Lineshape dispersive contributions

Previous sections have already made the case for acquiring COSY data such that it may be presented in the phase-sensitive mode. The pure-absorption lineshapes associated with this provide the highest possible resolution and allow one to extract information from the fine-structure within crosspeak multiplets. However, it was also pointed out that the basic COSY-90 sequence suffers from one serious drawback in that diagonal peaks possess dispersion-mode lineshapes when crosspeaks are phased into pure absorption-mode. The broad tails associated with these can mask crosspeaks that fall close to the diagonal, so there is potential for useful information to be lost. The presence of dispersive contributions to the diagonal may be (largely) overcome by the use of the double-quantum filtered variant of COSY [37], and for this reason DQF-COSY is the experiment of choice for recording phase-sensitive COSY data. 

The result from the filtration step, and the principal reason for its use, is that the diagonal peaks now possess antiphase absorption-mode lineshapes, as do the crosspeaks which are unaffected by the filtration. Strictly speaking, for spin systems of more than two spins the diagonal peaks still possess some dispersive contributions, but these are now antiphase so cancel and tend to be weak and rarely problematic. The severe tailing previously associated with diagonal peaks therefore is removed, providing a dramatic improvement in the quality of spectra (Fig. 5.42). 

The Echo/Antiecho method [2.45] In the introduction to the discussion of phase and amplitude modulated 2D data sets, see Table 2.8, it was emphasized that frequency discrimination in the fl dimension was inherent in phase modulated data sets. However the lineshapes was phase twisted because of the absorptive and dispersive contributions to the real part of s(coi, CO2) which describes the lineshapes in the final spectrum. 

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). 

Thus, a potentially very useful application of the modulator is in polarisation spectroscopy (figure 18) where for uncrossed polarizers the signal is in general a mixture of dispersion and Lorentzian lineshapes. With a modulator the dispersion contribution alone can be extracted thus avoiding the systematic error in the determination of the linecentreC ]. 

The present treatment of solvent broadening is of course an oversimplification. It does not take into account the dynamic nature of the interaction or the contributions of solvent excitations to the resonant state. On a more elementary level, the representation of A by a Lorentzian is probably unrealistic since solvent-broadened lines often approximate a Gaussian shape. Our choice of a Lorentzian is made to obtain analytical expressions for the cross section a Gaussian lineshape requires numerical procedures, but presents no fundamental difficulties. It turns out (O. Sonnich Mortensen, unpublished) that, for a given halfwidth A, a Gaussian tends to distort REPs and polarization dispersion curves more strongly than a Lorentzian. 

The last term is the vibrationally resonant contribution of all Raman transitions excited, and it becomes large when the frequency difference between pump and Stokes matches the frequency of a Raman transition. Its real part has a dispersive lineshape and the imaginary part, which mirrors the spontaneous Raman band, has a Lorentzian shape. 

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