Phase-twisted line

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. 

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... 

This simple phase-incrementation idea, not particularly emphasized by the authors at the time, has more recently had a considerable impact on NMR methodology. First, it was made the basis of one of the standard methods for obtaining pure-phase two-dimensional spectra, replacing the undesirable phase-twist line shape with a pure absorption-mode signal. Secondly, it has provided a neat way to generate an extensive array of simultaneous soft radiofrequency pulses covering an... 

Figure 5.21. A stacked plot illustration of (a) the phase-twisted line shape and (b) the double-absorption lineshape. Clearly the resolution in (b) is far superior and for this reason phase-sensitive methods are preferred.

Sometimes absolute value mode, as opposed to pure phase spectra, can be preferable for easy assignment, despite the theoretical disadvantages of a phase-twist line shape. Carbohydrate line widths are generally narrower than those of proteins and nucleic acids, and the use of absolute value spectra... 

The phase-twisted peak shapes (or mixed absorption-dispersion peak shape) is shown in Fig. 3.9. Such peak shapes arise by the overlapping of the absorptive and dispersive contributions in the peak. The center of the peak contains mainly the absorptive component, while as we move away from the center there is an increasing dispersive component. Such mixed phases in peaks reduce the signal-to-noise ratio complicated interference effects can arise when such lines lie close to one another. Overlap between positive regions of two different peaks can mutually reinforce the lines (constructive interference), while overlap between positive and negative lobes can mutually cancel the signals in the region of overlap (destructive interference). 

There are generally three types of peaks pure 2D absorption peaks, pure negative 2D dispersion peaks, and phase-twisted absorption-dispersion peaks. Since the prime purpose of apodization is to enhance resolution and optimize sensitivity, it is necessary to know the peak shape on which apodization is planned. For example, absorption-mode lines, which display protruding ridges from top to bottom, can be dealt with by applying Lorentz-Gauss window functions, while phase-twisted absorption-dispersion peaks will need some special apodization operations, such as muliplication by sine-bell or phase-shifted sine-bell functions. 

FIGURE 10.11 Example of a phase-twisted 2D NMR line. Courtesy of Ad Bax (National Institutes of Health). 

This is a single line at = (+Q +Q2) with the phase-twist lineshape,... 

This is a two lines, both with the phase-twist lineshape one is located at (+Q1,+Q2) and the other is at (-f2j,+f22). As expected for a data set which is cosine modulated in tl the spectrum is symmetrical about co] = 0. 

This is two lines, located at (+X21,+f22) and (-f2,+f22), but in contrast to the above both have the double absorption lineshape. There is still lack of frequency discrimination, but the undesirable phase-twist lineshape has been avoided. 

A very different model of tubules with tilt variations was developed by Selinger et al.132,186 Instead of thermal fluctuations, these authors consider the possibility of systematic modulations in the molecular tilt direction. The concept of systematic modulations in tubules is motivated by modulated structures in chiral liquid crystals. Bulk chiral liquid crystals form cholesteric phases, with a helical twist in the molecular director, and thin films of chiral smectic-C liquid crystals form striped phases, with periodic arrays of defect lines.176 To determine whether tubules can form analogous structures, these authors generalize the free-energy of Eq. (5) to consider the expression... 

Fig. 2. Evolution of twist angle around the P-bond (grey) and I-bond (black) after photoexcitation of the neutral form of GFP chromophore in the gas phase (left panel) and solvated by 150 water molecules (right panel). Solid lines are population-weighted averages over die trajectory basis functions. Dashed lines represent the twist angles for the individual trajectory basis functions. The sense of rotation for the two torsions is defined such that HT motion corresponds to both angles moving towards more negative values.

Fig. 17a-c. Elastic constants for a splay b twist c bend deformations of a nematic phase. The full lines represent the director... 

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