Overtone linear molecules

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). 

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. 

The general absorptions of methylene groups are illustrated in Figure 2.7, a spectrum of n-decane. 23.1 First Overtone Region — Linear Molecules... 

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. 

Equations (6.5) and (6.12) contain terms in x to the second and higher powers. If the expressions for the dipole moment /i and the polarizability a were linear in x, then /i and ot would be said to vary harmonically with x. The effect of higher terms is known as anharmonicity and, because this particular kind of anharmonicity is concerned with electrical properties of a molecule, it is referred to as electrical anharmonicity. One effect of it is to cause the vibrational selection mle Au = 1 in infrared and Raman spectroscopy to be modified to Au = 1, 2, 3,. However, since electrical anharmonicity is usually small, the effect is to make only a very small contribution to the intensities of Av = 2, 3,. .. transitions, which are known as vibrational overtones. 

The Hamiltonians of the previous sections describe realistic vibrational spectra of linear triatomic molecules except when accidental degeneracies (resonances, cf. Section 3.3) occur. A particularly important case is that in which the bending overtone (02°0) is nearly degenerate with the stretching fundamental (10°0) of the same symmetry Fermi, 1929, resonance). This situation occurs when the coefficient in Eq. (4.67) is nearly equal to -A (Figure 4.13). The Majorana... 

Cooper, I. L., and Levine, R. D. (1991), Computed Overtone Spectra of Linear Triatomic Molecules by Dynamical Symmetry, /. Mol. Spectr. 148, 391. 

Furthermore, polyatomic molecules consisting of n atoms have 3n - 6 vibrational degrees of freedom (or 3n — 5 in the special case of a linear polyatomic molecule), instead of just one as in the case of a diatomic molecule. Some or all of these may absorb infrared radiation, leading to more than one infrared absorption band. In addition, overtone bands (Av > 1)... 

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). 

Molecules consist of atoms which have a certain mass and which are connected by elastic bonds. As a result, they can perform periodic motions, they have vibrational deitrees of freedom All motions of the atoms in a molecule relative to each other are a superposition of so-called normal vibrations, in which all atoms are vibrating with the same phase and normal frequency. Their amplitudes are described by a normal coordinate. Polyatomic molecules with n atoms possess 3n - 6 normal vibrations (linear ones have 3n - 5 normal vibrations), which define their vibrational spectra. These spectra depend on the masses of the atoms, their geometrical arrangement, and the strength of their chemical bonds. Molecular aggregates such as crystals or complexes behave like super molecules in which the vibrations of the individual components are coupled. In a first approximation the normal vibrations are not coupled, they do not interact. However, the elasticity of bonds does not strictly follow Hooke s law. Therefore overtones and combinations of normal vibrations appear. 

Table Il-2e lists the vibrational frequencies of iriaiomic interhalogeno compounds. The resonance Raman spectrum of the I3 ion gives a series of overtones of the v vibration. - The resonance Raman. spectra of the l2Br" and IBri ions and their complexes with amylose have been studied. The same table also lists the vibrational frequencies of XHY-type (X, Y halogens) compounds. All these species are linear except the ClHCl" ion, which was found to be bent in an inelastic neutron scattering (INS) and Raman spectral studySalt-molecule reactions such as CsF+Fj=Cs[F3] have been utilized to produce a number of novel triaiomic and other anions in inert gas matrices.

Another effect of the anharmonic terms is to change the transition probabilities of vibrational transitions. If the electric moment were a linear function of the displacements from equilibrium and if the vibrational wave functions were accurately given by harmonic oscillator functions, no overtones or combinations should appear in infrared spectra. The fact that such bands do occur shows that one or the other of these conditio)is is not met in fact, it is probable that neither condition is lived up to in actual molecules. It is evident from the convergerice of overtone levels that the harmonic oscillator approximation is not exact, while considerations of intensities indicate that in addition the electric moment is not a strictly linear function of the displacements. For a further discussion of the effect of these factors on the intensities, the reader may refer to the work of Crawford and collaborators. ... 

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