Absolute value mode

Two-dimensional spectra are often recorded in the absolute-value mode. The absolute value A is the square root of the sum of the squares of the real (R) and imaginary (/) coefficients ... 

Although this eliminates negative contributions, since the imaginary part of the spectrum is also incorporated in the absolute-value mode, it produces broad dispersive components. This leads to the broadening of the base of the peaks ( tailing ), so lines recorded in the absolute-value mode are usually broader and show more tailing than those recorded in the pure absorption mode. 

The weighting functions used to improve line shapes for such absolute-value-mode spectra are sine-bell, sine bell squared, phase-shifted sine-bell, phase-shifted sine-bell squared, and a Lorentz-Gauss transformation function. The effects of various window functions on COSY data (absolute-value mode) are presented in Fig. 3.10. One advantage of multiplying the time domain S(f ) or S(tf) by such functions is to enhance the intensities of the cross-peaks relative to the noncorrelation peaks lying on the diagonal. 

Heteronuclear-shift-correlation spectra, which are usually presented in the absolute-value mode, normally contain long dispersive tails that are suppressed by applying a Gaussian or sine-bell function in the F domain. In the El dimension, the choice of a weighting function is less critical. If a better signal-to-noise ratio is wanted, then an exponential broadening multiplication may be employed. If better resolution is needed, then a resolution-enhancing function can be used. 

In homonuclear 2D /-resolved spectra, couplings are present during <2 in heteronuclear 2D /-resolved spectra, they are removed by broad-band decoupling. This has the multiplets in homonuclear 2D /-resolved spectra appearing on the diagonal, and not parallel with F. If the spectra are plotted with the same Hz/cm scale in both dimensions, then the multiplets will be tilted by 45° (Fig. 5.20). So if the data are presented in the absolute-value mode and projected on the chemical shift (F2) axis, the normal, fully coupled ID spectrum will be obtained. To make the spectra more readable, a tilt correction is carried out with the computer (Fig. 5.21) so that Fi contains only /information and F contains only 8 information. Projection... 

Peaks in homonuclear 2D /-resolved spectra have a phase-twisted line shape with equal 2D absorptive and dispersive contributions. If a 45° projection is performed on them, the overlap of positive and negative contributions will mutually cancel and the peaks will disappear. The spectra are therefore presented in the absolute-value mode. 

Absorption-mode spectrum The spectrum in which the peaks appear with Lorentzian line shapes. NMR spectra are normally displayed in absolute-value mode. 

Sine-beU An apodization function employed for enhancing resolution in 2D spectra displayed in the absolute-value mode. It has the shape of the first halfcycle of a sine function. 

Figure 15 HMBC and broadband HMBC spectra of cyclosporine in C6D6 recorded with the pulse sequence shown in Figure 14. (A) HMBC spectrum recorded with A = 65.0 ms and 32 scans. (B) HMBC spectrum where two subspectra of 16 scans each recorded with A = 65.0 ms and 120 ms, and co-added in absolute-value mode. (C) broadband HMBC spectrum where four subspectra of eight scans each were recorded with A = 96.7, 84.4, 81.8, and 80.8 ms, respectively, and co-added in absolute-value mode.

Figure 16 u/tro-HMBC spectrum of cyclosporine in C6D6 recorded with the pulse sequence shown in Figure 14 where four subspectra of eight scans each were recorded with A = 181.1,160.0,115.0, and 99.3 ms, respectively, and co-added in absolute-value mode. 

For some purposes in 2D NMR it is sufficient to obtain only the absolute value mode, that is, the square root of the sums of the squares of absorption and dispersion. The absolute value mode is independent of the phase of the signals, hence is simpler to compute and avoids the need for interactive phasing. However, as a composite of absorption and dispersion, it includes the long wings characteristic of the dispersion mode (see Fig. 2.10) and thus has substantially greater overlap of lines than pure absorption. 

Equation 10.9 represents a complicated line shape, which is a mixture of absorptive and dispersive contributions. Figure 10.11 gives an example of such a phase-twisted line shape. The broad base of the line, caused by the dispersive contribution, and the difficulty in correctly phasing such a resonance make it unattractive for practical use. The phase twist problem can be alleviated by displaying only the absolute value mode... 

The absolute value mode of the expression in Eq. 10.9 is formed from the sum of the squares of the real part and the imaginary part of this expression. Show that this reduces to the expression given in Eq. 10.10. 

It will have been noticed [equations (3) and (5)] that although the absolute value mode is often used to display two-dimensional spectra it should in principle be possible also to get pure absorption mode spectra by a suitable combination of the individual computed sine and cosine transforms. This is of course highly desirable because the absolute value mode spectra can suffer from much line broadening especially at the base of the peaks. However, in the absence of any... 

Higher order binomial filters are efficient in applications where a relatively wide band, e.g. a strongly coupled multiplet, has to be suppressed (see Figure 13). A drawback of these filters is the introduction of a linear phase gradient which is usually easy to correct. Alternatively the spectra may be represented in the absolute value mode. 

As stated in Section 7-4b, digital resolution in the v domain is a function of the number of increments (ni) and the spectral width (swi). Spectral data describing the v dimension can be acquired in the either the phase-sensitive or the absolute-value mode. Real and imaginary ui-domain data sets exist for both types of acquisition, but are treated differently. The imaginary data are discarded in phase-sensitive acquisition, just as with the V2 dimension data previously described. By contrast, with absolute-value data, both the absorptive (real) and dispersive (imaginary) components of the v domain are used to describe the spectrum. The important point is that, for both kinds of data, the acquisition of 2M increments yields M points, after Fourier transformation, to characterize spectra in the ui dimension. Therefore, if swi = 2,100 Hz and ni = 512, then DR = swi/(ni/2) = 2,100 Hz/(512/2) = 8.2 Hz/point. If one level of zero filling is carried out, then the effective ni = 1,024 and it follows that DRi = 2,100 Hz/( 1,024/2) = 4.1 Hz/point. 

The gradient version of HMQC is performed in the absolute-value mode, whereas the nongradient experiment is conducted in the phase-sensitive mode. While the use of gradients does result in a 2 / decrease in sensitivity with respect to the nongradient version (Part C, introduction), this decrease is seldom important, because HMQC is inherently a relatively sensitive experiment. Sensitivity is, however, critical in other experiments, as will be seen in Section 7-9a. 

H decoupling for FLOCK typically is performed as the C signal is acquired and is accomplished with the WALTZ sequence (Section 5-8). FLOCK data are presented in either the phase-sensitive or the absolute-value mode. Because of uncertainty concerning both the location and intensity of correlations in FLOCK contour plots, cross sections should be taken through individual chemical shifts on both the H and C axes, as with HMBC spectra. 

COSY spectra are sometimes plotted in the absolute value mode, where all the sign information is suppressed deliberately. Although such a display is convenient, especially for routine applications, it is generally much more desirable to retain the sign information. Spectra displayed in this way are said to be phase sensitive more details of this are given in section 7.6. 

The greatest drawback with data collected with phase modulation is the inextricable mixing of absorption and dispersion-mode lineshapes. The resonances are said to possess a phase-twisted lineshape (Fig. 5.21a), which has two principal disadvantages. Firstly, the undesirable and complex mix of both positive and negative intensities and secondly, the presence of dispersive contributions and the associated broad tails that are unsuitable for high-resolution spectroscopy. To remove confusion from the mixed positive and negative intensities, spectra are routinely presented in absolute-value mode, usually after a magnitude calculation (Fig. 5.22). 

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