Couplings between vibrational modes

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. 

Another illustrative example of mode-specific decay is the dissociation of water. Local-mode and hyperspherical-mode resonance states exist in the same energy range and decay with significantly different rates [70,80,81]. Correlations between assignments and vibrational PSD s can also be established [51]. Often, molecules featuring mode-specific decay have low densities of states and shallow potential wells. However, the most important requirement is that the coupling between vibrational modes is weak, so that the dynamics is close to separable. Two examples, HCO and HOCl, will be discussed in Sect. 5. 

A virtually unique, and most interesting feature of van der Waals clusters is that such systems may exhibit strong anharmonic coupling between vibrational modes and large amplitude motions even in the ground state, or for the lowest excited states. 

This chapter begins with a classical treatment of vibrational motion, because most of the important concepts that are specific to vibrations in polyatomics carry over naturally from the classical to the quantum mechanical description. In molecules with harmonic potential energy functions, vibrational motion occurs in normal modes that are mutually uncoupled. Coupling between vibrational modes inevitably occurs in the presence of anharmonic potentials (potentials exhibiting cubic and/or higher order terms in the nuclear coordinates). In molecules with sufficient symmetry, the use of group theory simplifies the procedure of obtaining the normal mode frequencies and coordinates. We obtain El selection rules for vibrational transitions in polyatomics, and consider the rotational fine structure of vibrational bands. We finally treat breakdown of the normal mode approximation in real molecules, and discuss the local mode formulation of vibrational motion in polyatomics. 

Long-range polar coupling between vibrational modes has also been studied ... 

The reconstruction of the bandshape of the imidazole crystal was also performed using Car-Parrinello molecular dynamics (CPMD) simulation [73] of the unit cell of the crystal the results reproduce both the frequencies and intensities of the experimental IR spectrum of bands reasonably well, which we attribute to the application of dipole moment dynamics. The results are presented in Fig. 8 [70]. These and other recent CPMD calculations, on 2-hydroxy-5-nitrobenzamide crystal [71], oxalic acid dihydrate [72], and other systems [64-69], show that the CPMD method is adequate for spectroscopic investigations of complex systems with hydrogen bonds since it takes into account most of mechanisms determining the hydrogen bond dynamics (anharmonicity, couplings between vibrational modes, and intermolecular interactions in crystals). 

As noted at the beginning of this section, the coupling between vibrational modes k and k now appears in the potential energy, characterized by the coupling element A] (s). In many applications it... 

A typical problem of interest at Los Alamos is the solution of the infrared multiple photon excitation dynamics of sulfur hexafluoride. This very problem has been quite popular in the literature in the past few years. (7) The solution of this problem is modeled by a molecular Hamiltonian which explicitly treats the asymmetric stretch ladder of the molecule coupled implicitly to the other molecular degrees of freedom. (See Fig. 12.) We consider the the first seven vibrational states of the mode of SF (6v ) the octahedral symmetry of the SF molecule makes these vibrational levels degenerate, and coupling between vibrational and rotational motion splits these degeneracies slightly. Furthermore, there is a rotational manifold of states associated with each vibrational level. Even to describe the zeroth-order level states of this molecule is itself a fairly complicated problem. Now if we were to include collisions in our model of multiple photon excitation of SF, e wou d have to solve a matrix Bloch equation with a minimum of 84 x 84 elements. Clearly such a problem is beyond our current abilities, so in fact we neglect collisional effects in order to stay with a Schrodinger picture of the excitation dynamics. 

The 03 dependence of the force constant k(Q) = rnoP iQ) creates an anharmonic coupling between both modes q and Q. It is at the origin of the exceptional width of bands of H-bonds, and of their shifts towards lower wavenumbers when compared to bands of the same X H molecules, when they do not establish H-bonds. These most intense bands are 0 1 transitions, or transitions between the ground vibrational state of q and its first excited state. The other possible transitions, 0 n with n > 1, have intensities equal to 0 in the case of an harmonic oscillator in q (no terms in q, (f, etc. in V q, Q)). Overtones of v, particularly those corresponding to 0 2 transitions in the 6000-6500 cm region, however often... 

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