Vibrational rotational coupling

Pekeris C L 1934 The rotation-vibration coupling in diatomic molecules Phys. Rev. 45 98 Slater J C and Kirkwood J G 1931 The van der Waals forces in gases Phys. Rev. 37 682... 

Treating the full internal nuclear-motion dynamics of a polyatomic molecule is complicated. It is conventional to examine the rotational movement of a hypothetical "rigid" molecule as well as the vibrational motion of a non-rotating molecule, and to then treat the rotation-vibration couplings using perturbation theory. 

Bratos S., Chestier J. P. Infrared and Raman study of liquids. III. Theory of rotation-vibration coupling effects. Diatomic molecules in inert solutions, Phys. Rev. A9, 2136-50 (1974). 

Pekeris, C. L. (1934), The Rotation-Vibration Coupling in Diatomic Molecules, Phys. Rev. 45, 98. 

Brouard, M., Martinez, M.T., and O Mahony, J. (1990). Fragment pair correlations in the vibrationally mediated photodissociation of H2O2 Rotation-vibration coupling in the third OH stretching overtone, Mol. Phys. 71, 1021-1041. 

As shown by Bliimel and co-workers [227], the Icicked Csl molecule is particularly appropriate candidate for this study since it has a large dipole moment, which increases the molecule-field coupling strength, and the rotation-vibration coupling is small at low excitation energies so that one may consider solely rotational excitation. We consider then the dynamics of Csl in the indicated pulsed field, in a parameter range known to display classical chaos [231].. ... 

Figure 4 shows the Raman spectra of CsgC. The high frequency Ag mode is now at 1430 1 cm , and has a resolution-limited FWHM of 7 cm . The further narrowing of this mode may be due to continued freezing out of the rotational-vibrational coupling, as NMR (13) and synchrotron x-ray (19) results indicate that the molecules are completely frozen at room temperature in K C o- of... 

The hardness can be written as H — AfI I9a. The values of a, ai and 2 can be found from a detailed analysis of the rotation-vibration spectra of the molecule. The experimental results are presented as Ue, the vibrational frequency, the rotational constant, uj X, the anharmonicity constant, and the rotation-vibration coupling constant. The subscript e refers to the ground-state or equilibrium value. 

Pekeris C L 1934 The rotation-vibration coupling in diatomic molecules Phys. Rev. 45 98... 

Figure 6 The differences between energies of bend overtones in H O with 7=2 and K = 2 and the energies of the corresponding 7 = 0 states are plotted as a function of the number of quanta in the bend. The results of variational, eighth, sixth, fourth, and second-order perturbative calculations are denoted by, , O, A, and 0 respectively. The perturbative results model the rotation-vibration coupling as a polynomial expansion in the bend quantum number. Given the actual form of this coupling, as obtained from the variational calculation, the slow convergence of CVPT is not surprising. (From Ref. 49.)...

The three terms in have the interpretation as curvature couplings, Coriolis coupling, and centrifugal distortion, respectively. The latter two obviously involve rotation-vibration coupling—i.e., they are zero if J 0. The first (curvature coupling) term describes energy transfer between the reaction coordinate s and the transverse vibrational modes The coupling functions... 

Note that pure rotational motion is rarely realized in nuclei the rotational and vibrational excitations are usually mixed. It is very general that there are rotational bands built on the Ojand 2f vibrational levels, these are the so-called P- and y-vibrational bands. The rotation-vibration coupling is discussed, e.g., in Bohr and Mottelson (1974) and Garrett (2001) publications. 

By retaining the Vanh term in eqn (20.27), anharmonicity in the individual modes and anharmonic coupling between the modes are included, but rotational energy and rotational/vibrational coupling are neglected. At low... 

The coupling of rotation and vibration gives an additional term in the expression for (e — So)/hc of — a(y + i)J(J + 1) where a is the rotational-vibrational coupling constant. The effect of centrifugal stretching is expressed by a further term of — DJ%J + 1) where D is the rotational stretching coefficient, which is related to the rotational constant for equilibrium separation, jBe. by Z) = ABljvl. If So is the rotational constant for the first vibrationally excited state, then Bq = Be — a/2. 

On the contrary, the Q-branch of the anisotropic Raman spectrum broadens monotonously until it merges with the 0-and S-branches (11). The major restriction of these theories is that they are essentially gas phase theories however, this restriction is less stringent for the theory by Burshtein et al. Moreover, the rotation-vibration coupling effects due to intermolecular forces are neglected here again. This is done in the Sobel man theory by neglecting the v-dependence of the S matrix. 

This Section may be concluded by giving a brief estimate of the actual situation in this area. It is probably fair to say that the spectral manifestation of the intramolecular rotation-vibration coupling are qualitatively understood. Nevertheless, no quantitative study has yet been published. It is probable that the use of computer simulation techniques will accelerate the progress. Unfortunately, the treatment of diluted solutions is technically difficult. 

To further simplify the RPH, rotations of the reaction complex in three-dimensional space are excluded by assuming zero angular momentum (J = 0). In this way, the RPH does not contain a rotational part and possible rotational-vibrational coupling terms. 

Vibronic Transition Molecular transition involving states which are split by rotation that is induced through rotation-vibrational coupling the fine-structure states of electronic transitions. 

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