Diffusion and vibrational relaxation of a diatomic molecule in the pore network of a pure silica zeolite: A molecular dynamics study

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The validity of the physical premise of the Rice–Ramsperger–Kassel–Marcus (RRKM) theory is investigated in terms of the classical dynamics of isomerization reaction in Ar7-like molecules (clusters). The passage times of classical trajectories through the potential basins of isomers in the structural transitions are examined. In the high energy region corresponding to the so-called liquidlike phase, remarkable uniformity of the average passage times has been found. That is, the average passage time is characterized only by a basin through which a trajectory is currently passing and, hence, does not depend on the next visiting 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 strange uniformity to the strong mixing (chaos) lying behind the rate process. That is, as soon as a classical path enters a basin, it gets involved into a chaotic zone in which many paths having different channels are entangled among each other, and effectively (in the statistical sense) loses its memory about which basin it came from and where it should visit next time. This model is verified by confirming that the populations of the lifetime of transition from one basin to others are expressed in exponential functions, which should have very similar exponents to each other in each passing-through basin. The inverse of the exponent is essentially proportional to the average passage time, and consequently brings about the uniformity. These populations set a foundation 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 phase. 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 direct paths, which lead to dissociation before the phase-space mixing is completed, increase the probability of short-time passage. In contrast, we have found in our Ar7-like molecules that trajectories of short passage time are fewer than expected by the statistical theory. It is conceived that somewhat a long time in the initial stage of the isomerization is spent by a trajectory to find its ways out to the next basins.

FIG. 8. The distribution of the crossing points determined by means of the quenching method. The symbols P, C, I, and S denote the next visiting basins PBP, COCT, IST, and SKEW, respectively. 4931

The dependence of lifetime distribution in isomerization dynamics of Ar7-like clusters on the potential topography is reported. Using the scaled Morse potential V=∑i<j(e−2(ρij−ρ0)−2e−(ρij−ρ0)), where ρij is an internuclear distance, and ρ0, the equilibrium distance of the isolated diatomic molecule, is the only independent parameter that uniquely specifies the system Hamiltonian, we have examined the dynamics for two typical values of ρ0. In the high enough energy region, which is called the liquidlike phase, the cluster of a small ρ0 (called a compact cluster) has an exponential form for the lifetime distribution. In contrast, dynamics on the potential with a large ρ0 (a loose cluster) exhibits a large deviation from the exponential form, its mixing dynamics notwithstanding; it displays a large hole in the short lifetime region and a steep clifflike structure in the even shorter lifetime region embedded in the hole. Since the deviation is so clear, the present system offers an excellent example with which to investigate the dependence of phase space structure on the potential topography. We have identified the mechanisms of formation both of the hole and cliff. The hole is particularly important to understand how mixing dynamics can deviate from the statistically simple exponential distribution. By comparing a variety of quantities that characterize the system dynamics, we propose a conceptual picture to understand the basic difference between the dynamics on compact and loose potentials, in which the complexity of the dynamics is ascribed to the bifurcation of the reaction tubes and to the turning-point distributions clinging to the branching places of such bifurcated tubes.