Quantum effects in competitive unimolecular reactions

The decay law P(t) of a microcanonical ensemble of metastable states prepared in an energy interval δE is usually nonexponential because the widths Γ of each individual resonance fluctuate around an energy-dependent average K(E) which is satisfactorily approximated by RRKM theory. The kinetic equations used at the macroscopic level are therefore not necessarily transferable to elementary processes when the interval δE contains more than a single resonance. For example, two competitive unimolecular reactions need not be characterized by the same effective evolution in time. Particular attention is focused on the quantum expressions of the yields of fragmentation Yk(E, t) when they differ from those Fk(E, t) derived from the macroscopic kinetic scheme. The discussion is based on the value of the parameter νeff = 2K(E)2/σ2 which is a measure of the dispersion of the individual rate constants. Two applications are presented. First, we consider a competition between an electronic and a vibrational predissociation in a triatomic van der Waals-like model with a sparse density of states and a maximum number of selection rules. The shorter the lifetime, the larger the dispersion of the widths of the resonances lying within δE, and the more severe the discrepancy between Yk(E, t) and Fk(E, t). In the quantum treatment, fragmentation proceeds with unequal effective rate constants in the two decay channels. The second application deals with the other extreme where the density of states is so large that statistical methods are useful. Explicit quantum mechanical expressions of the yields in a competitive fragmentation process are given for some distributions of the widths, χν 2 and convolutions of χν 2. Here again, a discrepancy can be observed between Yk(E, t) and Fk(E, t): competitive unimolecular reactions need not be characterized by the same rate. It is demonstrated that, when the density of states is so large that the resonances are quasi-degenerate, the mean and the variance of the widths can be obtained from the invariant Ω matrix. When the resonances overlap, the variance of the widths is always greater than the variance of any kind of zero-orders widths. Except in unrealistic cases (either because a single resonance is excited or because all the widths are the same) it is dubious to disprove a mechanism on the basis of arguments borrowed from conventional macroscopic kinetics in an energy-resolved experiment as has been done many times in the past. © 1991.