Benzene molecular vibrations analysis

Both the Raman and the infrared spectrum yield a partial description of the internal vibrational motion of the molecule in terms of the normal vibrations of the constituent atoms. Neither type of spectrum alone gives a complete description of the pattern of molecular vibration, and, by analysis of the difference between the Raman and the infrared spectrum, additional information about the molecular structure can sometimes be inferred. Physical chemists have made extremely effective use of such comparisons in the elucidation of the finer structural details of small symmetrical molecules, such as methane and benzene. But the mathematical techniques of vibrational analysis are. not yet sufficiently developed to permit the extension of these differential studies to the Raman and infrared spectra of the more complex molecules that constitute the main body of both organic and inorganic chemistry. 

See, for example, the following and references contained therein E. L. Sibert 111, W. P. Reinhardt, and J. T. Hynes, /. Chem. Phys., 81, 1115 (1984). Intramolecular Vibrational Relaxation and Spectra of CH and CD Overtones in Benzene and Perdeuterobenzene. S. P. Neshyba and N. De Leon,. Chem. Phys., 86, 6295 (1987). Qassical Resonances, Fermi Resonances, and Canonical Transformations for Three Nonlinearly Coupled Oscillators. S. P. Neshyba and N. De Leon,. Chem. Phys., 91, 7772 (1989). Projection Operator Formalism for the Characterization of Molecular Eigenstates Application to a 3 4 R nant System. G. S. Ezra, ]. Chem. Phys., 104, 26 (1996). Periodic Orbit Analysis of Molecular Vibrational Spectra Spectral Patterns and Dynamical Bifurcations in Fermi Resonant Systems. Also see Ref. 6. 

Since the pulse time is so short (see Sec. 3.6.2.2.3) one can coherently excite many vibrational modes at a time and monitor relaxation processes in real time. The first reported femtosecond time-resolved CARS experiments (Leonhardt et al., 1987 Zinth et al., 1988) showed beautiful beating patterns and fast decays of the coherent signal for several molecular liquids. The existence of an intermolecular coherence transfer effect was suggested from the analysis of the beating patterns (Rosker et al., 1986). Subsequent studies by Okamoto and Yoshihara (1990) include the vibrational dephasing of the 992 cm benzene mode. A fast dephasing process was found that is possibly related to... 

The time-dependent classical statistical mechanics of systems of simple molecules is reviewed. The Liouville equation is derived the relationship between the generalized susceptibility and time-correlation function of molecular variables is obtained and a derivation of the generalized Langevin equation from the Liouville equation is given. The G.L.E. is then simplified and/or approximated by introducing physical assumptions that are appropriate to the problem of rotational motion in a dense fluid. Finally, the well-known expressions for spectral intensity of infrared and Raman vibration-rotation bands are reformulated in terms of time correlation functions. As an illustration, a brief discussion of the application of these results to the analysis of spectral data for liquid benzene is presented. 

Figure 2 Far-IR spectra of an 0.2 M iodine solution in benzene. The upper diagram shows the absorption coefficient and the lower diagram the infrared spectral density Uriy) as calculated according to Eq. (6) see text. [From M Besnard. Chemical kinetics and vibrational spectroscopy An analysis of weak charge transfer complexing reactions. In Molecular Liquids New Perspectives in Physics and Chemistry, JJC Teixeira-Dias, ed. Dordrecht Kluwer Academic, 1992, p 469. Reproduced with kind permission from Kluwer Academic Publishers.]...

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