A SCRUTINY OF THE PREMISE OF THE RICE-RAMSPERGER-KASSEL-MARCUS THEORYIN ISOMERIZATION REACTION OF AN AR-7-TYPE MOLECULE

The validity of the physical premise of the Rice-Ramsperger-Kassel-Mar cus (RRKM) theory is investigated in terms of the classical dynamics o f isomerization reaction in Ar-7-like molecules (clusters). The passag e times of classical trajectories through the potential basins of isom ers in the structural transitions are examined. In the high energy reg ion corresponding to the so-called Liquidlike phase, remarkable unifor mity of the average passage times has been found. That is, the average passage time is characterized only by a basin through which a traject ory is currently passing and, hence, does not depend on the next visit ing basins. This behavior is out of accord with the ordinary chemical law in that the ''reaction rates'' do not seem to depend on the height of the individual potential barriers. We ascribe this seemingly stran ge uniformity to the strong mixing (chaos) lying behind the rate proce ss. That is, as soon as a classical path enters a basin, it gets invol ved into a chaotic zone in which many paths having different channels are entangled among each other, and effectively (in the statistical se nse) loses its memory about which basin it came from and where it shou ld visit next time. This model is verified by confirming that the popu lations of the Lifetime of transition from one basin to others are exp ressed in exponential functions, which should have very similar expone nts to each other in each passing-through basin. The inverse of the ex ponent is essentially proportional to the average passage time, and co nsequently brings about the uniformity. These populations set a founda tion for the multichannel generalization of the RRKM theory. Two cases of the non-RRKM behaviors have been studied. One is a nonstatistical behavior in the low energy region such as the so-called coexistence ph ase. The other is the short-time behavior. It is well established [M. Berblinger and C. Schlier, J. Chem. Phys. 101, 4750 (1994)] that in a relatively simple and small system such as H-3(+), the so-called direc t paths, which lead to dissociation before the phase-space mixing is c ompleted, increase the probability of short-time passage. In contrast, we have found in our Ar-7-like molecules that trajectories of short p assage time are fewer than expected by the statistical theory. It is c onceived that somewhat a long time in the initial stage of the isomeri zation is spent by a trajectory to find its ways out to the next basin s. (C) 1996 American Institute of Physics.