Rotation-vibration coupling

Including an additional term can make a further improvement to the truncation made in Equation 6-18. 

If the original vibrational potential, V(s + r, is taken to be harmonic, the effective potential has the same form as in Equation 645 with a different effective force constant  

The vibrational frequency will now depend on the rotational state J. 

The effect of the additional term 2c is to increase the effective vibrational frequency, coj, causing an increase in energy for each eigenstate except for when J = 0. This effect is called vibration-rotation coupling. 

Another more standard approach is to treat the additional term in the effective potential as a perturbation. Perturbation theory yields the following vibration/rotation energy eigenvalues  

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The only tenn in this expression that we have not already seen is a, the vibration-rotation coupling constant. It accounts for the fact that as the molecule vibrates, its bond length changes which in turn changes the moment of inertia. Equation B1.2.2 can be simplified by combming the vibration-rotation constant with the rotational constant, yielding a vibrational-level-dependent rotational constant. 

D. Perturbative Treatment of Vibration-Rotation Coupling III. Rotation of Polyatomic Molecules... 

Fig, 19. Infrared spectra of the symmetric CHj bend mode of ethylidyne (CCHj) on Pt(l 11) at 82 K and 300 K. The dotted lines are calculated assuming a vibrational-rotational coupling. Inset shows the suggested orientation. (Reproduced by permission from Malik et... 

It should be noted that the spacings between the experimentally observed peaks in HC1 are not constant as would be expected based on the above P- and R- branch formulas. This is because the moment of inertia appropriate for the v = 1 vibrational level is different than that of the v = 0 level. These effects of vibration-rotation coupling can be modeled by allowing the v = 0 and v = 1 levels to have rotational energies written as... 

The fifth term in (4.67) represents an interaction between vibration and rotation, and ae is called a vibration-rotation coupling constant. [Do not confuse ae with a in (4.26).] As the vibrational quantum number increases, the average internuclear distance increases, because of the anharmonicity of the potential-energy curve (Fig. 4.4). This increases the effective moment of inertia, and therefore decreases the rotational energy. We can define a mean rotational constant Bv for states with vibrational quantum number v by... 

The main contributions to the frequency-time correlation function are assumed to be, as in the earlier works [123, 124], from the vibration-rotation coupling and the repulsive and attractive parts of the solvent-solute interactions. In several theories, the (faster) repulsive and the (slower) attractive contributions are assumed to be of widely different time scales and are treated separately. However, this may not be true in real liquids because the solvent dynamic interactions cover a wide range of time scales and there could be a considerable overlap of their contributions. The vibration-rotation coupling contribution takes place in a very short time scale and by neglecting the cross-correlation between this mechanism and the atom-atom forces, they... 

Note that the angular momentum-momentum correlation function related to the vibrational-rotation friction too is highly nonexponential. This again could significantly alter the 2 dependence of the rate. However, for the systems studied here, the contribution of vibration-rotation coupling is negligible. 

P. Botschwina and J. Fliigge, Chem. Phys. Lett., 180, 589 (1991). Ab Initio Vibration-Rotation Coupling Constants and the Equilibrium Geometries of NCCN and CNCN. 

Vibration-rotation coupling constant Distortion polarizability... 

The thermodynamic functions of this table are analogous to those in the JANAF table for H20(g) (j ) both tables are taken from Freidman and Haar (1 ). Friedman and Haar applied their non-rigid-rotor, anharmonic-oscillator treatment (with vibrational-rotational coupling terms and low-temperature rotational corrections) to the infrared-spectra analyses of Benedict et al. (J ), and... 

Intermolecular vibration-rotation coupling through the fluctuations of the relative orientations of neighboring molecules ac, p... 

Another type of vibration-rotation coupling which involves the modulation of the frequency o>(t) by the internal rotational state of the molecule (through centrifugal or Coriolis coupling). 

Note that the simplified expressions obtained here would be complicated by the inclusion of resonant V-V transfer, which could also give a large many-body contribution to dephasing if multipolar interactions are involved. Also a very common source of motional narrowing arises from vibration-rotation coupling to which the present discussion is not adapted. 

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