Band-envelopes

The band envelope is asymmetrical with insufficient resolution to identify the position of the weaker component. 

Another difficulty with the infrared method is that of determining the band center with sufficient accuracy in the presence of the fine structure or band envelopes due to the overall rotation. Even when high resolution equipment is used so that the separate rotation lines are resolved, it is by no means always a simple problem to identify these lines with certainty so that the band center can be unambiguously determined. The final difficulty is one common to almost all methods and that is the effect of the shape of the potential barrier. The infrared method has the advantage that it is applicable to many molecules for which some of the other methods are not suitable. However, in some of these cases especially, barrier shapes are likely to be more complicated than the simple cosine form usually assumed, and, when this complication occurs, there is a corresponding uncertainty in the height of the potential barrier as determined from the infrared torsional frequencies. In especially favorable cases, it may be possible to observe so-called hot bands i.e., v = 1 to v = 2, 2 to 3, etc. This would add information about the shape of the barrier. 

Figure 35 Top row XPS C(ls) and O(ls) band envelopes and curve-fitted components for (a) PMMA and (b) PEEK films A is untreated, B the DBD-treated at 5.7J cm-2 and C the post-treatment-aged (stored) sample. Bottom row contact angle and XPS O/C variation of (c) PMMA film and (d) PEEK film solid lines are for the freshly treated in air DBD samples, the dashed lines are for the post-process-aged films. Reprinted from Upadhyay et al. [98]. Copyright 2005, with permission of Elsevier.

Measurement of integrated absorption requires a knowledge of the absorption line profile. At 2000-3000 K, the overall line width is about 10-2 nm which is extremely narrow when compared to absorption bands observed for samples in solution. This is to be expected, since changes in molecular electronic energy are accompanied by rotational and vibrational changes, and in solution collisions with solvent molecules cause the individual bands to coalesce to form band-envelopes (p. 365). The overall width of an atomic absorption line is determined by ... 

Martin (1971) gives a brief tutorial on the subject of optimization. Fletcher (1971) gives an excellent review and presents criteria for the selection of an appropriate method. Rigler and Pegis (1980) discuss the various methods from the viewpoint of optical applications. Pitha and Jones (1966) compare several methods applied to fitting infrared band envelopes. 

Molecules in crystals or dispersed in host lattices are often present in a range of environments, and this results in a broadening of the electronic absorption spectrum. Such an inhomogeneously broadened absorption band (envelope of transitions) may be considered as a superposition of several distinguishable sites. A narrow line laser can saturate one of the transitions under the envelope and the corresponding molecules will no longer take part in the absorption process. This phenomenon is referred to as hole... 

Proton NMR spectra of coal derivatives generally give rise to either broad peaks or complicated multiplets which can be easily divided into band envelopes. For example, the H1 spectrum of a coal-hydrogenation asphaltene (4) consists of three peaks, two of which overlap. A broad peak at lowest field is caused by protons in aromatic and phenolic systems, whereas two higher field peaks are caused by protons bonded to carbons situated o to aromatic rings and those bonded to other nonaromatic carbons, respectively. The ratios of these spectral areas are the same as the ratios of the hydrogens in each of these three hydrogen classes. This accounts for one of the most important characteristics of proton NMR spectra—namely, no calibration data are necessary. 

RR excitation profiles from a series of M(CO)4(a,a -diimine) complexes have identified additional y-polarized (dx2-z2) ai - b2 (n ) and x-polarized (dxy) a2 -> b2 (n ) MLCT transitions in the absorption band envelope, although the latter component is relatively weak for substituted phen derivatives [63], These absorption features are observable in the 80 K spectrum of W(CO)4(4-Me-phen) in EPA (see Fig. 2). The most intense MLCT components in the low-temperature spectrum appear at 444 and 468 nm, and these are associated with the ai -> b i and b2 -> b i transitions, respectively [60],... 

When evaluating the energy differences, one should take the 0-phonon transitions of 1S and 3T into account and not the maximum of the band envelope. 

Josef Pitha and Richard Norman Jones, Optimization Methods for Fitting Curves to Infrared Band Envelopes—Computer Programs, National Research Council of Canada, Ottawa, 1968. 

Figure 7 Complete set of 45 bands required to fill the absorption and MCD band envelopes of the phthalocyanine-rmg-reduced radical anion species [ZnPc(—3)] . The absorption spectrum was recorded at 77K, and the MCD spectrum at 40K. The bands were fitted using Gaussian-shaped bands with the identical band centers and bandwidths for pairs of absorption and MCD bands. A weak, Faraday term located at 14 860cm is due to a residual 1% impurity of neutral ZnPc(—2). Experimental data (sohd fine) fitted data (broken line). (Reproduced with permission from J. Mack, Y. Asano, N. Kobayashi, M. J. Stilhnan (2005) J. Am. Chem. Soc. 127 17697-17711. 2005 American Chemical Society)...

Although it is possible in principle to derive the ground state g-factor value by measuring the Co/Ih ratio from the Method of Moments analysis, this is usually not practical, as the absorption bands lack a baseline-to-baseline band envelope or due to overlap with bands associated with other metal centers or chromophores. It should be noted that in some instances, excited state parameters also have to be carefully considered. For example, when ground state degeneracy (and the associated Boltzmaim distribution of population across... 

DFT calculations, as discussed in Section 6.3.1, yield a similar picture. Furthermore, modification of the valence band envelope as a function of hv was characteristic for all Ml and reference catalysts. Therefore it should be stressed that although we adopt the formalism of oxidation states it is essentially always only a formal oxidation state, which is just a chemical tool but does not represent any serious physical meaning, since the electron occupations are considerably different. 

Because of the use of finite slit widths, the radiation is not monochromatic (and covers an appreciable part of the band envelope) and the measured quantity is an apparent integrated absorption intensity (B),... 

---