Rotational vibrations vibration coupling

Translational, Rotational and Vibrational Coupling of Molecules to Their Local Helium Environment... 

The second term in fk is a Coriolis type term which does not induce vibrational transition but tries to distort (stretch or bend) the molecule during the rotation of the complex and is referred to as the centrifugal stretch term . The last term in in eq. (5.9) arises from the expectation value of the quadratic term of the potential and is the V-V (vibration-vibration) coupling term. The quadratic forces are given by the expression... 

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... 

For a RRKM calculation without any approximations, the complete vibrational/rotational Flamiltonian for the imimolecular system is used to calculate the reactant density and transition state s sum of states. No approximations are made regarding the coupling between vibration and rotation. Flowever, for many molecules the exact nature of the coupling between vibration and rotation is uncertain, particularly at high energies, and a model in which rotation and vibration are assumed separable is widely used to calculate the quantum RRKM k(E,J) [4,16]. To illustrate this model, first consider a linear polyatomic molecule which decomposes via a linear transition state. The rotational energy for tire reactant is assumed to be that for a rigid rotor, i.e. 

The close-coupling equations are also applicable to electron-molecule collision but severe computational difficulties arise due to the large number of rotational and vibrational channels that must be retained in the expansion for the system wavefiinction. In the fixed nuclei approximation, the Bom-Oppenlieimer separation of electronic and nuclear motion pennits electronic motion and scattering amplitudes f, (R) to be detemiined at fixed intemuclear separations R. Then in the adiabatic nuclear approximation the scattering amplitude for ... 

Also, rotational state resolution of cross-sections can be obtained by employing a coherent state analysis [51] for the situation of weak coupling between rotational and vibrational degrees of freedom. A suitable rotational coherent state can be expressed as... 

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. 

Fig. 56. Contour plots of (a) shaking and (b) breathing vibrations coupled to hindered rotation around the three-fold axis. The MEP is shown.

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). 

NH (X n) for which (4d) vibration of the N-H bond couples only weakly to the non-bonding 2pn orbital and for which rotation-to-electronic coupling can be dominant in causing electron ejection for high rotational levels. 

The Hamiltonian operator for molecular rotational-vibrational spectra, which in the uncoupled form is written as in Eq. (2.17), can now be written in the coupled form as... 

The formulation of the preceding section is very general. We are interested, however, in rotations and vibrations of polyatomic molecules. We therefore discuss now specific applications of the algebraic method beginning with the simple case of one-dimensional coupled oscillators, presented in Section 3.3 in the Schrodinger picture. In the algebraic theory, as mentioned, one associates to each coordinate, x, and related momentum, px = — iti d/dx, an algebra. For... 

There is no direct coupling between lb = + 2 and lb = - 2 because of the selection rule (4.128). The values of a, and a2 are obtained by using the equations of the previous sections and are given in general in terms of qu, q22, quin view of the special form of the rotation-vibration matrices, it is convenient to introduce a transformed basis (Wang s basis, 1929 see also Herman et al., 1991 Holland et al., 1992), defined as... 

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

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