Coherence Pathway Selection in NMR Experiments

Below the pulse sequence we can show the desired coherence level, p, at each stage of the pulse sequence. This diagram defines the coherence pathway that is desired for a particular NMR experiment. Coherence order is mixed for Cartesian product operators 

The Cartesian operators have mixed coherence order because they are linear combinations of the spherical operators 

2 Coherence Order Pathway Selection by Phase Cycling 

There is a key observation that makes coherence pathway selection possible by phase cycling. Starting with a pure 1+ (p = 1) coherence, consider the effect of changing the phase of a 90° pulse on the phases of the resulting coherences  

Where X and Y are the real and imaginary FIDs coming out of the ADC. Thus, we can speak of the receiver phase as the point of view from which we view the FID signal in the rotating frame of reference. If the receiver phase is shifted by 90° (from x to y axis), we mean that the real channel has been shifted counterclockwise by 90° from the x axis to the y axis, and the imaginary channel has been shifted counterclockwise by 90° from the y axis to the -x axis. With this 90° shift, for example, a coherence of Iv would be observed as Ix, and in a four-scan phase cycle with A t r = 90°, we would observe a four-scan sequence of coherences lx, y, —Ix, —Iy as 4IX in the sum-to-memory. To keep track of these phase shifts, a shorthand notation is often used where 0 stands for a 0° phase shift (real part of receiver on the x axis), 1 stands for a 90° phase shift (receiver on the y axis), 2 stands for a 180° phase shift (receiver on the —x axis), and 3 stands for a 270° phase shift (receiver on the —y axis). In this notation, the four-scan receiver phase cycle with A br = 90° would be written 0 12 3. 

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A 2D NMR experiment can lead to a data set that is either phase modulated or amplitude modulated as a function of fj, depending on the particular experiment and coherence pathways selected. A regular ID spectrum consists of absorption A(p) and dispersion peaks corresponding to the real and imaginary parts of the spectral lines, respectively. In 2D experiments, phase modulation in fj results in twisted 2D real lineshapes as a result of the Fourier transformation of bi-exponential time domain... 

It is common practise to separate NMR experiments according to dimensionality, this approach is not absolute because it is possible to convert a 2D experiment into a ID experiment without changing the basic principles, correlation mechanism, sensitivity enhancement or coherence pathway selection by using selective pulses. The experiments in this chapter are divided into three parts using the following criteria ... 

Phase cycling is a fundamental procedure in most NMR experiments and is used not only for removing instrument artifacts, but also for selecting or suppressing signals, specially for achievement of specific coherence transfer pathways [5,13]. In NMR experiments, one must be aware of the importance of phase cycling, which sometimes is more difficult to understand than the basic aspects of the pulse sequences. 

In recent years, gradient versions of many of the basic 2D NMR experiments have become very popular. One of the main reasons is that the use of gradients eliminates the need for phase cycling in the selection of a coherence pathway. Experiments involving detection can, therefore, often be performed with one to two transients per increment. 

Another method for achieving selective detection of certain types of spin systems is through the application of pulsed magnetic field gradients. This can be used to select particular coherence pathways for spins in a multiple pulse experiment, for example, in multidimensional NMR spectroscopy, to crush unwanted magnetization such as solvent resonance, to measure molecular diffusion coefficients, and, hence, to edit spectra on the basis of the diffusion coefficients of the molecules giving rise to individual peaks. 

R295 G. Bodenhausen, Reflections of Pathways A Short Perspective on Selection of Coherence Transfer Pathways in NMR Pulse Experiments , J. Magn. Reson., [online computer file], 2011, 213, 295. 

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