Comparison of quantum, classical, and statistical behavior in dissociating triatomics

Time-dependent calculations are presented which compare the dynamics of quantum and classical one-dimensional triatomic systems undergoing intramolecular vibrational energy transfer and dissociation. The purpose of these calculations is to determine whether statistical dissociative behavior in classical systems implies similar behavior in the analogous quantum systems and to test for the presence of quantum mechanical effects that reduce the tendency of the systems to decompose statistically. The intramolecular vibrational energy transfer is monitored by computing the probability for the systems to remain in their initial, coarsely grained states, and the dissociation is followed by calculating the time-dependent decomposition probability and the product distribution. The classical calculations are performed by a version of the quasiclassical technique while the quantum calculations are carried out by an R-matrix method. The results show that the two forms of dynamics usually result in similar intramolecular evolution and unimolecular decay. Since the behavior of the classical systems is statistical in a well-defined sense, it is argued that the behavior of the quantum mechanical systems can likewise be labeled as statistical in these typical cases. Important exceptions to the generally good quantum-classical agreement occur, however, when the systems are prepared with high energy in a dissociable bond and low energy in the other bond. In such cases, the quantum behavior differs significantly from the classical behavior; the quantum dynamics of decomposition is nonstatistical even though the classical dynamics is statistical. It is found that the "quantum trapping" states which lead to the nonstatistical quantum mechanical behavior are associated with narrow Feshbach resonances which accumulate in certain specific energy regions. It is further concluded that these states occupy a significant proportion of the classical phase space available to molecular complexes with energy below the first vibrational threshold.