Spectroscopic line shapes

The natural line width (or intrinsic fine width in the absence of external influences) of an energy level is determined by the lifetime due to the Heisenberg uncertainty principle  

Homogeneous interaction (Lorentzian line shape function) 

Natural broadening. The natural line width is determined by the lifetime of the excited energy level from which the transition line originates. 

Collisional or pressure broadening. Collisions shorten the lifetime of the excited state and thus broaden the spectroscopic line width. 

Power broadening. Power broadening is due to stimulated emission out of the excited state this shortens the lifetime. 

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Kador L (1991) Stochastic-theory of inhomogeneous spectroscopic line-shapes reinvestigated. J Chem Phys 95 5574... 

To perform the VES calculations it is necessary to consider a finite duration pulse, which has a finite bandwidth. In addition, the actual shape of the vibrational echo spectrum depends on the bandwidth of the laser pulse and the spectroscopic line shape. Several species with different concentrations, transition dipole moments, line shapes, and homogeneous dephasing times can contribute to the signal. Therefore, VES calculations require determination of the nonlinear polarization using procedures that can accommodate these properties of real systems. 

D. W. Alderman, M. S. Solum and D. M. Grant, Methods for analyzing spectroscopic line shapes. NMR solid powder patterns. J. Chem. Phys., 1986, 84, 3717-3725. 

Bohr magneton f E) is a spectroscopic line shape function (often approximated as a Gaussian) Ai, Bq, and Co are the A, B, and C term parameters (the subscripts indicate their relation to the spectral moment of order n, see below) k is Boltzmann s constant and T is kelvin temperature. The dipole strength for the absorption band is given by Equation (2), where the parameter Dq is proportional to the intensity. Equation (1) shows that A terms... 

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

After the completion of this manuscript a paper concerning conformational analyses of 1,1, 3,3 -tetra-r< H-alkylmctallocene of iron and ruthenium including 6 based on thorough NMR spectroscopic measurements (line-shape analysis) has appeared in which the nature of the transition states has conclusively been discussed in detail [164]. 

Many recombination and spectroscopic studies have been carried out in decaying rare-gas plasmas. Invariably, the buffer gas was the parent gas of the ion under study. In addition to recording the emitted spectra, Frommhold and Biondi60 examined the line shapes of many afterglow lines in neon and in argon. The intent was to find spectroscopic evidence for Doppler broadening of the lines which would prove that... 

Treating vibrational excitations in lattice systems of adsorbed molecules in terms of bound harmonic oscillators (as presented in Chapter III and also in Appendix 1) provides only a general notion of basic spectroscopic characteristics of an adsorbate, viz. spectral line frequencies and integral intensities. This approach, however, fails to account for line shapes and manipulates spectral lines as shapeless infinitely narrow and infinitely high images described by the Dirac -functions. In simplest cases, the shape of symmetric spectral lines can be characterized by their maximum positions and full width at half maximum (FWHM). These parameters are very sensitive to various perturbations and changes in temperature and can therefore provide additional evidence on the state of an adsorbate and its binding to a surface. 

This reaction has been reexamined using optical, IR and NMR spectroscopic methods to probe NO reactions with Fe(TPP)(NO) and the more soluble Fe(TmTP)(NO) (92). These studies confirmed the formation of Fe(Por)(NO)2 in toluene-dg at low temperature (Eq. (43)). NMR line shape analysis was used to calculate K43 = 23 M-1 at 253 K (3100 M-1 at 179 K, AH° = —28kJmol 1) (92). The failure of the Fen(Por) complexes to promote NO disproportionation, in contrast to the behavior of the respective Ru(II) and Os(II) analogs, may find its origin partly in the relatively low stability of the dinitrosyl intermediate (K52 estimated to be 2.8 M-1 at 298 K) and unfavorable kinetics of subsequent reaction of this species with NO. 

Determination of chemical exchange rate constants based on the shapes of spectroscopic lines (frequently NMR resonances) of dynamic processes. 

The increase in time resolution of advanced sorption uptake methods and the joint use of sorption and radio-spectroscopic techniques allow for a more detailed analysis of the so-called "non-Fickian" behaviour of sorbing species in the intracrystalline bulk phase [18,28,29,76]. Correspondingly, information on molecular dynamics has been obtained for n-butane and 2-but ne in NFI zeolites by means of the single step frequency response method and C n.m.r. line-shape analysis [29]. As can be seen from Figures 4 and 5, the ad- / desorption for both sorbates proceeds very quickly, but with a... 

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. 

There are many more solvent effects on spectroscopic quantities, that cannot be even briefly discussed here, and more specialized works on solvent effects should be consulted. These solvent effects include effects on the line shape and particularly line width of the nuclear magnetic resonance signals and their spin-spin coupling constants, solvent effects on electron spin resonance (ESR) spectra, on circular dichroism (CD) and optical rotatory dispersion (ORD), on vibrational line shapes in both the infrared and the UV/visible spectral ranges, among others. 

Interpretation of NMR spectra is subject to the same types of errors encountered in other spectroscopic analyses. There are, however, several pitfalls unique to NMR that may not be avoided if all the factors that can affect resonance-line shape are not clearly understood. These factors are considered here to emphasize the need for care in interpretation. 

Spectroscopic techniques have been applied most successfully to the study of individual atoms and molecules in the traditional spectroscopies. The same techniques can also be applied to investigate intermolecular interactions. Obviously, if the individual molecules of the gas are infrared inactive, induced spectra may be studied most readily, without interference from allowed spectra. While conventional spectroscopy generally emphasizes the measurement of frequency and energy levels, collision-induced spectroscopy aims mainly for the measurement of intensity and line shape to provide information on intermolecular interactions (multipole moments, range of exchange forces), intermolecular dynamics (time correlation functions), and optical bulk properties. 

We emphasize the line shape problem perhaps a little more than usual in the spectroscopic literature. Collision-induced spectra have little structure. Yet, the diffuse line and band spectra extend over wide frequency bands and must often be subtracted, say from the complex spectra of planetary or stellar atmospheres, for a more detailed analysis of other, less well known components. The subtraction requires accurate knowledge of the profile and its variation with temperature, composition, etc., often over frequency bands of hundreds of cm-1. 

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. 

Fitting line shapes. In the next Chapter, we will discuss various approaches to computing spectral line shapes. Such computations require as input a reliable model of the interaction potential and of the dipole components. Once a profile is computed on the basis of an imperfect empirical dipole moment, the comparison with spectroscopic measurements may reveal certain inconsistencies which one may more or less successfully correct by small adjustments of the free parameters. After a few iterations, one may thus arrive at an empirical model that is consistent with a spectroscopic measurement [39], If measurements at various temperatures exist, the dipole model must reproduce all measured spectra equally well. 

The high rigidity of the catenane segments has been demonstrated by a temperature-dependent NMR spectroscopic study of the catenane monomers 44 and 46 [37, 52], Almost no temperature dependence was observed for the line shape of the spectra of the catenane monomers 44 and 46 whereas the temperature had a dramatic influence on the spectra of the unmethylated catenanes 41b,d and 42b,d [30, 37, 52, 56]. Therefore, the poly[2]catenanes 48 and 49 represent one extreme case where there is very little relative mobility of the macrocycles of the catenane segments. 

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