Quantum coherences

1 Carbon-Carbon Connectivity Plot (CCCP) by Double-Quantum Coherence 

In an earlier section (5.2.1) we have described the one dimensional INADEQUATE experiment which allowed the study of couplings in 

Double-or multiple-quantum coherence cannot be detected as such but must be converted into single-quantum coherence (or observable magnetization in the -plane) by the application of a selective 180° pulse to the X spin. This results in the introduction of a phase shift of the signals which allows one to distinguish the pairs of doublets due to couplings from the undesired 

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 

The main drawbacks in the procedure are that due to the low sensitivity of the experiment, several hundred milligrams of the compound are required and the spectra need to be recorded for many hours before good spectra can be obtained. However, the power of the method is obvious since the entire carbon framework can be worked out in one experiment by determining the carbon-carbon connectivities. 

Consider, now, the alternative—that at time 4 only a 13C 90y pulse is applied. Then at time 5 

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. 

Except for being unobservable, these coherences (and antiphase coherences, as well) behave much like magnetizations in that they have relaxation times, which are different from those of single quantum coherences. Multiple quantum coherences can be further manipulated to produce observable magnetization, as we shall see in Chapter 12. 

We have seen that the density matrix can be applied in principle to any spin system, but even for the two-spin system the algebra often becomes very tedious. There are computer programs that permit larger spin systems and more complex experiments to be treated by density matrix procedures. However, it is often 

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Sun X, Wang H and Miller W H 1998 Qn the semiclassical description of quantum coherence in thermal rate constants J. Chem. Phys. 109 4190... 

A H(detected)- C shift correlation spectrum (conmion acronym HMQC, for heteronuclear multiple quantum coherence, but sometimes also called COSY) is a rapid way to assign peaks from protonated carbons, once the hydrogen peaks are identified. With changes in pulse timings, this can also become the HMBC (l eteronuclear multiple bond coimectivity) experiment, where the correlations are made via the... 

Although the natural abundance of nitrogen-15 [14390-96-6] leads to lower sensitivity than for carbon-13, this nucleus has attracted considerable interest in the area of polypeptide and protein stmcture deterrnination. Uniform enrichment of is achieved by growing protein synthesi2ing cells in media where is the only nitrogen source. reverse shift correlation via double quantum coherence permits the... 

An alternative way of acquiring the data is to observe the signal. These experiments are referred to as reverse- or inverse-detected experiments, in particular the inverse HETCOR experiment is referred to as a heteronuclear multiple quantum coherence (HMQC) spectmm. The ampHtude of the H nuclei is modulated by the coupled frequencies of the C nuclei in the evolution time. The principal difficulty with this experiment is that the C nuclei must be decoupled from the H spectmm. Techniques used to do this are called GARP and WALTZ sequences. The information is the same as that of the standard HETCOR except that the F and F axes have been switched. The obvious advantage to this experiment is the significant increase in sensitivity that occurs by observing H rather than C. 

HC HMQC (heteronuclear multiple quantum coherence) and HC HSQC (heteronuclear single quantum coherence) are the acronyms of the pulse sequences used for inverse carbon-proton shift correlations. These sensitive inverse experiments detect one-bond carbon-proton connectivities within some minutes instead of some hours as required for CH COSY as demonstrated by an HC HSQC experiment with a-pinene in Fig. 2.15. 

HMQC Heteronuclear multiple quantum coherence, e.g. inverse CH correlation via one-bond carbon proton-coupling, same format and information as described for ( C detected) CH COSY but much more sensitive (therefore less time-consuming) because of H detection... 

Figure 1.33 The underlying principle of the Redfield technique. Complex Fourier transformation and single-channel detection gives spectrum (a), which contains both positive and negative frequencies. These are shown separately in (b), corresponding to the positive and negative single-quantum coherences. The overlap disappears when the receiver rotates at a frequency that corresponds to half the sweep width (SW) in the rotating frame, as shown in (c). After a real Fourier transformation (involving folding about n = 0), the spectrum (d) obtained contains only the positive frequencies.

Apparently, all coherence pathways will therefore start at zero coherence levels and end at -t-1 coherence levels since the quadrature receiver is sensitive only to the +1 polarization, only the single-quantum coherence is detected. 

