one spectrum. The two-dimensional variations segregate these AB systems on the basis of their individual double quantum frequencies (the sum of the C shifts of A and B) as a second dimension. Using the simple example of 1-butanol (12), Fig. 2.12a demonstrates the use of the two-dimensional INADEQUATE technique for the purpose of structure elucidation. For every C—C bond the contour diagram gives an AB system parallel to the abscissa with double quantum frequency as ordinate. By following the arrows in Fig. 2.12a, the carbon connectivities of butanol can be derived immediately. The individual AB systems may also be shown one-dimension-ally (Fig. 2.12b) the C- C coupling constants often provide useful additional information. 

Marcei, T. H., and Freeman, R. (1982) Echoes and antiechoes in coherence transfer NMR determining the signs of double-quantum frequencies. J. Magn. Reson. 48(1), 158-163. Braun, S., Kalinowski, H.-O., and Berger, S. (1996) 100 and More Basic NMR Experiments A Practical Course, VCH, New York. 

Schematic spectrum showing the relationship between the single- and double-quantum frequencies for coupled spins.

Homonuclear correlation experiments are not just restricted to the standard COSY experiment, but also include the TOCSY and INADEQUATE experiments. The separation of TOCSY and INADEQUATE from the homonuclear COSY experiment is based on the different coherence evolution and transfer processes involved. Thus the TOCSY experiment is based on cross-polarization in contrast to the polarization transfer used in the homonuclear COSY experiments. INADEQUATE experiments are characterized by the double quantum state of two scalar-coupled nuclei during the tl period such that the second dimension (fl) is scaled into a double quantum frequency. Nevertheless these experiments can all be considered together because they are based on homonuclear scalar coupling and the fl and f2 dimension of the corresponding 2D spectra are related to the same nucleus. 

Polarization transfer and detection of coherences which evolve due to the chemical shift of two coupled nuclei in the tl period (double quantum frequency in fl)... 

Homonuclear correlation of nuclei of with low natural abundance, spin-echo sequence for scalar coupling evolution, DQF to suppress unwanted coherences, a double quantum frequency scaled dimension in 2D spectra... 

Applying the idea of using multiple quantum coherence to correlate protons has also been explored. Mated and Freeman [60] reported the first experimental demonstration of proton double quantum correlated spectroscopy. The Fi axis in these experiments is used to present H chemical shift in the usual fashion. In contrast, the Fj axis is used for the double quantum frequency axis. Protons correlated to one another via double quantum coherence will exhibit a response in Fj at the algebraic sum of the offsets of the coupled resonances relative to the transmitter frequency. A scant few apphcations have been reported including an exploratory study of strychnine (2) [61] and the structural characterization of the marine natural product plumericin [62],... 

INADEQUATE (Incredible Natural Abundance Double Quantum Transfer Experiment). On one axis one has the C-NMR spectrum while on the other axis the double quantum frequencies are present (Englert 1985). A direct carbon-carbon coupling is indicated by a pair of doublets at a certain double quantum frequency. In this experiment, in fact the C satellites of C signals are observed. It must be clear that this method has a low sensitivity, because two adjacent C nuclei are required. 

The INADEQUATE and APT spectra for the major product are shown in Figure 7. In an INADEQUATE spectrum, the pairs of adjacent carbons, and hence the connectivity, can be mapped out similarly to a COSY spectrum. The major difference here is that the original spectrum is not on the diagonal in an INADEQUATE spectrum (as in a COSY spectrum), but is in the x-axis direction (= normal C frequencies) along the line = 0 (residual single quantum signals). The y-axis is the frequency v, the double quantum frequency that is the sum of the frequencies of the two coupled nuclei referenced to a transmitter frequency at zero. The peaks arising from two coupled nuclei (here adjacent carbons) with shifts and Vj, have coordinates of (( a + ) where X is the frequency of the carbon... 

The fourth class of experiments is multiple quantum spectroscopy such as 2D-INADEQUATE. In these experiments, homonuclear shifts (such as those of are plotted along the fi dimension. If two or more nuclei are /-coupled to each other, then they can be made to share a common multiple quantum precession frequency during the period. In the 2D-INADEQUATE experiment if and Cg are coupled to each other, then the signals from each of these components will precess at a common double quantum frequency (/ + in the dimension. 

The first Fourier transformation in the 2 domain affords a series of satellite spectra in which the signals are modulated by the corresponding double quantum frequencies. A second Fourier transformation in the domain results in a two-dimensional plot which contains chemical shift and C- C coupling information on the t2 axis and C—C scalar coupling information on the axis. Since bonded nuclei share a common... 

Peaks due to methylene-methine coupling appear at their normal frequency 4-5 ppm along /2 and in the 6-7 ppm in the /i (double quantum frequency) dimension. These peaks, due to smaller vicinal couplings, are prominent in the speamm in part B, collected with a delay of 18 ms. Since only rrm methylene groups can show correlations with both rr and mr methine groups, this unique spin system can be unambiguously identified. Qn the other hand, rmr methylenes can only produce correlations with mr methine protons. In part B, obtained with an 18 ms delay, prominent correlations from mm methine to mmr and mmm methylene proton resonances are also observed. 

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