Molecular vibrations totally symmetric modes

We now consider an electromagnetic wave with time dependence E = Egcoscoot incident upon a system of isotropically polarizable molecules. For simplicity, we assume the molecules undergo classical harmonic vibrational motion with frequency co in some totally symmetric mode Q. The normal coordinate then oscillates as Q = Qo cos(cot + <5), where S is the vibrational phase and Qo is the amplitude. If the molecular polarizability a is linear in Q (as a special case of Eq. 10.33), the vibrational motion will endow the molecule with the oscillating polarizability... 

Chemical enhancement is typically explained by the CT mechanism. When a molecule is adsorbed on a metal surface, new electronic states are formed due to chemisorption. The new electronic states may serve as resonant intermediate states in Raman scattering. If the Fermi level of the metal is located between the Highest Occupied Molecular Orbital (HOMO) Lowest Unoccupied Molecular Orbital (LUMO) in energy, CT excitations may likely occur at lower energy than intrinsic intramolecular excitations of the adsorbate [55-58]. According to Albrechts notation [55], in the CT mechanism via Albrechts A term Franck-Condon term) only the totally symmetric modes are resonantly enhanced when the laser excitation is close to an allowed electronic transition, and only one excited state is involved. The resonance Raman effects for vibrational modes that are non-totally symmetric, are usually observed when these modes couple two excited states of the chromophore. The product of the symmetry of both excited states should be equal or contain the non-totally symmetry. This mechanism is known as the Herzberg-Teller mechanism or B mechanism in Albrechts notation. 

Polarizability derivatives with respect to symmetry coordinates obtained from Eqs. (9.1) and (9.2) are not always purely intramolecular quantities since contributions from the compensatory molecular rotation accompanying some vibrations may be present. Such contributions arise in the cases of non-totally symmetric modes of molecules having a non-spherical polarizability ellipsoid. Polarizability derivatives corrected for contributions from molecular rotation can be obtained according to the relation... 

Vibrations of the symmetry class Ai are totally symmetrical, that means all symmetry elements are conserved during the vibrational motion of the atoms. Vibrations of type B are anti-symmetrical with respect to the principal axis. The species of symmetry E are symmetrical with respect to the two in-plane molecular C2 axes and, therefore, two-fold degenerate. In consequence, the free molecule should have 11 observable vibrations. From the character table of the point group 04a the activity of the vibrations is as follows modes of Ai, E2, and 3 symmetry are Raman active, modes of B2 and El are infrared active, and Bi modes are inactive in the free molecule therefore, the number of observable vibrations is reduced to 10. 

For a vibrational mode of the molecule to induce coupling between adiabatic electronic states p(r R), the direct product of the irreducible representations of < >.,(r R), p(r R), and the vibrational mode must contain the totally symmetric representation of the molecular point group,... 

The symmetry of the normal mode of vibration that can take the molecule out of the degenerate electronic state will have to be such as to satisfy Eq. (6-7). The direct product of E with itself (see Table 6-11) reduces to A + A 2 + E. The molecule has three normal modes of vibration [(3 x 3) - 6 = 3], and their symmetry species are A + E. A totally symmetric normal mode, A, does not reduce the molecular symmetry (this is the symmetric stretching mode), and thus the only possibility is a vibration of E symmetry. This matches one of the irreducible representations of the direct product E E therefore, this normal mode of vibration is capable of reducing th eZ)3/, symmetry of the H3 molecule. These types of vibrations are called Jahn-Teller active vibrations. 

A frequently discussed phenomenon of IR vibrational spectroscopy is the electron - molecular vibration coupling of totally symmetric in-plane molecular modes. As a consequence of coupling to the free carriers, these modes become visible in the IR absorption if the light is polarized parallel to the stacking direction. This effect was first observed in TEA(TCNQ)z (triethylammonium (TCNQ)2), as shown in Fig. 4.8-17a, b. 

The frequencies are for the totally symmetric GH stretching modes T. Shimanouchi, Tables of Molecular Vibrational Frequencies, National Standard Reference Data Series, National Bureau of Standards, Washington D.G., 1972. 

The mvestigation of molecular vibrations is a powerful too which can increase our knowledge on structures and on electron molecular vibrations, which are due to charge oscillation between dimerized molecules, coupled with totally symmetric intramolecular modes Raman scattering studies account for totally symmetric vibrations. In addition, Raman spectroscopy can take advantage of resonant effects. In fact, when resonant conditions are fulfilled, selected molecular vibrations are obtained as well as infor> mation on the electronic manifold involved in the resonance process. 

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