Vibrational overtones

Figure 3. Energy schemata of transitions involving vibrational states (a excitation of 1st vibrational state - mid-IR absorption b excitation of overtone vibrations - near-IR absorptions c elastic scattering - Rayleigh lines d Raman scattering - Stokes lines e Raman scattering - Anti-Stokes lines f fluorescence).

However, in polyatomic molecules, transitions to excited states involving two vibrational modes at once (combination bands) are also weakly allowed, and are also affected by the anharmonicity of the potential. The role of combination bands in the NIR can be significant. As has been noted, the only functional groups likely to contribute to the NIR spectrum directly as overtone absorptions are those containing C-H, N-H, O-H or similar functionalities. However, in combination with these hydride bond overtone vibrations, contributions from other, lower frequency fundamental bands such as C=0 and C=C can be involved as overtone-combination bands. The effect may not be dramatic in the rather broad and overcrowded NIR absorption spectrum, but it can still be evident and useful in quantitative analysis. 

Fig. 3. Deactivation of europium and terbium excited states by energy transfer to O-H and O-D oscillator overtone vibrations. Reprinted with permission from Acc. Chem. Res. 1981, 14, 384-392. Copyright 1981 American Chemical Society.

XVII. Subquadratic Quantum Number Dependence of the Overtone Vibrational Dephasing in Molecular Liquids... 

XVII. SUBQUADRATIC QUANTUM NUMBER DEPENDENCE OF THE OVERTONE VIBRATIONAL DEPHASING IN MOLECULAR LIQUIDS... 

Commercial cylindrical quartz cells can be adapted for gas-phase work as illustrated in Fig. 9.18. Such a cell finds use in the near infrared for the determination of overtone vibrational frequencies, and also in visible and ultraviolet spectroscopy. A much less expensive cell which is adequate for most gases may be constructed from Pyrex along the lines of the cell shown in Fig. 9.18. Quartz windows may then be attached by epoxy resin. A cell which is filled from a conventional vacuum line will generally contain mercury vapor which absorbs at 2537 A. Once the origin of this absorption is recognized, it causes little difficulty because of its narrow bandwidth. 

Rizzo, T.R., Hayden, C.C., and Crim, F.F. (1984). State-resolved product detection in the overtone vibration initiated unimolecular decomposition of HOOH(6i oh) J- Chem. Phys. 81, 4501-4509. 

Peak attribution of the O-H overtone vibrations in the near infrared region, according to Kratochvila... 

The most general vibrational motion of our solid is one in which each overtone vibrates simultaneously, with an arbitrary amplitude and phase. But in thermal equilibrium at temperature T, the various vibrations will be excited to quite definite extents. It proves to be mathematically the case that each of the overtones behaves just like an independent oscillator, whose frequency is the acoustical frequency of the overtone. Thus we can make immediate connections with the theory of the specific heats of oscillators, as we have done in Chap. XIII, Sec. 4. If the atoms vibrated according to the classical theory, then we should have equipartition, and at temperature T each oscillation would have the mean energy kT. This means that each of the N overtones would have equal... 

First, let us find the number of overtone vibrations in the range dv. We follow Chap. XIV in detail and for that reason can omit a great deal of calculation. In Sec. 2 of that chapter, we found the number of overtones in the range dv, in a problem of elastic vibration, in which the velocity of longitudinal waves was Vi, that of transverse waves vt. From Eqs. (2.20) and (2.21) of that chapter, the number of overtones of longitudinal vibration in the range dv, in a container of volume F, was... 

To minimize optical propagation caused by light absorption of a harmonic overtone vibration mode, Kim [2] and Ding [3] prepared polyether, (II), and polysulfone, (III), derivatives, respectively, where the majority of hydrogen atoms were replaced by fluorine. 

If the potential is anharmonic, the higher terms of the potential energy according to Eq. 2.1-16 are not negligible, the mechanical anharmonicity gives rise to overtones, vibrations with the double, triple, or multiple frequency of the fundamentals. Overtones are also produced by the higher terms of the dipole moment according to Eq. 2.3-1, the electrical anharmonicity. Since both equations may contain mixed terms, combinations of two or more normal vibrations, i.e., sums or differences, are produced. These appear in the spectra, but usually only with small intensity. Also Raman spectra show overtones and combinations due to mechanical and electrical anharmonicities (see below). 

Absorption bands that are attributed to overtone and combination vibrations are also observed in the IR spectrum of polyatomic molecules. Overtone vibrations occur at frequencies of approximately integral multiples of the fundamental frequencies. Combination vibrations appear at frequencies that are the sum or the difference of the frequencies of two or more frmdamental vibrations. Overtone and combination bands are much less intense than fundamental bands. 

Figure 4. Relative rotational state distributions of OH products from overtone-vibration-induced unimolecular decomposition of HOOH. The solid bars are populations for excitation of the main local mode transition (6v0H) and hatched bars are populations for excitation of the combination transition (6v0H + v ). The quantum number N denotes the rotational OH angular momentum. Figures 4a and 4b show results obtained probing the Q, and R, branches, respectively, of OH. The error bars in Fig. 4(a) show the maximum range of values obtained and are typical of the uncertainties for all states. (Reproduced with permission from Ref. 39.)...

Prediction of the overtone vibrational spectra of the CX3Y methylhalides can be based on the effective local and normal mode model Hamiltonian. D parameter, differs from De parameter of the Morse potential by E0 energy of zero-point vibrations, coincides with dissociation energy of separated C-Y bond with experimental accuracy in calculations using minimal basis set, if the correlation... 

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