Resonant unimolecular reactions

A) During the luultiphoton excitation of molecular vibrations witli IR lasers, many (typically 10-50) photons are absorbed in a quasi-resonant stepwise process until the absorbed energy is suflFicient to initiate a unimolecular reaction, dissociation, or isomerization, usually in the electronic ground state. 

Many bimolecular and unimolecular reactions are dominated by long-lived resonances. As a result, having knowledge about the positions and lifetimes of such resonance states is highly desired. Recursive calculations of resonance states have been reported for many molecular systems, including... 

There are a number of open issues associated with statistical descriptions of unimolecular reactions, particularly in many-dimensional systems. One fundamental issue is to find a qualitative criterion for predicting if a reaction in a many-dimensional system is statistical or nonstatistic al. In a recent review article, Toda [17] discussed different aspects of the Arnold web — that is, the network of nonlinear resonances in many-dimensional systems. Toda pointed out the importance of analyzing the qualitative features of the Arnold web— for example, how different resonance zones intersect and how the intersections further overlap with one another. However, as pointed out earlier, even in the case of fully developed global chaos it remains challenging to define a nonlocal reaction separatrix and to calculate the flux crossing the separatrix in a manydimensional phase-space. 

Resonances are prominent features in many helds of physics and chemistry such as nuclear [72] and atomic [73] physics, electron [74] and molecular [75] scattering, and photodissociation [76]. A detailed account of resonances in molecular systems, with particular emphasis on unimolecular reactions, has been given by Grebenshchikov et al. 

In ordinary unimolecular reaction rate theory, the usual assumptions of strong collisions and random distribution of the internal energy simply serve to wash out precisely those features of the molecular dynamics that become of primary importance in the cases of photochemical, chemical, and electron impact excitation. Whereas evaluation of all the consequences is incomplete at present, it is already clear that the representation of an excited molecule in terms of the properties of resonant scattering states holds promise for the elucidation of those aspects of the internal dynamics that are important in photochemistry. 

In the context considered here, a resonance is a near match of frequency between two coupled oscillations. Such a resonance will produce energy transfer from one of the oscillators to the other. A nonlinear resonance is a resonance arising from the nonlinearity of the restoring force in one or both of the oscillators, or in other words, due to the anharmonicity of one or both of the oscillators. For a harmonic oscillator, of course, the frequency of oscillation is independent of the energy or amplitude of the oscillation. Molecular vibrational modes, however, are both anharmonic, particularly at energies sufficient for unimolecular reaction, and the energy dependence of the oscillator frequency is critical to mode-mode energy transfer. 

To illustrate reactive vibrational dynamics in a very different type of unimolecular reaction, we consider the trans-cis isomerization of diimide (HNNH). The central N—N bond is a double bond, so the barrier to isomerization from trans to cis is quite high, 192 kJ/mol. Spears (63,64) developed a model to describe the high-energy vibrations of diimide in all six degrees of freedom. We demonstrated that nonlinear resonance interactions are critical to the dynamics of mode-mode energy transfer into and out of the torsional vibration (63). We also found, however, that these resonant interactions were detuned before the excitation of the torsional mode was sufficient to achieve isomerization. 

The advantage of a jet-cooled sample is at the same time also a disadvantage. If the role of the rotational states in unimolecular reactions is of interest, a jet-cooled sample in which most of the molecules are in the very low J levels is clearly not Suitable. For such investigations, it is necessary to study the sample in a bulb and use a laser to excite molecules in selected rotational states. This is extremely difficult for all but the smallest molecules because of the very large density of states and the difficulty in assigning all but the lowest energy levels. Double-resonance approaches help overcome this problem. 

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