Microcanonical rates, gap times, and phase space dividing surfaces

TL;DR

This paper revisits classical unimolecular reaction rate theory using phase space methods, analyzing gap time distributions and decay regimes for HCN isomerization, revealing statistical and nonstatistical behaviors.

Contribution

It provides a detailed phase space analysis of reaction dynamics, connecting classical rate theory with modern transition state concepts and identifying nonexponential decay regimes.

Findings

Both algebraic and exponential decay regimes identified.

Complete phase space symmetry is attained within 0.5 ps.

Nonexponential decay observed at intermediate times.

Abstract

The general approach to classical unimolecular reaction rates due to Thiele is revisited in light of recent advances in the phase space formulation of transition state theory for multidimensional systems. We analyze in detail the gap time distribution and associated reactant lifetime distribution for the isomerization reaction HCN $\rightleftharpoons$ CNH. Both algebraic (power law) and exponential decay regimes have been identified. Statistical estimates of the isomerization rate are compared with the numerically determined decay rate. Examination of the decay properties of subsensembles of trajectories that exit the HCN well through either of 2 available symmetry related product channels shows that the complete trajectory ensemble effectively attains the full symmetry of the system phase space on a short timescale $t \lesssim 0.5$ ps, after which the product branching ratio is 1:1, the "statistical" value. At intermediate times, this statistical product ratio is accompanied by nonexponential (nonstatistical) decay. We point out close parallels between the dynamical behavior inferred from the gap time distribution for HCN and nonstatistical behavior recently identified in reactions of some organic molecules.