Infrared -active modes

The Raman and infrared spectra for C70 are much more complicated than for Cfio because of the lower symmetry and the large number of Raman-active modes (53) and infrared active modes (31) out of a total of 122 possible vibrational mode frequencies. Nevertheless, well-resolved infrared spectra [88, 103] and Raman spectra have been observed [95, 103, 104]. Using polarization studies and a force constant model calculation [103, 105], an attempt has been made to assign mode symmetries to all the intramolecular modes. Making use of a force constant model based on Ceo and a small perturbation to account for the weakening of the force constants for the belt atoms around the equator, reasonable consistency between the model calculation and the experimentally determined lattice modes [103, 105] has been achieved. 

As the isoquinoline molecule reorients in the order listed above, the absorption of infrared radiation by the in-plane vibrational modes would be expected to increase, while that of the out-of-plane modes would be predicted to decrease (in accordance with the surface selection rule as described above). In the flat orientation there is no component of the dipole moment perpendicular to the surface for the in-plane modes, and under the surface selection rule these modes will not be able to absorb any of the incident radiation. However, as mentioned above, infrared active modes (and in some cases infrared forbidden transitions) can still be observed due to field-induced vibronic coupled infrared absorption (16-20). We have determined that this type of interaction is present in this particular system. 

If the symmetry analysis for the unit cell is compared with that for the single chain (section III. A. 1.), several interesting features of the vibrational spectrum are seen to emerge. First, infrared active modes of the single chain having a polarization should be split in the crystal, with... 

For an isotopically pure adsorbate in which one molecule i is surrounded by (N-l) identical molecules j eqn(l) leads to the following exact solution for the only infrared active mode (34),... 

Hammaker et al (34) deduced approximate expressions for the frequencies of the two infrared active modes of the system composed of a central adsorbed molecule of one isotopic species coupled to an environment of the other species. In one mode the labelled molecule vibrates in phase with its neighbours giving a frequency tojj higher than the frequency of the other mode where the motion is 180° out of phase. The two frequencies are related to wJ (the frequency of the 2-D lattice in the absence of the labelled molecule) and u>2 (the frequency of the labelled molecule in the absence of surrounding molecules, i.e. a labelled single-ton) by... 

Achievements Examples of vibrational spectra are shown in Fig. 3. ISTS is sensitive to both signal from internal (e.g. Fig. 3(a)) and external (e.g. Fig. 3(b)) modes. In every case, the number of modes detected is small, and does not follow any selection rule known for Raman or infrared active modes. Modes involving movement of a large number of atoms are... 

Fig. 16 Modification of the Tlu(4) infrared active mode with temperature in K4C60. (From [42])...

Before discussing other examples, we note here that, for a centrosymmet-ric molecule (one with an inversion center), rx, ry, and rz are u (from the German word ungerade, meaning odd) species, while binary products of x, y, and z have g (gerade, meaning even) symmetry. Thus infrared active modes will be Raman forbidden, and Raman active modes will be infrared forbidden. In other words, there are no coincident infrared and Raman bands for a centrosymmetric molecule. This relationship is known as the mle of mutual exclusion. 

Infrared active modes couple to the free carrier plasma and the energy of the coupled phonon-plasmon mode is sensitive to the electron density [3,20-22], In the range 1 x 1017 cm 3 < n < 1019 cm 3 the following approximation can be used for the free electron density as a function of the Ai(LO) mode frequency vmax [21] ... 

Indium nitride has twelve phonon modes at the zone centre (symmetry group Cev), three acoustic and nine optical with the acoustic branches essentially zero at k = 0. The infrared active modes are Ei(LO), Ei(TO), Ai(LO) and Ai(TO). A transverse optical mode has been identified at 478 cm 1 (59.3 meV) by reflectance [6] and 460 cm 1 (57.1 meV) by transmission [24], In both reports the location of a longitudinal optical mode is inferred from the Brout sum rule, giving respective values of 694 cm 1 (86.1 meV) and 719 cm 1 (89.2 meV). Raman scattering of single crystalline wurtzite InN reveals Ai(LO) and E22 peaks at 596 cm 1 and at 495 cm 1 respectively [25],... 

It is possible to make a valence force field analysis on this basis, by introducing radial forces between nearest neighbors and angular forces at the silicon and at the oxygen. For this, the model described earlier by Kleinman and Spitzer (1962) is appropriate. The three force constants are fitted by matching the highest three observed infrared-active modes with the frequencies and Then, these... 

The importance of the hyper Raman effect as a spectroscopic tool results from its symmetry selection rules. These are determined by products of three dipole moment matrix elements relating the four levels indicated in Fig. 3.6-1. It turns out that all infrared active modes of the scattering system are also hyper-Raman active. In addition, the hyper Raman effect allows the observation of silent modes, which are accessible neither by infrared nor by linear Raman spectroscopy. Hyper Raman spectra have been observed for the gaseous, liquid and solid state. A full description of theory and practice of hyper-Raman spectroscopy is given by Long (1977, 1982). 

R, Raman-active mode IR, infrared-active mode. 

In this contribution the concept of instantaneous normal modes is applied to three molecular liquid systems, carbon monoxide at 80 K and carbon disulphide at ambient temperature and two different densities. The systems were chosen in this way because pairs of them show similarities either in structural or in dynamical properties. The systems and their simulation are described in the following section. Subsequently two different types of molecular coordinates are used cis input to normal mode calculations, external, i.e. translational and rotational coordinates, and internal, i.e. vibrational coordinates of strongly infrared active modes, respectively. The normal mode spectra are related quantitatively to molecular properties and to those of liquid structure and dynamics. Finally a synthesis of both calculations is attempted on qualitative grounds aiming at the treatment of vibrational dephcising effects. 

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