Double single-quantum coherences

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. 

Double-quantum coherence Coherence between states that are separated by magnetic quantum numbers of 2. This coherence cannot be detected directly, but must be converted to single-quantum coherence before detection. 

Finally, the double quantum (DQ) spin spin relaxation time T2d can be determined using the pulse sequence 90° — x — 45° — 90° —t — 45°.51 The first three pulses create the DQ coherence, and the last read pulse converts the DQ to a single quantum coherence for detection. 

Product operators in which both components are in the x -y plane represent zero-quantum and double-quantum coherences (collectively called multiple-quantum coherences). DQC is a superposition of the spin states aid s and /3i/3s> which involves promotion of both nuclei I and S simultaneously from the a state to the P state or vice versa. ZQC is a superposition of the spin states a Ps and /fias, which involves nucleus I flipping from a to p while nucleus S flips from the p state to the a state, or the reverse process. Neither of these coherences can be directly observed, but we can convert them into observable (single-quantum) coherence and see the effect of evolution during the time spent as zero- and double-quantum coherences. In product operator notation they look like this... 

Figure 5 Maximum intensity as a function of log(fc) for simulated 14N (43.34 MHz) MAS spectra of a two-site jump process detecting either (A) single-quantum coherence or (B) double-quantum coherence. In both plots, the solid line corresponds to parameter set P6, the solid triangles to parameter set P7 and the solid squares to parameter set P8.

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. 

By allowing multiple-quantum coherence to process during the evolution period of a two-dimensional experiment, Drobny et al. were able to detect its effects indirectly. This idea subsequently blossomed into the new technique of filtration through double-quantum coherence. Multiple-quantum coherence of order n possesses an n-fold sensitivity to radiofrequency phase shifts, which permits separation from the normal single-quantum coherence. This concept inspired the popular new techniques of double-quantum filtered correlation spectroscopy (DQ-COSY) and the carbon-carbon backbone experiment (INADEQUATE), both designed to extract useful connectivity information from undesirable interfering signals. 

BIRD-HMQC. The most difficult aspect of implementing the HMQC experiment is the suppression of signals from protons attached to C (the center-band or single quantum coherences) in favor of the protons attached to C (the satellites or double quantum coherences). The use of pulse field gradients (PFG, Section 6-6) is the most effective technique, but relatively few spectrometers are equipped with the hardware required for their generation. Fortunately, there is an effective alternative for the suppression of center bands by means of the BIRD Bilinear Rotation Decoupling) sequence, which is outlined by the vector... 

Figure 5A6. Schematic energy level diagrams for a coupled two-spin AX system (see text). SQC = single-quantum coherence, DQC = double-quantum coherence and ZQC zero-quantum coherence.

This modification reflects the fact that a p-quantum coherence dephases at a rate proportional to p. Thus, double-quantum coherences dephase twice as fast as single-quantum coherences yet zero-quantum coherences are insensitive to field gradients. When the eoherence involves different nuclear species, allowance must be made for the magnetogyric ratio and coherence order for each, such that ... 

The DQF-COSY sequence (Fig. 5.40) differs from the basic COSY experiment by the addition of a third pulse and the use of a modified phase-cycle or gradient sequence to provide the desired selection. Thus, following tj frequency labelling, the second 90° pulse generates multiple-quantum coherence which is not observed in the COSY-90 sequence since it remains invisible to the detector. This may, however, be reconverted into single-quantum coherence by the application of the third pulse, and hence subsequently detected. The required phase-cycle or gradient combination selects only signals that existed as double-quantum coherence between the last two pulses, whilst all other routes are cancelled, hence the term double-quantum filtered COSY. 

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