Spectrum lineshape

All the processing steps in this section are intended to enhance the time domain data leading to the suppression of distortions or artefacts and an improvement in the overall spectral quality. The suitability of the methods can be estimated from the appearance of the FID in the main spectrum window of ID WIN-NMR as illustrated in the schematic FID shown in Fig. 3.6. The envelope of the exponentially decaying FID has a dc offset as it is not symmetrical about the zero line whilst the spectrum lineshape may be improved by either zero filling or apodization or possibly both. 

The energy spectrum of the resonance states will be quasi-discrete it consists of a series of broadened levels with Lorentzian lineshapes whose full-width at half-maximum T is related to the lifetime by F = Fn. The resonances are said to be isolated if the widths of their levels are small compared with the distances (spacings) between them, that is... 

Figure B2.4.5. Simulated lineshapes for an intennolecular exchange reaction in which the bond joining two strongly coupled nuclei breaks and re-fomis at a series of rates, given beside tlie lineshape. In slow exchange, the typical spectrum of an AB spin system is shown. In the limit of fast exchange, the spectrum consists of two lines at tlie two chemical shifts and all the coupling has disappeared.

It turns out that the CSP approximation dominates the full wavefunction, and is therefore almost exact till t 80 fs. This timescale is already very useful The first Rs 20 fs are sufficient to determine the photoadsorption lineshape and, as turns out, the first 80 fs are sufficient to determine the Resonance Raman spectrum of the system. Simple CSP is almost exact for these properties. As Fig. 3 shows, for later times the accuracy of the CSP decays quickly for t 500 fs in this system, the contribution of the CSP approximation to the full Cl wavefunction is almost negligible. In addition, this wavefunction is dominated not by a few specific terms of the Cl expansion, but by a whole host of configurations. The decay of the CSP approximation was found to be due to hard collisions between the iodine atoms and the surrounding wall of argons. Already the first hard collision brings a major deterioration of the CSP approximation, but also the role of the second collision can be clearly identified. As was mentioned, for t < 80 fs, the CSP... 

Fig. 23. Experimental room temperature Raman spectrum from a sample consisting primarily of bundles or ropes of single-wall nanotubes with diameters near that of the (10,10) nanotube. The excitation laser wavelength is 514.5 nm. The inset shows the lineshape analysis of the vibrational modes near 1580 cm . SWNT refers to singlewall carbon nanotubes [195].

The approach to the evaluation of vibrational spectra described above is based on classical simulations for which quantum corrections are possible. The incorporation of quantum effects directly in simulations of large molecular systems is one of the most challenging areas in theoretical chemistry today. The development of quantum simulation methods is particularly important in the area of molecular spectroscopy for which quantum effects can be important and where the goal is to use simulations to help understand the structural and dynamical origins of changes in spectral lineshapes with environmental variables such as the temperature. The direct evaluation of quantum time- correlation functions for anharmonic systems is extremely difficult. Our initial approach to the evaluation of finite temperature anharmonic effects on vibrational lineshapes is derived from the fact that the moments of the vibrational lineshape spectrum can be expressed as functions of expectation values of positional and momentum operators. These expectation values can be evaluated using extremely efficient quantum Monte-Carlo techniques. The main points are summarized below. 

The Compton scattering cannot be neglected, but it is independent of molecular structure. Then, fitting experimental data to formulas from gas phase theory, the concentration of excited molecules can be determined. Another problem is that the undulator X-ray spectrum is not strictly monochromatic, but has a slightly asymmetric lineshape extending toward lower energies. This problem may be handled in different ways, for example, by approximating its spectral distribution by its first spectral moment [12]. 

Two different approaches have been followed to calculate the lineshapes within a relaxation model. According to a phenomenological approach based on the modified Bloch equations [154, 155], the intensity distribution of the theoretical Mossbauer spectrum may be written as [156] ... 

Here, L(v) is a lineshape function that integrates to unity, v is the frequency,/ is the Lamb-Mossbauer factor, and the desired side bands have an area fraction / that is proportional to which hence determines the relative peak heights in a NIS spectrum. More details are provided in Appendix 2 (Part III, 3 of CD-ROM). An equivalent and often more suggestive display of the NIS spectrum is the PVDOS approach, which describes the NIS signal in terms of the partial vibrational density of states ... 

We can manipulate the FID mathematically in various ways before Fourier transformation, in order to optimize the spectrum with respect to the line-width or the lineshape. 

Fourier transformation without data manipulation leads to the multiplet at the bottom (a), which shows more fine structure when a negative LB value is used (b). The spectrum in the middle (c) results from use of the SSB function, and now all eight lines are clearly visible as the linewidth is much smaller. The price we pay is that the lineshape is completely changed, the positive central... 

The Davies pulsed ENDOR spectrum of canthaxanthin oxidized on silica-alumina measured in the temperature range of 3.3-80K showed no lineshape changes, which is in agreement with previous 330 GHz EPR studies of canthaxanthin radical cations (Konovalova et al. 1999). This implies very rapid rotation of the methyl groups down to 3.3 K. 

In molecularly rigid systems, the direct (through-space) dipole-dipole interaction between nuclear spins I = fe is normally the dominant source of broadening of the NMR lineshape. For a pair of similar nuclear spins i and j in a magnetic field Hq the dipolar splitting in their spectrum is given by... 

Hagen, W.R. 1981. Dislocation strain broadening as a source of anisotropic linewidth and asymmetrical lineshape in the electron paramagnetic resonance spectrum of metal-loproteins and related systems. Journal of Magnetic Resonance 44 447-469. 

In the opposite situation (y5 yG), lineshape (f), the band splitting vanishes such as the lineshape become close to the spectrum of an isolated fast mode (unique band, centered on the frequency oo0). 

As a consequence of the wide frequency range over which Fermi resonances may be effective, let us conclude that, in practical situations, several Fermi couplings may be involved in a spectrum, which must lead to puzzling spectral lineshapes. 

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