Band contours

The d-d bands of transition metal complexes are weak, sometimes very weak. Some of the bands are sharp, some broad and some so broad that it is difficult to be certain that they exist. In the next section we shall consider the problem of intensities in this section, the problem of band shapes. The two are related. The very weak peaks are usually sharp. If they were not, they would escape detection and no doubt many broad, very weak, peaks do pass undetected. 

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At higher pressures only Raman spectroscopy data are available. Because the rotational structure is smoothed, either quantum theory or classical theory may be used. At a mixture pressure above 10 atm the spectra of CO and N2 obtained in [230] were well described classically (Fig. 5.11). For the lowest densities (10-15 amagat) the band contours have a characteristic asymmetric shape. The asymmetry disappears at higher pressures when the contour is sufficiently narrowed. The decrease of width with 1/tj measured in [230] by NMR is closer to the strong collision model in the case of CO and to the weak collision model in the case of N2. This conclusion was confirmed in [215] by presenting the results in universal coordinates of Fig. 5.12. It is also seen that both systems are still far away from the fast modulation (perturbation theory) limit where the upper and lower borders established by alternative models merge into a universal curve independent of collision strength. 

LIF excitation spectra were recorded for alkyl aminobenzoates (165) under free jet conditions. The partially resolved band contours were different for the various compounds... 

Theoretical studies, based entirely on the local tetrahedral pentamer model of the liquid 47> but including isotropic expansion and contraction with the distribution of 00 separations matched to the observed 00 correlation function, cannot completely account for the observed OH stretching spectrum 90>. The addition of some weak hydrogen bonds improves the predicted spectrum 90>, but still leaves the widths of the band contours largely unaccounted for. It seems likely that inclusion of 000 angle distribution effects (i.e. bent hydrogen bonds as well as small dispersion about 109.5°) will improve the agreement between predicted observed spectra. 

A vibronic coupling model for mixed-valence systems has been developed over the last few years (1-5). The model, which is exactly soluble, has been used to calculate intervalence band contours (1, 3, 4, 5), electron transfer rates (4, 5, 6) and Raman spectra (5, 7, 8), and the relation of the model to earlier theoretical work has been discussed in detail (3-5). As formulated to date, the model is "one dimensional (or one-mode). That is, effectively only a single vibrational coordinate is used in discussing the complete ground vibronic manifold of the system. This is a severe limitation which, among other things, prevents an explicit treatment of solvent effects which are... 

In liquids the interactions between neighboring molecules are considerably more complicated than in gases. The resultant broadening obliterates the fine line structure seen in gas spectra, leaving only broad band profiles. There are many possible contributors to this broadening. In some cases, adequate approximation is obtained by assuming that the band contour is established by collisions. Ramsay (1952) has noted that substitution of appropriate molecular density and collision diameter numbers in the collision broadening formula results in realistic band widths for certain liquid-phase systems. In such systems, the bands typically show an approximately Lorentzian profile. Approximate deconvolution of inherently broadened liquid-phase spectra may therefore be obtained on the basis of the assumption of Lorentzian shape (Kauppinen et al., 1981). 

Van der Waals molecules of heavier homonuclear diatomics have also been studied, using similar techniques to the ones mentioned above. However, the numbers of bound states generally are much greater for such systems, and the band structures are richer and therefore harder to resolve. Detailed work has shown that for the more massive diatomics molecular rotation is more or less hindered and the level structures are much more complex than the ones seen in the H2-X systems. Rather uncertain band contour analyses are used in those cases but a few reasonably well resolved band spectra of van der Waals molecules are known [49, 267]. 

The infrared spectrum of [Au2(/a-I)2Me4] has been measured in solution and in the solid state (243, 244) and gives rise to identical band contours. This was taken to indicate that rotation about the gold-carbon bonds... 

The conditions of the expansion and the high resolution of the FT technique allowed an examination of the rotational structure of several bands. Rotational band contours could be modeled with an asymmetric rotor program, and this served as a method for determining both the rotational temperatures achieved in the expansion and structural parameters of the various electronic states. As shown in Figures 16 and 17, under quite dilute conditions the rotational temperature derived from a Boltzmann fit to the (5,0,0) band was 30 K, while for neat expansions of OCIO, the temperature determined from this fit yielded a rotational temperature of 80 K. High resolution spectra, such as those in Figure 18, were used to revise the excited state... 

The concept of transferability and a detailed understanding of these amide modes provides the basis for quantitative estimation of secondary structure for unknown proteins and polypeptides. The quantitative methods currently used to analyze vibrational spectra of proteins can be classified into two categories (1) methods based on decomposition of band contours into underlying components characterized by distinct frequencies, and (2) methods based on principles of pattern recognition. 

The lifetimes measured by Miller and Lee probably correspond to the decay times of the SVL species with the rotational-state distribution close to the Boltzmann population, since the entire rotational band contour was excited and the entire emission band profile was observed. The lifetimes measured by Yeung and Moore probably correspond to the decay times of the SVL species with an appreciable non-Boltzmann population of the rotational states, since a small segment of the rotational band contour (probably only a few rotational lines) was excited. 

It should be noted that spectroscopic data obtained over a wide range of a values show that Vi is not quite linear when plotted against 1/a, and the observed curvature is greater than that due to the coulombic term shown explicitly in Eq. (9). Such curvature is due to nonparabolic band contours and to a breakdown of the effective mass approximation. As a result, the filnig values obtained with Eqs. (7) and (9), and to a lesser extent the Epoi value, will depend on the range of a values used in the fits. 

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