Silent modes

At higher frequencies (above 200 cm ) the vibrational spectra for fullerenes and their cry.stalline solids are dominated by the intramolecular modes. Because of the high symmetry of the Cgo molecule (icosahedral point group Ih), there are only 46 distinct molecular mode frequencies corresponding to the 180 6 = 174 degrees of freedom for the isolated Cgo molecule, and of these only 4 are infrared-active (all with Ti symmetry) and 10 are Raman-active (2 with Ag symmetry and 8 with Hg symmetry). The remaining 32 eigcnfrequencies correspond to silent modes, i.e., they are not optically active in first order. 

The thirty-two silent modes of Coo have been studied by various techniques [7], the most fruitful being higher-order Raman and infra-red spectroscopy. Because of the molecular nature of solid Cqq, the higher-order spectra are relatively sharp. Thus overtone and combination modes can be resolved, and with the help of a force constant model for the vibrational modes, various observed molecular frequencies can be identified with specific vibrational modes. Using this strategy, the 32 silent intramolecular modes of Ceo have been determined [101, 102]. 

Similarly, the first-order expansion of the p° and a of Eq. (5.1) is, respectively, responsible for IR absorption and Raman scattering. According to the parity, one can easily understand that selection mles for hyper-Raman scattering are rather similar to those for IR [17,18]. Moreover, some of the silent modes, which are IR- and Raman-inactive vibrational modes, can be allowed in hyper-Raman scattering because of the nonlinearity. Incidentally, hyper-Raman-active modes and Raman-active modes are mutually exclusive in centrosymmetric molecules. Similar to Raman spectroscopy, hyper-Raman spectroscopy is feasible by visible excitation. Therefore, hyper-Raman spectroscopy can, in principle, be used as an alternative for IR spectroscopy, especially in IR-opaque media such as an aqueous solution [103]. Moreover, its spatial resolution, caused by the diffraction limit, is expected to be much better than IR microscopy. 

The numbers of IR- and Raman-active modes are 4 (4tiJ and 10 (2ag + 8hg), respectively. On the other hand, hyper-Raman-active modes are all of the modes with u symmetry, including the silent modes. Compared with the theoretically calculated result, the expected modes are clearly seen in the spectmm. (The appearance of Raman-active modes is due to magnetic dipole contributions.)... 

The selection rules for fi hyper-Raman scattering were derived by Cyvin, Rauch, and Decius, 02) and those for y hyper-Raman scattering, which has not yet been detected experimentally, by Christie and Lockwood 103>. From their tables one can see that silent modes become 3-active for such important point groups as C6, D6, C3v, C6v, C. D, 0 and Oh. Examples of additional 7 activity can be found in the point groups C4v, C. D. D, and Oh. Long and Stanton 104) have derived a quantum-mechanical theory of the hyper-Raman effect which indicates several possibilities for resonance enhancement of hyper-Raman intensities. Iha and Woo 105) extended the theory of nonlinear... 

Figure 9 shows the result of such a fit made by minimising the squares of the errors between predicted and observed frequencies. A problem here is that there are 13 constants to determine and only 14 experimental frequencies known accurately. It is clear that a good fit to the visible modes can be obtained. However, we can never be sure that the fit obtained represents a global minimum in the error function. The data in Fig. 9 must therefore be viewed upon as the best fit currently available. The values of the force constants themselves must be viewed with some scepticism. However, as more data becomes available, i.e., accurate frequencies of some of the silent modes are obtained, the model may be refined to improve these initial estimates. 

So XeF4 has three bands in its infrared spectrum as well as in its Raman spectrum. None of the bands are coincident, as this molecule is centrosymmetric. In addition, there is a silent mode, with Z 2u symmetry, which does not show up in either spectrum. The normal modes and their frequencies are given in Fig. 7.3.6. 

As compared to eq. (7.3.5), the only difference is that the silent mode Z 2u in that expression is converted to Z iu here, and now V2 has Z 2g symmetry and V4 has Big symmetry. All deductions concerning infrared and Raman activities remain unchanged. 

Both A - and Ei-modes are Raman and IR active. The two nonpolar E2-modes E and E are Raman active only. The Bi-modes are IR and Raman inactive (silent modes). Phonon dispersion curves of wurtzite-structure and rocksalt-structure ZnO throughout the Brillouin Zone were reported in [106-108]. For crystals with wurtzite crystal structure, pure longitudinal or... 

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). 

In centrosymmetric molecules, HRS gains intensity via Herzberg-Teller term (the first vibronic B-term), indicating that IR-active modes and silent modes are enhanced. In the case of non-centrosymmetric molecules, however, Franck-Condon mechanism (A-term) dominantly contributes to the enhancement. Moreover, the mutual exclusive rules between HRS and RS are broken, and hence, some of RS-active modes selectively appear in the spectra. In the case of plasmonic enhancement, the spectral appearance is more sensitive to molecular orientations at the metal surface because of the surface selection rules [25]. 

The numbers of IR- and RS-active modes are 4 (4tiu) and 10 (2ag -i- 8hg), respectively. All other modes are IR- and RS-forbidden silent modes (au, tig, t2g, t2 , gg, gu. hu)- Conversely, the number of HRS-active modes are 22 (4tiu -i- 5t2u + 6g -i-7hu) including 18 silent modes. Since these HRS modes are mutually exclusive with RS-active modes, combination of resonance RS and resonance HRS should be useful for understanding the electron-vibration coupled system. 

Wurtzite ZnO structure with four atoms in the unit cell has a total of 12 phonon modes (one longitudinal acoustic (LA), two transverse acoustic (TA), three longitudinal optical (LO), and six transverse optical (TO) branches). The optical phonons at the r point of the Brillouin zone in their irreducible representation belong to Ai and Ei branches that are both Raman and infrared active, the two nonpolar 2 branches are only Raman active, and the Bi branches are inactive (silent modes). Furthermore, the Ai and Ei modes are each spht into LO and TO components with different frequencies. For the Ai and Ei mode lattice vibrations, the atoms move parallel and perpendicular to the c-axis, respectively. On the other hand, 2 modes are due to the vibration of only the Zn sublattice ( 2-low) or O sublattice ( 2-high). The expected Raman peaks for bulk ZnO are at 101 cm ( 2-low), 380 cm (Ai-TO), 407 cm ( i-TO), 437 cm ( 2-high), and 583 cm ( j-LO). 

S.F. Parker, H. Herman, A. Zimmerman K.P.J. Williams (2000). Chem. Phys., 261, 261-266. The vibrational spectmm of K2[PdCl4] first detection of the silent mode V5. 

It is possible that some of the vibrational modes are neither IR nor Raman-active and we shall call these silent modes. 

The next water-soluble derivative [Ru(C0)3C1(k -H2NCH2C02)] (CORM-3) [32-34] recapitulated the biological activity of CORM-2 and addressed an extremely broad palette of indications. One of the most intriguing features of its pharmacological profile is the very low increase of the systemic levels of COHb in the treated mice [35]. Altogether 200 papers and several patents deal with CORM-2 and CORM-3, both in vitro and in vivo [36]. Notwithstanding, its COHb silent mode of action (MoA) remains elusive, as discussed in Section 2.4.1. 

The importance of the hyper-Raman effect as a spectroscopic tool results from its symmetry selection rules. 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. 

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