Structural broadening

We will show below when and how the line interference and its special case, spectral exchange , appear in spectral doublets considered as an example of the simplest system. It will be done in the frame of conventional impact theory as well as in its modern non-Markovian generalization. Subsequently we will concentrate on the impact theory of rotational structure broadening and collapse with special attention to the shape of a narrowed Q-branch. 

As the temperature of the system approaches —85°, the triplet fine structure broadens and finally merges. Then these two peaks broaden with further temperature increase and finally merge at about —45° this single broad peak then progessively sharpens with further temperature increase. The F19 spectra of SF4 in the temperature range —98 to 23° are pre-... 

The appearance of the IR spectrum of a compound depends somewhat on the sample s phase. Under high resolution, gas-phase IR bands consist of closely spaced lines—the rotational fine structure however, IR bands of liquids and solids very rarely show rotational fine structure. In most solids, the molecules are held in fixed lattice positions and are not free to rotate. In liquids, the high rate of intermolecular collisions and the substantial intermolecular interactions cause random shifts in the rotational energies, thereby broadening the rotational lines of a band sufficiently to merge them into one another, and eliminate the rotational fine structure. (Broadening of fine structure lines is also observed in gas-phase spectra when the pressure is increased.)... 

When increasing temperature (T > 2 K), so introducing thermal disorder, the structure broadens rapidly. For each bulk reflectivity spectrum at a given temperature T, determining the radiative surface width by (3.26), we looked for the value of rle(T) allowing the best reproduction of the experimental spectrum. The various values obtained for re(T) vs T are plotted in Fig. (3.13) and compared with the width of the bulk exciton obtained by KK analysis (in Section II.C.3).70127... 

Ab initio molecular dynamics ° ° calculations performed on vinyl cation confirm that the ground-state structure of C2H is best described as a quasi-planar bridged structure broadened significantly by anisotropic delocalization of the protons due to zero point motion. 

The formation of ion pairs may occur either by direct dissociation or by predissociation [processes (3) and (4) of Section 3. ]. The behavior of the cross section for such processes is the same as that for dissociation or predissociation into neutral fragments a smooth continuum indicates direct dissociation, while predissociation is characterized by a band structure broadened according to the lifetime of the state. The most intense ion-pair formation processes usually exhibit the structure characteristic of predissociation. The occurrence of intense ion-pair formation requires a favorable set of potential curves (or surfaces) and is not readily predictable. The mere fact that a molecule contains an atom or radical of high electron affinity gives no assurance that the negative ion will be formed in detectable amounts by photon absorption. 

Experimental information pertinent to our discussion is presented in fig. 16, which shows combined XPS/BIS spectra for CeRUj (Allen et al. 1983). The data contain two expected features and a surprising one. The expected characteristics are the A = — Sf peak in the XPS spectrum and the A = S[ + U structure, broadened by... 

High-resolution spectroscopy used to observe hyperfme structure in the spectra of atoms or rotational stnicture in electronic spectra of gaseous molecules connnonly must contend with the widths of the spectral lines and how that compares with the separations between lines. Tln-ee contributions to the linewidth will be mentioned here tlie natural line width due to tlie finite lifetime of the excited state, collisional broadening of lines, and the Doppler effect. 

In electron-spin-echo-detected EPR spectroscopy, spectral infomiation may, in principle, be obtained from a Fourier transfomiation of the second half of the echo shape, since it represents the FID of the refocused magnetizations, however, now recorded with much reduced deadtime problems. For the inhomogeneously broadened EPR lines considered here, however, the FID and therefore also the spin echo, show little structure. For this reason, the amplitude of tire echo is used as the main source of infomiation in ESE experiments. Recording the intensity of the two-pulse or tliree-pulse echo amplitude as a function of the external magnetic field defines electron-spm-echo- (ESE-)... 

Many fonns of disorder in a surface structure can be recognized in the LEED pattern. The main manifestations of disorder are broadening and streaking of diffraction spots and diffuse intensity between spots [1]. 

Each vibrational peak within an electronic transition can also display rotational structure (depending on the spacing of the rotational lines, the resolution of the spectrometer, and the presence or absence of substantial line broadening effects such as... 

Experimental confirmation of the metal-nitrogen coordination of thiazole complexes was recently given by Pannell et al. (472), who studied the Cr(0), Mo(0), and W(0) pentacarbonyl complexes of thiazole (Th)M(CO)5. The infrared spectra are quite similar to those of the pyridine analogs the H-NMR resonance associated with 2- and 4-protons are sharper and possess fine structure, in contrast to the broad, featureless resonances of free thiazole ligands. This is expected since removal of electron density from nitrogen upon coordination reduces the N quad-rupole coupling constant that is responsible for the line broadening of the a protons. 

Figure 9.18 shows a typical energy level diagram of a dye molecule including the lowest electronic states Sq, and S2 in the singlet manifold and and T2 in the triplet manifold. Associated with each of these states are vibrational and rotational sub-levels broadened to such an extent in the liquid that they form a continuum. As a result the absorption spectrum, such as that in Figure 9.17, is typical of a liquid phase spectrum showing almost no structure within the band system. 

The Q and ft) dependence of neutron scattering structure factors contains infonnation on the geometry, amplitudes, and time scales of all the motions in which the scatterers participate that are resolved by the instrument. Motions that are slow relative to the time scale of the measurement give rise to a 8-function elastic peak at ft) = 0, whereas diffusive motions lead to quasielastic broadening of the central peak and vibrational motions attenuate the intensity of the spectrum. It is useful to express the structure factors in a form that permits the contributions from vibrational and diffusive motions to be isolated. Assuming that vibrational and diffusive motions are decoupled, we can write the measured structure factor as... 

The discussion of diffraction so far has made no reference to the size of the 2D grating. It has been assumed that the grating is infinite. In analogy with optical or X-ray diffraction, finite sizes of the ordered regions on the surface (finite-sized gratings) broaden the diffracted beams. From an analysis of the diffracted-beam shapes, the types of structural disorder in the surface region can be identified and quantified. - ... 

Diffraction is usefiil whenever there is a distinct phase relationship between scattering units. The greater the order, the better defined are the diffraction features. For example, the reciprocal lattice of a 3D crystal is a set of points, because three Laue conditions have to be exactly satisfied. The diffraction pattern is a set of sharp spots. If disorder is introduced into the structure, the spots broaden and weaken. Two-dimensional structures give diffraction rods, because only two Laue conditions have to be satisfied. The diffraction pattern is again a set of sharp spots, because the Ewald sphere cuts these rods at precise places. Disorder in the plane broadens the rods and, hence, the diffraction spots in x and y. The existence of streaks, broad spots, and additional diffuse intensity in the pattern is a common... 

One of the great advantages of Modulation Spectroscopy is its ability to fit the line shapes of sharp, localized structures, as illustrated in the lower part of Figure 1. These fits yield important relevant parameters, such as the value of the energy gap and the broadening parameter. 

Figure 4 Raman spectra of a series of strontium titanates showing typicai iine shapes and information avaiiabie for fingerprinting. The broadening of the high-wavenumber lines is related to the polar character of the TiOs octahadra that occur in all of these structures.

---