Vibrational mode bending

The coupling of light with molecular vibrations forms the basis for traditional IR spectroscopy. The consequent absorptions result in many of the minima (in transmission) observed from typical IR spectra. The light wave interacts with various vibrational modes (bending, rotational, etc.) of molecular groups that are not coupled with others of the same species. Such vibrational modes can in the broadest sense be termed localized in order to emphasize that the vibrations are not transmitted long distances throughout the crystal. 

Variational RRKM theory is particularly important for imimolecular dissociation reactions, in which vibrational modes of the reactant molecule become translations and rotations in the products [22]. For CH —> CHg+H dissociation there are tlnee vibrational modes of this type, i.e. the C—H stretch which is the reaction coordinate and the two degenerate H—CH bends, which first transfomi from high-frequency to low-frequency vibrations and then hindered rotors as the H—C bond ruptures. These latter two degrees of freedom are called transitional modes [24,25]. C2Hg 2CH3 dissociation has five transitional modes, i.e. two pairs of degenerate CH rocking/rotational motions and the CH torsion. 

Figure Bl.6.10 Energy-loss spectrum of 3.5 eV electrons specularly reflected from benzene absorbed on the rheniiun(l 11) surface [H]. Excitation of C-H vibrational modes appears at 100, 140 and 372 meV. Only modes with a changing electric dipole perpendicular to the surface are allowed for excitation in specular reflection. The great intensity of the out-of-plane C-H bending mode at 100 meV confimis that the plane of the molecule is parallel to the metal surface. Transitions at 43, 68 and 176 meV are associated with Rli-C and C-C vibrations.

Figure Bl.25.12 illustrates the two scattering modes for a hypothetical adsorption system consisting of an atom on a metal [3]. The stretch vibration of the atom perpendicular to the surface is accompanied by a change m dipole moment the bending mode parallel to the surface is not. As explained above, the EELS spectrum of electrons scattered in the specular direction detects only the dipole-active vibration. The more isotropically scattered electrons, however, undergo impact scattering and excite both vibrational modes. Note that the comparison of EELS spectra recorded in specular and off-specular direction yields infomiation about the orientation of an adsorbed molecule.

Figure 7-13. Cross-terms combining internal vibrational modes such as bond stretch, angle bend, and bond torsion within a molecule.

Different motions of a molecule will have different frequencies. As a general rule of thumb, bond stretches are the highest energy vibrations. Bond bends are somewhat lower energy vibrations and torsional motions are even lower. The lowest frequencies are usually torsions between substantial pieces of large molecules and breathing modes in very large molecules. 

Finally, the S(CH) bending frequencies are practically independant of the physical state of the sample as are the nuclear vibration modes (Table 1-27). 

In order to calculate q (Q) all possible quantum states are needed. It is usually assumed that the energy of a molecule can be approximated as a sum of terms involving translational, rotational, vibrational and electronical states. Except for a few cases this is a good approximation. For linear, floppy (soft bending potential), molecules the separation of the rotational and vibrational modes may be problematic. If two energy surfaces come close together (avoided crossing), the separability of the electronic and vibrational modes may be a poor approximation (breakdown of the Bom-Oppenheimer approximation. Section 3.1). 

FIGURE 2 la The three normal vibrational modes of 11,0. Two of these modes are principally stretching motions of the bonds, but mode v2 is primarily bending, (b) The four normal vibrational modes of C02. The first two are symmetrical and antisymmetrical stretching motions, and the last two are perpendicular bending motions. 

While the vibrations (stretching, bending, torsion) in high symmetrical rings (Ss, Ss, S12) are almost uncoupled [80], the vibrations in the low symmetrical Sy ring are heavily mixed, especially the bending and torsional modes [81]. 

The Raman spectra of WO3, 25-NiO-TiO2/30-WO3, 25-Ni0-Ti02/15-W03, 25- NiO-Ti02/5-W03, and Ti02 under ambient conditions are presented in Fig. 1. The WO3 structure is made up distorted WO3 octahedra. The major vibrational modes of WO3 are located at 808, 714, and 276 cm, and have been assigned to the W=0 stretching mode, the W=0 bending mode, and the W-O-W deformation mode, respectively [7]. The Raman spectrum of the 25-... 

If a vibrational mode is not a pure stretching mode but contains bending contributions, the composition factor may deviate from in both directions. 

Only the low-energy vibrational modes ( 20% of the 147 modes) contribute to ASvib- Furthermore, only the 15 modes of the central FeNg octahedron (six Fe-N stretching modes and nine N-Fe-N bending modes, marked by the letters s and b, respectively, in Fig. 9.38b) account for 75% of ASvib-... 

The potential U3 of the bending mode has been generally approximated by a harmonic potential [22,23,53,71-73]. Extension of this model should go beyond the harmonic approximation used in the description of the three vibrational modes, by substituting to the previous potentials (66), (67), and (68) a Morse-type potential [13]. 

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