Rovibrational motion

In the dense interstellar medium characteristic of sites of star fonuation, for example, scattering of visible/UV light by sub-micron-sized dust grains makes molecular clouds optically opaque and lowers their internal temperature to only a few tens of Kelvin. The thenual radiation from such objects therefore peaks in the FIR and only becomes optically thin at even longer wavelengths. Rotational motions of small molecules and rovibrational transitions of larger species and clusters thus provide, in many cases, the only or the most powerfiil probes of the dense, cold gas and dust of the interstellar medium. 

Molecules vibrate at fundamental frequencies that are usually in the mid-infrared. Some overtone and combination transitions occur at shorter wavelengths. Because infrared photons have enough energy to excite rotational motions also, the ir spectmm of a gas consists of rovibrational bands in which each vibrational transition is accompanied by numerous simultaneous rotational transitions. In condensed phases the rotational stmcture is suppressed, but the vibrational frequencies remain highly specific, and information on the molecular environment can often be deduced from hnewidths, frequency shifts, and additional spectral stmcture owing to phonon (thermal acoustic mode) and lattice effects. 

Infrared spectroscopy has broad appHcations for sensitive molecular speciation. Infrared frequencies depend on the masses of the atoms iavolved ia the various vibrational motions, and on the force constants and geometry of the bonds connecting them band shapes are determined by the rotational stmcture and hence by the molecular symmetry and moments of iaertia. The rovibrational spectmm of a gas thus provides direct molecular stmctural information, resulting ia very high specificity. The vibrational spectmm of any molecule is unique, except for those of optical isomers. Every molecule, except homonuclear diatomics such as O2, N2, and the halogens, has at least one vibrational absorption ia the iafrared. Several texts treat iafrared iastmmentation and techniques (22,36—38) and thek appHcations (39—42). 

Although apparently simple, there is a lot of subtlety in this model. The most important parameter in determining the translational energy dependence of the activation energy is AE. If we reduce AE, then the slope of E (Elmm) increases, which is found in the results of the full quantum dynamics calculations the slope is greater for the J 0 -> 4 transition than for J 0 - 6. AE is the shift in the threshold due to the thermal motion, it is the amount of energy surface motion contributes to aid the dissociation or rovibrational excitation. Why this should vary from one particular transition to... 

Extending the theory to interpret or predict the rovibrational state distribution of the products of the unimolecular dissociation, requires some postulate about the nature of the motion after the unimolecularly dissociating system leaves the TS on its way to form products. For systems with no potential energy maximum in the exit channel, the higher frequency vibrations will tend to remain in the same vibrational quantum state after leaving the TS. That is, the reaction is expected to be vibrationally adiabatic for those coordinates in the exit channel (we return to vibrational adiabaticity in Section 1.2.9). The hindered rotations and the translation along the reaction coordinate were assumed to be in statistical equilibrium in the exit channel after leaving the TS until an outer TS, the PST TS , is reached. With these assumptions, the products quantum state distribution was calculated. (After the system leaves the PST TS, there can be no further dynamical interactions, by definition.)... 

Thus in this approximation the (/)", constitute a complete set of rovibrational wave functions for each electronic state effective potential function governing the motion of the nuclei. This choice for ", is called the Born adiabatic approximation and amounts to neglect of the off-diagonal terms Cn, n, in equation (2.131) which mix different electronic states. 

Qei and Qvtbrot denote electronic and rovibrational partition fimctions, respectively. In general, the contributions of the internal degrees of freedom of A and B cancel in g and gviiroXA)gv iro((B ), such that only contributions Irom the external rotations of A and B and the relative motion, summarized as "transitional modes", need to be considered. Under low temperature quantum conditions, these can be obtained by statistical adiabatic channel (SACM) calculations [9],[10] while classical trajectory (CT) calculations [11]-[14] are the method of choice for higher temperatures. CT calculations are run in the capture mode, i.e. trajectories are followed Irom large separations of A and B to such small distances that subsequent collisions of AB can stabilize the adduct. 

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