Combination Bands, Linear Molecules

Figure 6.27 shows fhe f Sg infrared combination band of acefylene, where Vj is fhe symmefric CFI sfrefching vibration and Vj fhe cis bending vibration, as an example of a 77 — Zg band of a linear molecule. Nofe fhaf fhe P branch sfarts wifh P(2), rafher fhan / (f) as if would in a Z-Z fype of fransifion, and fhaf fhere is an intensify alternation of 1 3 for J"... 

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). 

Another complication arises in the interpretation of absorption spectra. If a molecule vibrates with pure harmonic motion and the dipole moment is a linear function of the displacement, then the absorption spectrum will consist of fundamental transitions only. If either of these conditions is not met, as is usually the case, the spectrum will contain overtones (multiples of the fundamental) and combination bands (sums and differences). Most of these overtones and combination bands occur in the near-infrared (0.8-2.0/un). 

The same rules for number of bands in a spectrum apply to Raman spectra as well as IR spectra 3N—6 for nonlinear molecules and 3N—5 for linear molecules. There may be fewer bands than theoretically predicted due to degeneracy and nonactive modes. Raman spectra do not usually show overtone or combination bands they are much weaker than in IR. A rule of thumb that is often tme is that a band that is strong in IR is weak in Raman and vice versa. A molecule with a center of symmetry, such as CO2, obeys another rule if a band is present in the IR spectrum, it will not be present in the Raman spectrum. The reverse is also true. The detailed explanation for this is outside the scope of this text, but the rule explains why the symmetric stretch in carbon dioxide is seen in the Raman spectrum, but not in the IR spectrum, while the asymmetric stretch appears in the IR spectrum but not in the Raman spectmm. 

Methylene groups in linear, aliphatic molecules have two primary peaks at about 5800 cm" (1723 nm) and 5680 cm" (1762 nm) in the first overtone region. The 5800-cm" peak is generally thought to be a combination band, " reported as The 5680-cm" peak is considered to be a pure... 

The theoretical background developed for the diatomic molecules explains well the essential spectral features of overtones. However, the near-infrared spectra also contain combination bands because an infrared photon can excite two (and more) distinct vibrational modes in the same molecule. For a molecule containing N atoms, we now have ON - 6) normal vibrations, or (31V — 5) if the molecule is linear. The potential function has the form ... 

The perpendicular vibrations of linear polyatomic molecules can be doubly degenerate and can therefore show /-type doubling. Some combination bands of linear molecules will not show intensity alternation but will be subject to /-type splitting. 

In general, there are three types of bands for linear molecules two types of fundamentals (parallel and perpendicular vibrations) and the combination and overtone bands of these fundamentals. The parallel vibrations have only P- and R-branches. The perpendicular vibrations have P-, Q-, and R-branches, with the Q-branch fairly intense. The combination bands can have P-, Q-, and R-branches, with the Q-branch weak in some instances. 

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