Transitions, vibrational overtones

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. 

Although we have been able to see on inspection which vibrational fundamentals of water and acetylene are infrared active, in general this is not the case. It is also not the case for vibrational overtone and combination tone transitions. To be able to obtain selection mles for all infrared vibrational transitions in any polyatomic molecule we must resort to symmetry arguments. 

In Section 6.1.3 it was noted that vibrational overtone transitions, whether observed by infrared or Raman spectroscopy, are very weak. They become even weaker as the vibrational quantum number increases. The high sensitivity of CRDS makes it an ideal technique for attempting to observe such transitions. 

The number of peaks in an IR spectrum may increase due to overtones. Normally, the vibrational level is allowed to change by +1. If the vibrational energy level changes by 2 or more (a forbidden transition), an overtone results. It is also possible for two normal mode vibrations to combine into a third. 

Benjamin, I., Cooper, I. L., and Levine, R. D. (1987), Dipole Operator and Vibrational Overtone Transitions in Diatomic Molecules Via an Algebraic Approach, Chem. Phys. Lett. 139, 285. 

A rule of thumb for hydride stretches [56, 57] is that the intensities of the vibrational overtone and combination transitions decrease, approximately, as IQ-Ay jjjg drop-off in intensity for the first few quanta of excitation may be even steeper, by another factor of 10. This implies that, in a specific spectral interval, the strongest vibrational transitions from the vibrationless ground state level correspond to the transition with the smallest Av and the greatest anharmonicity. However, as shown later, even these small absorption cross sections of vibrational overtone transitions can be sufficient for overtone preexcitation. 

Naturally, the bands in this region may well represent a blend of the (v = 1) —(v = 2) and (n = 2) — (n = 3) aromatic CH stretching transitions with overtones and combinations involving aromatic CC stretches as well as aliphatic CH stretches. Many PAHs which do not have aliphatic side groups show weak absorptions near these frequencies. For example, Fig. 6 shows that chrysene, pyrene and coronene all show substructure on a broad component. Chrysene and coronene show a peak at about 2910 and 2845 cm-1 while pyrene has a broad (weak) plateau from 2950-2880 cm-1, which is similar to the emission plateau observed from the astronomical object BD + 30°3639 [44]. In the laboratory spectra these are due to overtone and combination bands which have been perturbed sufficiently by solid state effects to absorb weakly [35, 36, 37, 38, 39]. The perturbations within the PAH clusters that are suspended in salt pellets induce IR activity and broaden the individual bands causing them to overlap. In free vibrationally excited PAHs, perhaps Fermi resonances between the overtones and combinations of C-C stretching vibrations with the highly excited C-H modes can sufficiently enhance the intensities of these presumably weak bands to produce the observed intensites. 

Vaida et al. calculated the atmospheric /-values (the integrated value of the cross section, photon flux and quantum yield) for the vibrational overtone initiated visible photolysis and UV photolysis. The /-values were obtained assuming the local mode calculated third and fourth OH-stretching overtone cross sections for the vibrational transitions and the experimental upper limit for the UV cross section across the 179-224 nm range, and a unitary quantum yield for both regions [22]. These /-values showed that at altitudes below 45 km, the OH-stretching overtone initiated photolysis was the predominant process, whereas for higher alti-... 

The vapor spectra of the M(thd)3 compounds with M = Pr, Nd, Sm, Eu, Dy, Ho, Er, and Tm are shown in Figures 5 and 6. The arrows indicate absorption owing to vibrational overtone and combination bands of the organic chelate moiety. The remaining absorption bands arise from f f transitions of the rare-earth constituents. The energies and molar absorptivities of the f f absorption maxima are shown in Table VII. 

The doublet structure of each vibrational overtone results from the AJ = 1 rotational selection rule for an electric-dipole transition. 

B. Continuum resonance-Raman scattering fromj2 gas with excitation at 488.0 nm which is above the dissociation limit of the B( ITou) <- X( Sg) transition. The fine structure of each vibrational overtone is attributable to the Q, O and S branches of the multitude of rotational transitions occurring... 

In the spectra of those alkanes for which a clear gap is observed it is possible to regard 80 cm" as fflh,ax and the spectrum below as that of the lattice vibrations. A complicating feature of the gap region is the presence of lattice vibration overtones, or multiphonon contribution. However, since the lattice fundamentals are not a sequence of individual transitions their overtone intensity appears as a broad contribution. It builds up rapidly from the very lowest frequency to its strongest underneath the TAMs and provides a decreasing background for the LAM region, it has died away completely by about 600 cm". Beyond dodecane the lack of a clear gap makes the upper firequency bound of the external vibrations unidentifiable and we simply assume that the earlier cut-off (fiw = 80 cm ) remains representative. 

The polarization of all the bands in the heme spectra from 25,000 to 5000 cm " is in-plane. The proposed character of the transitions at 20,000, 16,000, and 10,000 cm as being mixed charge-transfer and ligand bands (Day et al., 1964) was supported by the polarization data of Day et al. (1967a), for the symmetry of all the transitions was of necessity the same and, as the transitions of the ligand were in-plane, was required to be in-plane. Besides these bands there is a series of very weak bands at 7200,8300, and 9400 cm Mn the spectra of the mesoporphyrin IX iron (III) methoxide crystals. These are possibly spin-forbidden components of the lowest electronic excited state, all polarized in the same direction, i.e., in the heme plane. Sharp, weak bands at lower wave numbers were assigned to vibrational overtones. 

The observed OH stretching vibrational overtone levels of the H2O molecule are shown in Figure 5, to illustrate the pattern of the transition from normal modes to local modes. One should note that already at V=3 the two lowest levels are only 13 cm i apart, with a gap of 250 cm up to the next level at V=4 the lowest pair are only 2 cm" apart with a gap of 400 cm i to the next level. This is characteristic of the local mode pattern, and it would already be inappropriate to label the levels at Vs3 as 3v, +... 

Because of the increased sensitivity of an intracavity arrangement, even weak vibrational overtone bands with Ap > 1 can be recorded with rotational resolution. For illustration. Fig. 3.7 shows the rotationally resolved Q-branch of the D2 molecule for the transitions (p = 2 p" = 0) [318]. The photon counting rate for the overtone transitions was about 5000 times smaller than those for the fundamental... 

---