Band-shape analysis

Figure 2 Spectral parameters typically used in band shape analysis of an FTIR spectrum peak position, integrated peak area, and FWHM.

For many applications, quantitative band shape analysis is difficult to apply. Bands may be numerous or may overlap, the optical transmission properties of the film or host matrix may distort features, and features may be indistinct. If one can prepare samples of known properties and collect the FTIR spectra, then it is possible to produce a calibration matrix that can be used to assist in predicting these properties in unknown samples. Statistical, chemometric techniques, such as PLS (partial least-squares) and PCR (principle components of regression), may be applied to this matrix. Chemometric methods permit much larger segments of the spectra to be comprehended in developing an analysis model than is usually the case for simple band shape analyses. 

Fig. 14. Factor analysis loadings (first and second spectral components) for thermal unfolding of RNase A as monitored with amide F FTIR and far-UV ECD. In each case a pretransition is evident in the curves before the main transition at 55°C. This full band shape analysis can sense smaller variations and can be partitioned to give added insight. Since the main ECD change could be shown to be loss of intensity, the major structural change was unfolding of a helix. The frequency dispersion of the FTIR change showed that some /3-sheet loss accompanied this pretransitional helix unfolding, but that most sheet loss was in the main transition.

Binsch, G. Band-Shape Analysis." In Dynamic Nuclear Magnetic Resonance Spectroscopy Jackman, L. M. Cotton, F. A., Eds. Academic Press New York, 1975 pp. 45-81. See also Binsch, G. Top Stereochem., 1968, 3, 97-192. 

Most of the data in Table 12 come from the work of Shvo et al. (78). Careful band-shape analysis and solvent-effect studies permitted evaluation of the rate constants and AG values at 298 K, which renders the discussion of substituent effects more meaningful than usual. The authors obtained reasonably linear Hammett plots when correlating log km with Or (79) for X and Y, holding one of these substituents constant. They also found that the dihydropyridine system may act as an unusually efficient donor, giving a AG of 17.6 kcal/mol with X, Y = H, CN, the only barrier below 25 kcal/mol reported for any donor-substituted cyanoethylene. However, with other acceptor combinations the dihydropyridine moiety is not so outstanding, and this illustrates the difficulty of measuring donor and/or acceptor effects by rotational barriers alone (vide infra). 

Unfortunately, the chemical shift differences between die four methyl sites in the 2,2 -diisopropyl derivatives are very small (0. II to 0.12 ppm in the Z form, 0.01 to 0.03 ppm in the form), and no detailed band-shape analysis is possible. However, additional information was obtained by a study of the ther-mochromic forms of several bianthronylidenes (167). These species are now regarded as having the B form (TWZ and TWE in Fig. 10), which is also seen as identical to a colored species formed on photolysis of the A form (168,169). Because of its strong absorption at 650 to 730 nm (e = 15,500) where the A form is transparent, the equilibrium concentration of the B form could be measured as a function of the temperature, and AH° (A B) could be obtained from the slope of a plot of log K versus 1 IT. Note that K = [(TWE) + (TWZ) ... 

An excess of the twisted form (B) was prepared from the photostable 2,2 -bis(trifluoromethyl)-129c by laser flash photolysis, and its decay to the folded form (A) was followed photometrically. From the rate constants at four temperatures, AH (B- A) = 16.1 0.7 kcal/mol was obtained. For this compound, AH° (A B) = 4.2 kcal/mol had been found, and the sum of these two values agrees well with AG (E- Z) = 21.5 0.3 kcal/mol obtained by band-shape analysis, which probably corresponds to a A// value of 20 to 21 kcal/mol, assuming AS to be -2 to -5 e.u. 

Further complication in semiconductor band shape analysis concerns the spectral region near the fundemental absorption onset. Ideal semiconductor crystal at 0 K should not absorb any photons with energies lower than Eg. Real systems, however, show pronounced absorption tails at energies lower than the bandgap energy (Figure 7.7). The absorption profile within the tail region can be very well approximated by the empirical Urbach s rule [23-26] ... 

Band fitting (curve fitting, or band shape analysis) is conveniently performed with commercially available software packages which fit, interactively or automatically, Gaussian or Lorentzian line shapes (or their combinations) to an unknown band profile. The applicability of this technique to lignin chemistry is not known at present. 

G. Binsch, Band-Shape Analysis, in L. M. Jackman and F. A. Cotton (eds.). Dynamic Nuclear Magnetic Resonance Spectroscopy, Academic Press, New York (1975). 

