Molecular vibrational modes

There are two general cases of dipole-dipole forces those between molecules in which the distribution of electronic charge is centrosymmetric and those in which it is not. In the first case, there are no permanent electrical dipoles, whereas there is a permanent dipole if the charge distribution is non-centro-symmetric. When permanent dipoles are not present, there are nevertheless fluctuating dipoles as a result of atomic vibrations. These are always present because of zero-point motion. At temperatures greater than 0°K, thermal energy further excites the molecular vibrational modes which create fluctuating electric dipoles. 

The theory of electron-transfer reactions presented in Chapter 6 was mainly based on classical statistical mechanics. While this treatment is reasonable for the reorganization of the outer sphere, the inner-sphere modes must strictly be treated by quantum mechanics. It is well known from infrared spectroscopy that molecular vibrational modes possess a discrete energy spectrum, and that at room temperature the spacing of these levels is usually larger than the thermal energy kT. Therefore we will reconsider electron-transfer reactions from a quantum-mechanical viewpoint that was first advanced by Levich and Dogonadze [1]. In this course we will rederive several of, the results of Chapter 6, show under which conditions they are valid, and obtain generalizations that account for the quantum nature of the inner-sphere modes. By necessity this chapter contains more mathematics than the others, but the calculations axe not particularly difficult. Readers who are not interested in the mathematical details can turn to the summary presented in Section 6. 

This way of expressing the overall modes for the pair of molecular units is only approximate, and it assumes that intramolecular coupling exceeds in-termolecular coupling. The frequency difference between the two antisymmetric modes arising in the pair of molecules jointly will depend on both the intra- and intermolecular interaction force constants. Obviously the algebraic details are a bit complicated, but the idea of intermolecular coupling subject to the symmetry restrictions based on the symmetry of the entire unit cell is a simple and powerful one. It is this symmetry-restricted intermolecular correlation of the molecular vibrational modes which causes the correlation field splittings. 

Infrared spectroscopy can provide a great deal of information on molecular identity and orientation at the electrode surface [51-53]. Molecular vibrational modes can also be sensitive to the presence of ionic species and variations in electrode potential [51,52]. In situ reflectance measurements in the infrared spectrum engender the same considerations of polarization and incident angles as in UV/visible reflectance. However, since water and other solvents employed in electrochemistry are strong IR absorbers, there is the additional problem of reduced throughput. This problem is alleviated with thin-layer spectroelectro-chemical cells [53]. 

Most SHG studies involve incident energies in the visible or near-infrared spectrum. Infrared SHG studies are hindered by the current lack of sufficiently sensitive IR detectors. However, the sum frequency generation (SFG) technique allows one to obtain surface-specific vibrational spectra. In SFG, two lasers are focused on the sample surface, one with a fixed frequency in the visible and one with a tunable range of IR frequencies. The sample surface experiences the sum of these frequencies. When the frequency of the infrared component corresponds to a molecular vibrational mode, there is an increase in the total SHG signal, which is detected at the visible frequency [66]. The application of such... 

The vibrations within a molecular crystal cell are not only a result of molecular motions, but also the relative motions between neighboring molecules. Dominant features of the THz spectra are the sharp absorption peaks caused by phonon modes directly related to the crystalline structure [14], This result originates from the molecular vibrational modes and intramolecular vibrations associated, for example, with RDX [39], Consequently, vibrational modes are unique and distinctive feature of the crystalline explosive materials. The presence of broad features might also be caused by scattering from a structure with dimensions comparable to the THz wavelength. This can occur in materials that contain fibers or grains [37],... 

Okumura K, Tanimura Y. The (2w + l)th-order off-resonant spectroscopy from the (n + 1 )th-order anharmonicities of molecular vibrational modes in the condensed phase. J Chem Phys 1997 106 1687-1698. 

The energy and the frequency of the molecular vibrational modes depend on the mass of the atoms directly involved as well as on the bond energy. Consequently, the position of the absorption peaks are shifted when isotopically labeled molecules are used. This is a useful property for the confirmation of the assignment of vibrational modes when needed. The adsorption of heavy water allows investiga-... 

