ISSN:
1089-7690
Source:
AIP Digital Archive
Topics:
Physics
,
Chemistry and Pharmacology
Notes:
It is shown that the usual primitive adiabatic theory of classical reaction dynamics is inconsistent when separatrix crossing occurs. In such cases, primitive theory yields errors in the reaction probabilities and other observables which do not scale to zero even when the time scale ratios become infinitely large, i.e., the adiabatic limit. This motivates a fundamental modification to the classical adiabatic theory of reactions to include the effects of separatrix crossing. The approach is explicitly formulated for direct heavy–light–heavy collinear reactions where two separatrix crossings must occur during the course of each reactive trajectory: once when the orbit untraps from the incoming reactant channel well and once again when it retraps in the final product channel well. The uniform adiabatic invariance analysis we propose reduces the classical reaction dynamics to the form of a simple measure preserving map. That is, the final conditions of the product trajectory are written as explicit analytic functions of the initial conditions. This eliminates the need to propagate any trajectories. The map is formulated in terms of the quantities from the adiabatic theory of reactions, i.e., vibrationally adiabatic potential curves, instantaneous frequency, etc., which are easily computed numerically. It is found that the imaginary frequency of the potential surface along the ridge separating reactants from products is a crucial parameter in the reaction dynamics. The uniform adiabatic analysis permits the calculation of vibrational inelasticity, complex lifetimes, the structure of reactivity bands, and other quantities inaccessible in usual adiabatic theory of reactions. Numerical result are presented for the I+HI reaction where it is found that the theory is quite accurate.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.456336
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