What is the difference between single-quantum coherence and zero-... 

Many subspectral editing techniques alternative to DEPT, such as SEMUT (Subspectral Editing using a Multiple Quantum Trap) (Bildsoe et al., 1983) and SEMUT GL, have been developed that utilize the fact that the transfer of magnetization to unobservable multiple-quantum coherence for CH, CHj, and CH spin systems is dependent on the last flip angle 0. However, these experiments have not been widely used. 

Single-quantum coherence is the type of magnedzadon that induces a voltage in a receiver coil (i.e., Rf signal) when oriented in the xy-plane. This signal is observable, since it can be amplified and Fourier-transformed into a frequency-domain signal. Zero- or multiple-quantum coherences do not obey the normal selection rules and do not... 

No. The vector presentation is suitable for depicting single-quantum magnetizations but is not appropriate when considering zero-, double-, and higher-order quantum coherences. Quantum mechanical treatment can be employed when such magnetizations are considered. 

H-Detected Heteronuclear Multiple-Quantum Coherence (HMQC) Spectra... 

In contrast, in a two-spin system the two nuclei coupled with each other by the coupling constant, J, will have four energy levels available for transitions (Fig. 5.56). Such a system not only has single-quantum coher-... 

The delay is generally kept at Vi x> The coupling constant Jcc for direcdy attached carbons is usually between 30 and 70 Hz. The first two pulses and delays (90J -t-180 2-t) create a spin echo, which is subjected to a second 90J pulse (i.e., the second pulse in the pulse sequence), which then creates a double-quantum coherence for all directly attached C nuclei. Following this is an incremented evolution period tu during which the double quantum-coherence evolves. The double-quantum coherence is then converted to detectable magnetization by a third pulse 0,, 2, and the resulting FID is collected. The most efficient conversion of double-quantum coherence can... 

The heteronuclear multiple-quantum coherence (HMQC) spectrum, H-NMR chemical shift assignments, and C-NMR data of podophyllo-toxin are shown. Determine the chemical shifts of various carbons and connected protons. The HMQC spectra provide information about the one-bond correlations of protons and attached carbons. These spectra are fairly straightforward to interpret The correlations are made by noting the position of each crossf)eak and identifying the corresponding 8h and 8c values. Based on this technique, interpret the following spectrum. 

SELINQUATE (Berger, 1988) is the selective ID counterpart of the 2D INADEQUATE experiment (Bax et al., 1980). The pulse sequence is shown in Fig. 7.4. Double-quantum coherences (DQC) are first excited in the usual manner, and then a selective pulse is applied to only one nucleus. This converts the DQC related to this nucleus into antiphase magnetization, which is refocused during the detection period. The experiment has not been used widely because of its low sensitivity, but it can be employed to solve a specific problem from the connectivity information. 

The SELINCOR experiment is a selective ID inverse heteronuclear shift-correlation experiment i.e., ID H,C-COSYinverse experiment) (Berger, 1989). The last C pulse of the HMQC experiment is in this case substituted by a selective 90° Gaussian pulse. Thus the soft pulse is used for coherence transfer and not for excitation at the beginning of the sequence, as is usual for other pulse sequences. The BIRD pulse and the A-i delay are optimized to suppress protons bound to nuclei As is adjusted to correspond to the direct H,C couplings. The soft pulse at the end of the pulse sequence (Fig. 7.8) serves to transfer the heteronuclear double-quantum coherence into the antiphase magnetization of the protons attached to the selectively excited C nuclei. 

Coherence A condition in which nuclei precess with a given phase relationship and can exchange spin states via transitions between two eigenstates. Coherence may be zero-quantum, single-quantum, double-quantum, etc., depending on the AM of the transition corresponding to the coherence. Only single-quantum coherence can be detected directly. 

DEPT (distortionless enhancement by polarization transfer) A onedimensional C-NMR experiment commonly used for spectral editing that allows us to distinguish between CH, CH2, CH, and quaternary carbons. Detectable magnetization The magnetization processing in the x y -plane induces a signal in the receiver coil that is detected. Only single-quantum coherence is directly detectable. 

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