K. Takatsuka et C. Seko, A SCRUTINY OF THE PREMISE OF THE RICE-RAMSPERGER-KASSEL-MARCUS THEORYIN ISOMERIZATION REACTION OF AN AR-7-TYPE MOLECULE, The Journal of chemical physics, 105(23), 1996, pp. 10356-10366
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.