Band positions overtone

Note that the value of the anharmonicity constant can thus be derived from a comparison between the fundamental n = 0 to n = 1 absorption band frequency and the first and subsequent overtone band positions. Given the form of the Morse Curve, Xe can be calculated from De, and hence an estimate of the bond dissociation energy... 

Finally we turn to the structured nature of the overtone bands. First we note that the structure in bands at low energies, due to dispersion effects, becomes washed out in their overtone spectra. In this respect the bands about 650 and 944 cm", assigned to components in the librational (2-<—0) and (3<—0) manifolds, are unusually sharp. They are sharper than the fundamental from which they derive and their widths are limited only by the spectrometer s resolution. These effects have been assigned to the impact of anharmonicity, since the librational well is more sinusoidal than quadratic in shape. Further analysis would address, mostly, band positions and this type of treatment can be followed in several texts [11]. We shall not pursue this avenue further except to draw attention to the distribution of intensities between the bands within any one overtone manifold. The intensities should be distributed according to the local density of states ( 2.6.2) of the symmetry species of the individual components in each manifold tables of these species have been published [12]. In this case the librational ground state species for a ion, imder T symmetry, is F2 and this gives rise to the (2<—0) overtone species A, E and F2. The distribution of intensity in the (3 —0) band will be according to A, F, 2F2. 

There is some correlation between molecular structure and band position for certain bands, but because these are often overtone and combination bands, their positions are not as structure-dependent as the fundamental bands in the mid-IR. For example, primary amines, both ahphatic and aromatic, have two absorption bands, one at about 1500 nm and the second at about 1990 nm. Secondary amines have only one band at about 1500 nm. As expected, a tertiary amine has no NH band. Amides with an — NH2 group can be distinguished from R— NH—R amides by the number and position of the N—H bands. The reference by Goddu has a detailed table of NIR structure-wavelength correlations. 

Fig. 2.2. Schematic summary of positions of bands in overtone infrared region for amide N—H group. (Klotz and Franzen, 1962.)...

Figure 12.2 Typical spectral response curves for high-0H (enhanced UV transmission) and low-OH" (enhanced IR transmission) fibres the 0H overtone and side band positions are marked. The dominant attenuation factors, indicated by the dashed lines, are Rayleigh scattering at short wavelengths and IR absorption at long wavelengths. The dotted lines mark the 90 per cent and 99 per cent transmission per metre limits...

Calculations of band positions using Equation 1.18 will more closely approximate observed band positions than those calculated from the ideal harmonic oscillator expression found in Equation 1.16. Eor a rule of thumb, the first overtone (2v) for a fundamental can be calculated as 1% shift due to anharmonicity, or Xj = (0.01). Thus, the expression using wavenumbers is... 

The first overtone stretching vibrations of methylene groups of strained-ring cyclic compounds such as cyclopropane occur near 6135 cm (1630 nm). The effects of various substituents on the ring have been studied by several authors. Gassman and Zalar list the band positions of 37 cyclopropane derivatives. Gassman also published a table of first overtone CH band positions of aliphatic nortricyclene derivatives. These overtones were at sUghtly lower wavenumber maxima than the cyclopropanes — about 6024 cm (1660 nm). 

FIGURE 2.9 Demonstration of the third overtone (4 v) harmonic and the second overtone (3 v) combination region, illustrating the relative intensities and band positions. The third overtone (4 v) near-infrared C-H stretching aromatic, methyl, and methylene band positions are shown. A region of second overtone (3 v) combination bands is also seen in this figure. 

The first overtone of the C-H stretch next to a double bond occurs at a higher wavenumber (lower wavelength) than saturated C-H stretch absorptions. This peak is strong and distinct in some structures, particularly the methylene group of terminal double. In most cases, however, it is weak and difficult to locate especially in the presence of methyl groups. The band position is near 61(X)-6200 cm (1640-1612 nm). 