From Fig. 1 we propose that the water molecule has temporarily tetrahedral-like structure in a short time, because if the water has been constructed by a simple H2O (C2v) molecule there should be only three molecular vibration modes (vi, V2, V3). In Fig. 1 we can see that between 1600 cm l and 4000 cm"l more than three molecular vibrations. They can be classiHed into essentially four kinds molecular vibrations (vi, V2, V3, V4). Besides three or four vibration components in the viAts modes region there exists an extra broad mode at about 2200 cm i. We had better to interpret this spectral pattern as the molecular vibradons of tetrahedral-like C2v symmetry which is composed by two O-H bonds and two 0---H hydrogen bonds in each oxygen. Although the conventional explanation of 2200 cm mode is the combination mode between the molecular vibration V2 and the lattice vibration v, there is no direct experimental evidence. Rather the tetrahedral-like C2v local structure can produce the four molecular vibration modes (Ai, Ai, Bi, B2) in the viA S frequency region and three molecular vibration modes (Ai, Bi, B2) which are bundled in the V4 frequency region. This latter modes correspond to the broad 2200 cm l mode. The above picture is consistent with the pentamer model of liquid water which is stressed in the interpretation of the low-frequency Raman specnal pattern. 

In the elpasolite (i.e., ordered perovskite) Cs2NaGdCl6, r amounts to 0.3. There are no molecular vibrational modes. Coupling occurs with the modes of the regular GdC octahedron (132). The values of a for Cl and are practically equal (69). It is questionable, however,... 

Raman tensors The Raman scattering of a molecule is generated by the interaction of its electrons with an incident light. The electric vector of the scattered light is related to the electric vector of the incident light through a characteristic Raman tensor. A unique Raman tensor exists for each Raman-active molecular vibrational mode [12]. 

Figure 2.5 shows the instantaneous frequencies (o t) at delay time t for G-N and N=N stretching modes, calculated by integrating the TFD along the lines at T parallel to frequency axis. In the case of PC-pulse excitation (F%ure 2.5A), the frequencies of both molecular vibration modes are modulated at the period of about 400fs. Furthermore, the phase difference between the two modulations in Figure 2.5A is about Jt, in contrast to Figure 2.5B, which shows less correlation between two frequency modulations. The phase difference between the two modulations can be even more clearly seen in... 

When the FTIR spectra of polymorph systems differ substantially, the results may readily permit the identification of a particular form. For instance, the two forms of ranitidine hydrochloride yielded spectra that differed in the region above 3000 cm and in the regions spanning 2300-2700 cm and 1570-1620 cm b Zanoterone has been found to crystallize in a number of different forms, each of which yields a characteristic infrared spectrum. When solvent molecules are incorporated in a crystal lattice, the new structure is often sufficiently different from that of the anhydrous phase so that many of the molecular vibrational modes are altered. 

It is possible to categorize the various modes of molecular vibration modes into four types ... 

Sainoo, Y., Kim, Y., Okawa,T., Komeda, T., Shigekawa, H. and Kawai, M. (2005) Excitation of molecular vibrational modes with inelastic scanning tunneling microscopy processes Examination through action spectra of ds-2-butene on Pd(110). Phys. Rev. Lett., 95, 246102-1-246102-4. 

In the context considered here, a resonance is a near match of frequency between two coupled oscillations. Such a resonance will produce energy transfer from one of the oscillators to the other. A nonlinear resonance is a resonance arising from the nonlinearity of the restoring force in one or both of the oscillators, or in other words, due to the anharmonicity of one or both of the oscillators. For a harmonic oscillator, of course, the frequency of oscillation is independent of the energy or amplitude of the oscillation. Molecular vibrational modes, however, are both anharmonic, particularly at energies sufficient for unimolecular reaction, and the energy dependence of the oscillator frequency is critical to mode-mode energy transfer. 

---