It has in fact been anticipated for many years that the CT free energy surfaces may deviate from parabolas. A part of this interest is provoked by experimental evidence from kinetics and spectroscopy. Eirst, the dependence of the activation free energy, Ff , for the forward (/ = 1 ) and backward i = 2) reactions on the equilibrium free energy gap AFq (ET energy gap law) is rarely a symmetric parabola as is suggested by the Marcus equation,Eq. [9]. Second, optical spectra are asymmetric in most cases and in some cases do not show the mirror symmetry between absorption and emission.In both types of experiments, however, the observed effect is an ill-defined mixture of the intramolecular vibrational excitations of the solute and thermal fluctuations of the solvent. The band shape analysis of optical lines does not currently allow an unambiguous separation of these two effects, and there is insufficient information about the solvent-induced free energy profiles of ET. 

As is easy to see from Eq. [80] and Figure 7, the Q model predicts the breaking of the symmetry between the absorption and emission widths (Eq. [11]) generated by a statistical distribution of solvent configurations around a donor-acceptor complex (inhomogeneous broadening). This fact may have a significant application to the band shape analysis of optical transitions since unequal absorption and emission width are often observed experimently. " ... 

In many practical cases, the factors f i are very close to unity and can be omitted. The parameters So, and mo,- are then equal to their gas-phase values oto, and mo,. Equation [100] then gives the polarizability change in terms of spectroscopic moments and gas-phase solute dipoles. Experimental measurement and theoretical calculation of Aao = aoi - ocoi is still challenging. Perhaps the most accurate way to measure Akq presently available is that by Stark spectroscopy,which also gives Awq. Equation [100] can therefore be used as an independent source of Aao, provided all other parameters are available, or as a consistency test for the band shape analysis. 

Spectral measurements open a door to access the rate constant parameters of ET. The connection between optical observables and ET parameters can be divided into two broad categories (1) analysis of the optical band profile (band shape analysis) and (2) the use of integrated spectral intensities (see... 

The challenges outlined above still await a solution. In this section, we show how some of the theoretical limitations employed in traditional formulations of the band shape analysis can be lifted. We discuss two extensions of the present-day band shape analysis. First, the two-state model of CT transitions is applied to build the Franck-Condon optical envelopes. Second, the restriction of only two electronic states is lifted within the band shape analysis of polarizable chromophores that takes higher lying excited states into account through the solute dipolar polarizability. Finally, we show how a hybrid model incorporating the electronic delocalization and chromophore s polarizability effects can be successfully applied to the calculation of steady-state optical band shapes of the optical dye coumarin 153 (C153). We first start with a general theory and outline the connection between optical intensities and the ET matrix element and transition dipole. 

The combination of Eq. [134] with Eq. [144] provides an effective formalism for the band shape analysis of CT spectra when a substantial degree of electronic delocalization is involved. Equation [134] is exact for a TS donor-acceptor complex and, therefore, can be used for an arbitrary degree of electronic delocalization as long as the assumption of decoupling of the vibrational and solvent modes holds. Figure 18 illustrates the application of the band shape... 

The Franck-Condon factors of polarizable chromophores in Eq. [153] can be used to generate the complete vibrational/solvent optical envelopes according to Eqs. [132] and [134]. The solvent-induced line shapes as given by Eq. [153] are close to Gaussian functions in the vicinity of the band maximum and switch to a Lorentzian form on their wings. A finite parameter ai leads to asymmetric bands with differing absorption and emission widths. The functions in Eq. [153] can thus be used either for a band shape analysis of polarizable optical chromophores or as probe functions for a general band shape analysis of asymmetric optical lines. 

The temperature dependence of the H-nmr spectrum of the isopropyl cation [38] prepared from isopropyl chloride in SOjClF-SbFg solution (Saunders and Hagen, 1968b) demonstrated rapid interchange of the two types of protons. Band shape analysis showed the reaction to be intramolecular and the activation energy to be 16.4 0.4 kcal mol-. It was suggested that the rearrangement involves n-propyl cation [39] as an intermediate (33) and that... 

Saunders and Rosenfeld (1969) extended their H-nmr investigation to temperatures above 100°C and discovered another, slower process which exchanges the two methylene protons with the nine methyl protons, resulting in coalescence of these bands above 130°C. The band shape analysis gave an activation energy of 18.8 1 kcal mol" for this new process. Since any mechanism involving primary alkyl cations is expected to have a barrier of ca 30 kcal mol" (the enthalpy difference between tertiary and primary carbo-cations), the formation of a methyl-bridged (corner protonated cyclopropane)... 

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