Spectral line shape

The coherent tunneling case is experimentally dealt with in spectroscopic studies. For example, the neutron-scattering structure factor determining the spectral line shape is... 

Fig. 9. Spectral line shape for tunneling doublet at different dimensionless temperatures, X = T/T, as indicated.

Fitz D. E., Marcus R. A. Semiclassical theory of molecular spectral line shapes in gases, J. Chem. Phys. 59, 4380-92 (1973). 

Natural Line Width and Spectral Line Shape... 

Spano, F. C. 2009. Analysis of the UV/Vis and CD spectral line shapes of carotenoid assemblies Spectral signatures of chiral H-aggregates. J. Am. Soc. 131 4267-4278. 

Spectral line shape studies by Frommhold and Biondi60 (using Fabry-Perot interferometry) indicated measurable broadening of several lines coming from Ne2 and Ar2 recombination. The authors showed that dissociative recombination,... 

As we have already mentioned, CDCI3 should be avoided as a solvent for salts for two reasons. Firstly, salts are unlikely to be particularly soluble in this relatively nonpolar solvent but more importantly, spectral line shape is likely to be poor on account of relatively slow proton exchange at the protonatable centre. The remedy is simple enough - avoid using CDCI3 and opt for one of the more polar options instead, e.g., deuterated DMSO or MeOH and you should obtain spectra every bit as sharp as those of free bases. 

To begin with, we consider how Eqs. (4.2.7), (4.2.8), and (4.2.11) reproduce the main results provided by the known exchange dephasing model147,148 as regards the spectral line shape for a high-frequency local vibration.14,15°... 

The exact Eq. (4.2.17) takes into account the effect of the reservoir (the condensed phase) on the spectral line shape through the parameter 77. Consideration of a concrete microscopic model of the valence-deformation vibrations makes it possible to estimate the basic parameters y and 77 of the theory and to introduce the exchange mode anharmonicity caused by a reorientation barrier of the deformation vibrations thereby, one can fully take advantage of the GF representation in the form (4.2.11) which allows summation over a finite number of states. 

The response of the system concerned to an external electromagnetic field is conveniently described in terms of double-time Green s function (GF) which can be introduced in a variety of representations.144,218 221 In what follows we will involve the representation in Matsubara s frequency space218 which is accepted in the theory of anharmonic crystals197 and provides a number of exact solutions in the case of a single adsorbed molecule.I50,1 2 In this approach, the spectral line shape for high-frequency vibrations can be determined as follows 184... 

Fortuitously for this project, the drug substance, and not the excipients, contained a fluorine moiety. Fluorine-19 MAS spectra were therefore also acquired at 500 MHz on the two samples, and they are shown to the right of the corresponding carbon spectra for each sample in Fig. 10.25. The fluorine-19 chemical shifts are sensitive enough in this example to show the API-excipients interaction directly. This is evident from the dramatic change in spectral line shape. 

With a horizontally oriented sample (a = 0°), the spectrum of the labeled bR in Figure 48(b) should display three quadrupole splittings corresponding to the three labeled methyl groups on the retinal. It is apparent, however, that the expected three pairs of resonances are not resolved because of spectral overlap of the broadened lines. A computer simulation approach was used to analyze the spectral line shapes despite the overlap, but much qualitative information about the cyclohexene ring can be gained by simple inspection of the experimental data in Figure 48. 

The spectral line shape in CARS spectroscopy is described by Equation (6.14). In order to investigate an unknown sample, one needs to extract the imaginary part of to be able to compare it with the known spontaneous Raman spectrum. To do so, one has to determine the phase of the resonant contribution with respect to the nonreso-nant one. This is a well-known problem of phase retrieval, which has been discussed in detail elsewhere (Lucarini et al. 2005). The basic idea is to use the whole CARS spectrum and the fact that the nonresonant background is approximately constant. The latter assumption is justihed if there are no two-photon resonances in the molecular system (Akhmanov and Koroteev 1981). There are several approaches to retrieve the unknown phase (Lucarini et al. 2005), but the majority of those techniques are based on an iterative procedure, which often converges only for simple spectra and negligible noise. When dealing with real experimental data, such iterative procedures often fail to reproduce the spectroscopic data obtained by some other means. 

This result, when substituted into the expressions for C(t), yields expressions identical to those given for the three cases treated above but with one modification. The translational motion average need no longer be considered in each C(t) instead, the earlier expressions for C(t) must each be multiplied by a factor exp(- co2t2kT/(2mc2)) that embodies the translationally averaged Doppler shift. The spectral line shape function 1(G)) can then be obtained for each C(t) by simply Fourier transforming ... 

Multiplying this expression by n yields the Voigt function that occurs in the description of spectral-line shapes resulting from combined Doppler and pressure broadening. We elaborate on these phenomena in Section I of Chapter 2. 

Time-dependent correlation functions are now widely used to provide concise statements of the miscroscopic meaning of a variety of experimental results. These connections between microscopically defined time-dependent correlation functions and macroscopic experiments are usually expressed through spectral densities, which are the Fourier transforms of correlation functions. For example, transport coefficients1 of electrical conductivity, diffusion, viscosity, and heat conductivity can be written as spectral densities of appropriate correlation functions. Likewise, spectral line shapes in absorption, Raman light scattering, neutron scattering, and nuclear jmagnetic resonance are related to appropriate microscopic spectral densities.2... 

The spectral line shapes of collision-induced spectra (like in Fig. 1.3) resemble a Lorentzian, but the profile shown in Fig. 1.1 looks quite... 

Time scales. For an understanding of spectral line shapes of induced absorption, at not too high gas densities, it is useful to distinguish three different times associated with collisions, namely the average time between collisions, the duration of a molecular fly-by and the duration of the spectroscopic interaction. 

Time-dependent correlation functions. Similar pair and triplet distributions, which describe the time evolution of a system, are also known [318]. These have found interesting uses for the theory of virial expansions of spectral line shapes, pp. 225 ff. below [297, 298],... 

The zeroth moment (n=0) gives the total intensity and is related to theory by familiar sum formulae (Chapter 5). For nearly classical systems (i.e., massive pairs at high temperature and not too high frequencies), the first moment (n=l) is very small and actually drops to zero in the classical limit as we will see in Chapter 5. The ratio of second and zeroth moment defines some average frequency squared and may be considered a mean spectral width squared. A complete set of moments (n = 0, 1,... 00) may be considered equivalent to the knowledge of the spectral line shape,... 

For the purposes of computing spectral line shapes and spectral moments, the dipole moment p is best expressed in spherical coordinates... 

Collision-induced dipoles manifest themselves mainly in collision-induced spectra, in the spectra and the properties of van der Waals molecules, and in certain virial dielectric properties. Dipole moments of a number of van der Waals complexes have been measured directly by molecular beam deflection and other techniques. Empirical models of induced dipole moments have been obtained from such measurements that are consistent with spectral moments, spectral line shapes, virial coefficients, etc. We will briefly review the methods and results obtained. 

---