The first overtone of the C-H stretch of the double bond in norbomenes was determined to be in the range of 5970-6080 cm (1645-1675 nm). The attribution of this absorption band to the C-H groups next to the double bonds and not the bridgehead C-H was confirmed by examination of model compounds that lacked the vinyl C-Hs and retained the bridgehead C-H. The effect of a number of different substituents on the band position was also studied. 

As in aromatic compounds, dienes demonstrate multiple bands associated with conjugated doublebond and C-H stretching. The mid-infrared spectra of conjugated polyenes exhibit a band in the 1000-to 900-cm" (10,000- to 11,111-nm) region, which does not have overtones or combination bands observed in the near-infrared. This band is indicative of cis and trans groups within the different polyenes. The near-infrared bands associated with v H-C=C are observed near 6110 cm (1637 nm), 5960 cm (1678 nm), 4710 cm (2123 nm), 4595 cwr (2176 nm), and 4470 cm i (2237 nm) and are very similar to those shown for 1-hexene in Figure 3.1. The 3v C=C band is observed near 4950 cm (2020 nm). Note that the Appendix material provides more examples of model spectra as well as tables showing precise band positions. 

Conjugation with aromatic rings and donble bonds, and interactions with halogens and cyclic structures, all affect the band positions, as in the mid-infrared. Also, these second overtones are sometimes split into two as there may be two or more small bands in the vicinity of the calculated second overtone. The second overtone of the C=0 of a carboxylic acid appears at about 5260 cm" (1900 nm) and is particnlarly clear in a spectrum of perfluorocaproic acid taken in solution, as this acid has no CH absorptions. It can be seen in Figure 7.2, a comparison between octanoic and octadecanoic acids in carbon tetrachloride. With the shorter-chain acid, the acid carbonyl peak is more prominent. 

Table 8.2 lists band positions and intensities of some primary aromatic amines in carbon tetrachloride, illustrating the effect of substituents. The table also includes the second overtone... 

The number of fundamental vibrational modes of a molecule is equal to the number of degrees of vibrational freedom. For a nonlinear molecule of N atoms, 3N - 6 degrees of vibrational freedom exist. Hence, 3N - 6 fundamental vibrational modes. Six degrees of freedom are subtracted from a nonlinear molecule since (1) three coordinates are required to locate the molecule in space, and (2) an additional three coordinates are required to describe the orientation of the molecule based upon the three coordinates defining the position of the molecule in space. For a linear molecule, 3N - 5 fundamental vibrational modes are possible since only two degrees of rotational freedom exist. Thus, in a total vibrational analysis of a molecule by complementary IR and Raman techniques, 31V - 6 or 3N - 5 vibrational frequencies should be observed. It must be kept in mind that the fundamental modes of vibration of a molecule are described as transitions from one vibration state (energy level) to another (n = 1 in Eq. (2), Fig. 2). Sometimes, additional vibrational frequencies are detected in an IR and/or Raman spectrum. These additional absorption bands are due to forbidden transitions that occur and are described in the section on near-IR theory. Additionally, not all vibrational bands may be observed since some fundamental vibrations may be too weak to observe or give rise to overtone and/or combination bands (discussed later in the chapter). 

Liittke and Mecke (1949) investigated e.g. the position of the second overtone OH vibration of phenol in 18 solvents and found that, on changing from an inert solvent to a solvent which has a strong interaction with the phenol, the OH-band is displaced to longer wavelengths and broadened. In some cases a splitting of the OH-band into two components was also observed. 

FIGURE 3.26. Benzoyl chloride. A. Aromatic C—H stretch, 3065 cm-1. B. The C=0 stretch, 1774 cm-1 (see Table 3.3). (Acid chloride C=0 stretch position shows very small dependence on conjugation aroyl chlorides identified by band such as at C.) C. Fermi resonance band (of C=0 stretch and overtone of 8/2 cm1 band), 1730 cm-1. 

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