Polyatomic molecules anharmonic couplings

In principle, one can induce and control unimolecular reactions directly in the electronic ground state via intense IR fields. Note that this resembles traditional thermal unimolecular reactions, in the sense that the dynamics is confined to the electronic ground state. High intensities are typically required in order to climb up the vibrational ladder and induce bond breaking (or isomerization). The dissociation probability is substantially enhanced when the frequency of the field is time dependent, i.e., the frequency must decrease as a function of time in order to accommodate the anharmonicity of the potential. Selective bond breaking in polyatomic molecules is, in addition, complicated by the fact that the dynamics in various bond-stretching coordinates is coupled due to anharmonic terms in the potential. 

The recent progress of computational quantum chemistry has made it possible to get realistic descriptions of vibrational frequencies for polyatomic molecules in solution. The first attempt in this direction was made by Rivail el al. [1] by exploiting a semiempirical QM molecular model coupled with a continuum description of the medium to compute vibrational frequency shifts for molecular solutes. An extension to ab initio QM methods, including the treatment of electron correlation effects and electrical and mechanical anharmonicities, was then proposed [2 1] in the framework of the Polarizable Continuum Model (PCM). 

An alternative approach widely used in polyatomic molecule studies is based on the Golden Rule and a perturbative treatment of the anharmonic coupling (57,62). This approach is not much used for diatomic molecules. In the liquid O2 example cited above, the Hamiltonian must be expanded to 30th order or so to calculate the multiphonon emission rate. But for vibrations of polyatomic molecules, which can always find relatively low-order VER pathways for each VER step, perturbation theory is very useful. In the perturbation approach, the molecule s entire ladder of vibrational excitations is the system and the phonons are the bath. Only lower-order processes are ordinarily needed (57) because polyatomic molecules have many vibrations ranging from higher to lower frequencies and only a small number of phonons, usually one or two, are excited in each VER step. The usual practice is to expand the interaction Hamiltonian (qn, Q) in Equation (2) in powers of normal coordinates (57,62) ... 

Both Ok and fl. - flj. provide useful insights into the causes and rates of specific dynamical processes. Sections 9.4.9 and 9.4.10 provide analyses of the dynamics of the S-uncoupling operator in a 25+1A state and the 1 2 anharmonic coupling operator that contributes to Intramolecular Vibrational Redistribution (IVR) in a polyatomic molecule and illustrate the diagnostic power of the flk + fij. and lk — resonance and rate operators. 

The origin of these multiple temperature effects lies in the dependence of the kinetic rate constants on only the translational (or more generally the bath ) temperature. For vibrational states, these results were first derived for diatomic anharmonic oscillators and used to explain laser action in CO via anharmonic pumping. Multiple vibrational temperature concepts were later applied to the polyatomic molecule SF to explain discrepancies between relaxation rates measured by ultrasonic and laser techniques. The close correspondence between the temperature picture for vibrational levels weakly coupled to a thermal bath and that for nuclear or electron spin levels also weakly coupled to a thermal bath will be immediately obvious to those familiar with spin temperature concepts. ... 

The vibrations of a polyatomic molecule can be considered as a system of coupled anharmonic oscillators. If there are N atomic nuclei in the molecule, there will be a total of 3N degrees of freedom of motion for all the nuclear masses in the molecule. Subtracting the pure translations and rotations of the entire molecule leaves (3N-6) vibrational degrees of freedom for a non-linear molecule and (3N-5) vibrational degrees of freedom for a linear molecule. These internal degrees of freedom correspond to the number of independent normal modes of vibration. Note that in each normal mode of vibration all the atoms of the molecule vibrate with the same frequency and pass through their equilibrium positions simultaneously. 

The local mode description with only one bond such as X-H being in motion at a time leads us to consider the polyatomic molecule as a single diatomic molecule M-H where H is hydrogen and M denotes the full rest of the molecule. The main advantage of this description is the dramatic reduction of the number of coupling constants. The anharmonic oscillator potential adopted in the local mode model is the Morse potential, which takes account of the dissociation energy De (53). 

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. 

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