Dispersion-mode spectrum

Fig. 3.—Fourier-transform, Proton Magnetic Resonance Spectra45 of 6-Deoxy-l,2 3,4-di-O-isopropylidene-6-phthalimido-a-D-gaIactopyranose (54) (0.06 mg) at 90 MHz, Obtained by Transformation (N = 4,096) of the Free-induction Decay Signal (1,024 Datum Points, see Fig. 2), After the Appendation of 3,072 Zero, Datum Points ( Zerofilling, See Text), [(a) Spectrum associated with the real part of the transform, and (b) with the imaginary part (c) absorption-mode spectrum computed by phase correction of the spectrum in (a) and (d) dispersion-mode spectrum computed by phase correction of the spectrum in (b). Parameters for phase correction, A —255° and B —215°. Note that the phase of the tetramethylsilane and chloroform signals in (c) is slightly different from that of the carbohydrate derivative. By coincidence, the peak for residual water in spectrum (c) has almost the same intensity as the methyl signals, and could have been mistaken for one, had other spectra not been recorded.]...

One of these sets of amplitudes is redundant, in that, when correctly phased, the real set defines the absorption-mode spectrum (see Fig. 3c), and the imaginary set, the dispersion-mode spectrum (see Fig. 3d), which is 90° out of phase with the absorption mode. 

Figure 3.10 Effect of different window functions (apodization functions) on the appearance of COSY plot (magnitude mode), (a) Sine-bell squared and (b) sine-bell. The spectrum is a portion of an unsymmetrized matrix of a H-COSY I.R experiment (400 MHz in CDCl, at 303 K) of vasicinone. (c) Shifted sine-bell squared with r/4. (d) Shifted sine-bell squared with w/8. (a) and (b) are virtually identical in the case of delayed COSY, whereas sine-bell squared multiplication gives noticeably better suppression of the stronger dispersion-mode components observed when no delay is used. A difference in the effective resolution in the two axes is apparent, with Fi having better resolution than F. The spectrum in (c) has a significant amount of dispersion-mode line shape.

Dispersion mode A Lorentzian line shape that arises from a phase-sensitive detector (which is 90 out of phase with one that gives a pure-absorption-mode line). Dispersion-mode signals are dipolar in shape and produce long tails. They are not readily integrable, and we need to avoid them in a 2D spectrum. 

The solution of eq. (2.11) is a complex function. FFT computation therefore yields both real and imaginary PFT NMR spectra, v(co) and i u(to), which are related to the absorption and dispersion modes of CW spectra. The two parts of the complex spectrum are usually stored in different blocks of the memory and can be displayed on an oscilloscope to aid in further data manipulations. 

Fig. 2.13 (b, c) illustrates a phase correction. For correcting the phase, either the real or the imaginary part of the spectrum can be used. Correction of the real part for the absorption mode yields the dispersion mode in the imaginary part and vice versa (Fig. 2.13). 

Fig. 8.16. Aromatic ring part of the COSY spectra of the complex shown in the inset. (A) Magnitude mode spectrum (B) phase-sensitive spectrum, absorption mode (C) phase-sensitive spectrum, dispersion mode (D) ISECR [20] spectrum (sequence in Fig. 8.2D). Sin2 weighting functions have been used for spectra (A)-(C) and a cos2 weighting function for spectrum (D). Peaks in (A) and (D) are in phase and positive. The positive components of the 6-5 peak in (B) and (C) are shown in the enlargements.

The lineshape function which describes the absorption and dispersion modes of an unsaturated, steady-state NMR spectrum is proportional to the Fourier transform of the function MxID(t) (24, 25, 99)... 

Recall that the raw NMR data (FID) consists of two numbers for each data point one real value and one imaginary value. After the Fourier transform, there are also two numbers for each frequency point one real and one imaginary. In a perfect world, the real spectrum would be in pure absorptive mode (normal peak shape) and the imaginary spectrum would be in pure dispersive (up/down) mode. In reality, each spectrum is a mixture of absorptive and dispersive modes, and the proportions of each can vary with chemical shift (usually in a linear... 

Figure 4. Background spectrum taken in x-ray energy dispersive mode.

Figure 6-15 Phase-sensitive COSY diagram for two spins, with the diagonal peaks in dispersion mode and the cross peaks in antiphase absorption mode. The ID spectrum is on the right. (Reproduced from F. J. M. van de Ven, Multidimensional NMR in Liquids, VCH, New York, 1995, p. 171.)...

Fig. 4.7 Illustration of the effect of a phase shift of the time domain signal on the spectrum. In (a) the signal starts out along x and so the spectrum is the absorption mode in the real part and the dispersion mode in the imaginary part. In (b) there is a phase shift, , of 45° the real and imaginary parts of the spectrum are now mixtures of absorption and dispersion. In (c)the phase shift is 90° now the absorption mode appears in the imaginary part of the spectrum. Finally in (d) the phase shift is 180° giving a negative absorption line in the real part of the spectrum. The vector diagrams illustrate the position of the signal at time zero.

In a spectrum with just one line, the dispersion mode lineshape might be acceptable - in fact we can think of reasons why it might even be desirable (what might these be ). However, in a spectrum with many lines the dispersion mode lineshape is very undesirable - why ... 

Thus, displaying the real part of S(co) will not give the required absorption mode spectrum rather, the spectrum will show lines which have a mixture of absorption and dispersion lineshapes. 

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