Anharmonic vibrational mode

Figure 27.4 Potential energy contours (thin solid curves) from -10 to 20 kcal moh (spaced eve S kcal mol" ) are shown for the collinear Cl-H-Br reaction as a function of internal coordinates x and y (see text). A solid diamond denotes the saddle point and the thick straight line through the saddle point is the anharmonic vibrational mode. The thick solid curve is the minimum energy path.

Fig. 6.5 Wavefunctirais and transition dipole magnitudes for an anharmonic vibrational mode. (A) Relative amplitudes of wavefunctions 0-3 of an oscillator with the Morse potential illustrated in Fig. 2.1 (curves 0,7,2 and i, respectively). Wavefimction 13 is shown in (B), and 14 in (C). The abscissa is the relative departure of the vibrational coordinate (r) fixnn its equilibrium value (ro). The curves are normalized to the same integrated probabilities (squares of the wavefimction amplitudes) in the range 0 < (r — r )/r < 11.5, and are scaled relative to the peak of wavefimction 0. This normalization considers only part of wavefimctitm 14, which is at the dissociation energy and continues indefinitely off scale to the right. (D) The relative magnitudes of the transition dipoles ((Xm Xo)) for excitati

Okumura, K., Tanimura, Y. (1997). Femtosecond two-dimensional spectroscopy from anharmonic vibrational modes of molecules in the condensed phase. J. Chem. Phys. 107 2267-2283. 

Large amplitude (floppy) vibrational modes often exhibit significant anharmonicity that may increase errors in computed frequencies. In addition to anharmonicity, usually there is coupling between vibrational modes. 

The above picture points to the very interesting possibility of selectively inducing or enhancing the polymerisation process, at a temperature where this is unlikely, by resonantly driving with an intense laser beam in the infrared the vibrational modes and wc that are involved in the polymerisation. As a consequence of their anharmonicity (45) these modes, when driven near resonance by an electromagnetic field, beyond a certain critical value of the later, can reach amplitudes comparable to the critical ones required for the polymerisation to be initiated or proceed the anharmonicity in the presence of the intense laser beam acts as a defect and localizes the phonons creating thus a critical distorsion. 

However, in polyatomic molecules, transitions to excited states involving two vibrational modes at once (combination bands) are also weakly allowed, and are also affected by the anharmonicity of the potential. The role of combination bands in the NIR can be significant. As has been noted, the only functional groups likely to contribute to the NIR spectrum directly as overtone absorptions are those containing C-H, N-H, O-H or similar functionalities. However, in combination with these hydride bond overtone vibrations, contributions from other, lower frequency fundamental bands such as C=0 and C=C can be involved as overtone-combination bands. The effect may not be dramatic in the rather broad and overcrowded NIR absorption spectrum, but it can still be evident and useful in quantitative analysis. 

The formula (6.56), which includes anharmonicity corrections, is applicable only to molecules with no degenerate vibrational modes. Degenerate... 

A non-perturbative theory of the multiphonon relaxation of a localized vibrational mode, caused by a high-order anharmonic interaction with the nearest atoms of the crystal lattice, is proposed. It relates the rate of the process to the time-dependent non-stationary displacement correlation function of atoms. A non-linear integral equation for this function is derived and solved numerically for 3- and 4-phonon processes. We have found that the rate exhibits a critical behavior it sharply increases near a specific (critical) value(s) of the interaction. 

L. Goodman, M. J. Berman, A. G. Ozkabak, J. Chem. Phys. 90, 2544 (1989). The Benzene Ground State Potential Surface. III. Analysis of b2u Vibrational Mode Anharmonicity Through Two-Photon Intensity. 

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