Phonon overtones

Molecules vibrate at fundamental frequencies that are usually in the mid-infrared. Some overtone and combination transitions occur at shorter wavelengths. Because infrared photons have enough energy to excite rotational motions also, the ir spectmm of a gas consists of rovibrational bands in which each vibrational transition is accompanied by numerous simultaneous rotational transitions. In condensed phases the rotational stmcture is suppressed, but the vibrational frequencies remain highly specific, and information on the molecular environment can often be deduced from hnewidths, frequency shifts, and additional spectral stmcture owing to phonon (thermal acoustic mode) and lattice effects. 

It should be emphasized, however, that we are dealing in this article mainly with one-phonon processes, i.e. fundamentals. For multiple phonon processes, i.e. overtones and combinations which are observed in second-order Raman scattering, the whole of BZ 1 comes into play. Because the sum or difference of two large k vectors can have a relatively small magnitude, it can... 

Romero-Rochin V, Koehl RM, Brennani CJ, Nelson KA. Theory of anharmonic phonon-polariton excitation in LiTaOj by ISRS and detection by wavevector overtone spectroscopy. J Chem Phys 1999 111(8) 3559—3571. 

If the two-phonon state is formed from phonons belonging to the same branch of the phonon dispersion curves and have equal energy, the corresponding state is called an overtone. If the two-phonon state represents the sum or difference of two phonons with unequal energy the state, it is termed a combination. 

Single crystal studies of solid hydrates are scarce. There are two experimental procedures possible (i) transmission spectra of thin crystal plates (see, for example. Refs. 16, 17) and (ii) reflection spectra of crystal faces . Using polarized infrared radiation, the species (symmetry) and other directional features of the water bands can be determined. In the case of reflection measurements, the true transverse and longitudinal optic phonon frequencies can be additionally computed by means of Kramers-Kronig analyses and oscillator fit methods, respectively. Both experimental techniques, however, are relatively difficult because of the lack of suitable monocrystals, the requirement of preparing sufficiently thin, i.e., <0.1 mm, crystal plates (except for studying overtone bands, see Sect. 4.2.6), and the efflorescence or absorption of water at the crystal surfaces. In favorable cases, thin sheets of orientated powdery material can be obtained . ... 

Figure 7 shows the HREELS spectrum acquired at room temperature and at an incidence angle of 60° from the surface normal for a 30 MLE titanium oxide film prepared as described above. Fundamental phonons of 54meV(v2) as well as overtone losses and combinations are seen. The loss at 149 meV is due to v + V2, and the loss at 245 meV is due to v + 2v2. That Ti02 films prepared in this manner are anatase and can be ruled out because the anatase phase exhibits fundamental surface phonons at 44 and 98meV for the (100) face and 48 and 92meV for the (001) face. The combined use of FEED, AES, XPS, and HREELS has revealed that the thin Ti02 films prepared via the above procedure are rutile with a surface structural orientation primarily (100). 

For both PF2/6 and PF8 the aforementioned main chain characteristics are essentially identical and so any pronounced differences are likely to originate in secondary structural characteristics of the functionalizing side chains. PF8 studies by Bradley and coworkers [16] first identified the unusual spectroscopic emission band now conventionally referred to as the phase . The hallmark signature of this peculiar chain structure is a relatively sharp series of emission bands red shifted some lOOmeV from those seen when the polymer is prepared in a glassy state, tt-Conjugated polymers have strong electron-phonon coupling and so, in addition to the it-it emission, there is a manifold of vibronic overtones spaced approximately 180 meV apart and red-shifted from the dominant n-n emission band. 

This can be seen in Fig. 9.9 where the phonon-wings and the higher overtones are shown and the fundamental transition spectra of H2O and D2O ice-VIII are shown separately. The effect of an improved Debye-Waller factor can be seen in the spectrum of D2O. It has a heavier Sachs-Teller mass and the bands appear at lower frequency and so lower Q. 

In this section we will consider polydimethylsiloxane (PDMS) as an example of the type of work that is possible with amorphous polymers. The structure and INS spectrum of PDMS are shown in Fig. 10.21a [40]. The repeat unit shown in Fig. 10.21b was used to model the spectrum using the Wilson GF matrix method [41]. The major features are reproduced skeletal bending modes below 100 cm", the methyl torsion and its overtone at 180 and 360 cm respectively, the coupled methyl rocking modes and Si-0 and Si-C stretches at 700-1000 cm and the unresolved methyl deformation modes 1250-1500 cm. The last are not clearly seen because the intensity of the methyl torsion results in a large Debye-Waller factor, so above 1000 em or so, most of the intensity occurs in the phonon wings. 

The bound state of two phonons for the overtone frequency region was evidently first identified by Ron and Hornig (34). In this investigation they measured the absorption spectrum of the HC1 crystal in the region of overtone frequen-... 

Let us now consider what is the analog of a Fermi resonance in a molecule when we consider the crystals. In going over from an isolated molecule to a crystal, the branches of optical phonons appear. In the region of overtone and sum frequencies, several bands of many-particle states arise and, if anharmonicity is sufficiently strong, bands of states with quasiparticles bound to one another (for instance, biphonons) will also appear. Thus, in crystals a large number of... 

It is an essential fact that the above-mentioned gaps in the polariton spectrum, if they arise, as well as the corresponding interaction between the photon and phonon, are nonzero within the framework of linear theory and, in general, do not require that anharmonicity be taken into account. Therefore, it makes sense to denote as a polariton Fermi resonance only such situations where vibrations of overtone or combination tone frequencies resonate with the polariton. We now turn our attention to an analysis of such rather complex situations, requiring that multiparticle excited states of the crystal be taken into consideration. Shown schematically in Fig. 6.6 is a typical polariton spectrum, as well as a band of two-particle states of B phonons. If, under the effect of anharmonicity, biphonons with energy E = E are formed, these states also resonate with the polariton, influencing its spectrum. 

Also worthy of further development is the theory of surface biphonons. The conditions required for the formation of these states are different from those of the formation of surface states for the spectral region of the fundamental vibrations. It was demonstrated on the model of a one-dimensional crystal (26) that situations may exist, in general, in which the surface state of the phonon is not formed and the spectrum of surface states begins only in the frequency region of the overtones or combination tones of the vibrations. 

There is only little known on both the anharmonicity of the vibrations of hydroxide ions (see, for example, Refs. [74-76]) and the TO/LO splitting of the respective phonon modes. Though investigations on overtone spectra of solid hydroxides are scarce [76,77] and, hence, only a few experimental data on the anharmonicity constants xca)e of the OH stretching modes are available in the literature [75,78] we assume that the anharmonicities of hydroxide modes do not differ from those of the vibrations of other OH groups, e.g. water molecules [40,79]. For calculation of at least crude anharmonicity constants of OH-vibrations, we recommend the procedure reported by Engstrom et al. [74] using the frequencies of the respective OH and OD modes recorded from spectra of isotopically dilute samples [79]. 

Fig. 13. Multiphonon and doorway mode models for phonon pumping of vibrations. The continuous states at right represent phonons. States from zero frequency to ttfe (lighter color) represent phonon fundamentals higher energy states are phonon combinations and overtones,...

---