Intramolecular vibrational energy principles

To start the mathematical integration of the equations of motion for one particular trajectory, a set of initial values of coordinates and either velocities or momenta must be specified. These, however, are dependent on the experimental conditions which need be reproduced, such as collision energy, intramolecular vibrational energies etc... In addition, some other variables, for instance intramolecular instantaneous elongations, molecular orientations, impact parameter, etc..., are necessarily specified in classical mechanics but are not observable microscopically because of the Uncertainty Principle. The ensemble of these result in a set of trajectories associated with a given set of observable initial conditions. 

In the semiclassical regime, the value of coordinate Q must be conserved on transition of an electron from the reactant and the product state under the Franck Condon principle. Since the diabatic potentials for these states are composed of multiple parabolas due to participation of large-energy-quantum intramolecular vibrations, the transition is specified by a simultaneous change in the quantum state of these vibrations, for example, from the wth state m r> in the reactant state to the... 

Owing to their relatively simple electronic structure, the alkali trimers can be regarded as such model systems, to study, for example the principles of intramolecular vibrational redistribution (IVR) in photoexcited molecules or clusters. Among the alkali trimers Naa, especially when excited to its electronic B state, seems to be the best known. It acts in this section as a prototype for exploration of details of photoinduced IVR processes in real-time. Figure 3.35 sketches the principle of the experimental approach for triatomic s systems such as the Jahn-Teller distorted Naa B system. Compared to the investigations on the dimer systems, the only difference is that the energy surfaces involved get a dittle more complicated. 

We denote by G the set of all the experimentally observable quantities (called physical observables) which must be reproduced. Such quantities are, for instance, the collision energy, the quantum numbers defining the intramolecular state (vibrations and the principal quantum number of rotation), the total angular momentum etc... However, there are other dynamical variables which have a clear meaning in Classical Mechanics but correspond to no physical observable because of the Uncertainty Principle. We call them phase variables and denote them globally by g. The phase variables must be given particular values to obtain, at given G, a particular trajectory. Such variables are, for instance, the various intramolecular normal vibrational phases, the intermolecular orientation, the secondary rotation quantum numbers, the impact parameter, etc... Thus we look for relationships of the type qo = qq (G, g) and either qo = qo (G, g) or po = Po (G, g)... 

The data on Infrared photodlssoclatlon of vdW molecules provides, In principle. Information on several topics of great current Interest In addition to colllslonal resonances. One of these Is the structure of weakly bound systems. Another Is the rate of "intramolecular" energy flow from the vibration which Is initially localized within A or B Into the vdW coordinates which express the... 

In liquids and dense gases where collisions, intramolecular molecular motions and energy relaxation occur on the picosecond timescales, spectroscopic lineshape studies in the frequency domain were for a long time the principle source of dynamical information on the equilibrium state of manybody systems. These interpretations were based on the scattering of incident radiation as a consequence of molecular motion such as vibration, rotation and translation. Spectroscopic lineshape analyses were intepreted through arguments based on the fluctuation-dissipation theorem and linear response theory (9,10). In generating details of the dynamics of molecules, this approach relies on FT techniques, but the statistical physics depends on the fact that the radiation probe is only weakly coupled to the system. If the pertubation does not disturb the system from its equilibrium properties, then linear response theory allows one to evaluate the response in terms of the time correlation functions (TCF) of the equilibrium state. Since each spectroscopic technique probes the expectation value... 

---