New approaches to a classical theory of unimolecular reaction rate

Abstract

Backgroundtudies of the rate of a unimolecular reaction S have been central to the development of our understanding of reaction dynamics for almost a century. In the early 1900s, such reactions appeared mysterious, since the source of the energy required for reaction to occur was not immediately apparent. Indeed, it took careful experimental work to demonstrate that thermal unimolecular reactions were induced by collisions and not by absorption of ambient radiation and that the observed unimolecular kinetics held in only a limited pressure range. A molecular model of the reaction dynamics was provided, in the late 1920s, by Rice, Ramsberger, and Kessel (RRK) [ 11. These investigators bypassed the very difficult analysis of the nonlinear dynamics of an excited molecule with the assumption that the intramolecular transfer of energy is very rapid on the time scale of the reaction; hence, all memory of the initial state of excitation is lost and the reaction rate depends only on the energy of the molecule. The RRK theory was recast in the 1950s by Marcus [21, who showed it was possible to take into account major elements of the state structure of the molecule imposed by quantum mechanics, while retaining the assumption that intramolecular energy transfer is complete before reaction occurs. The resultant RRKM * For Jens Peder Dahl, on the occasion of his 60th birthday.statistical theory [3] of reaction rate, by any measure, is one of the great successes of chemical physics; it is widely applicable and provides an excellent description of the experimental data in the overwhelming majority of cases. There are, however, some instances in which the statistical theory of unimolecular reaction rate gives very inaccurate predictions. In many of these instances, the failure of the RRKM theory can be traced to a breakdown of the assumption that the rate of intramolecular energy transfer is greater than the rate of reaction.Within the last decade, there has been a renaissance in the development of the classical theory of unimolecular reaction rate. In particular, the seminal work of Davis and Gray [4, 51, for model systems with 2 degrees of freedom, greatly improves our understanding of the dynamics of intramolecular energy flow and of the competition between intramolecular energy flow and the dynamical event that generates the reaction. The Davis-Gray analysis draws heavily on the properties of two-dimensional mappings in phase space, in particular, the properties of the stroboscopic representation generated when the trajectory of the system intersects the Poincar6 surface of section [6, 71. The most important elements of the theory are the calculation of the bottlenecks to intramolecular energy transfer (in a 2 degrees of freedom system, these are the canton) and the identification of the exact separatrix of the system with the transition state for the reaction. It is worth noting

Microcanonical rates, gap times, and phase space dividing surfaces

“…173 The value of the mean lifetime computed by Tang et al at E = −11.5 is close to the mean gap time ͑0.174 ps͒ computed at E = −11.88 eV. 156 Both approximate rate theories applied to the problem by Tang 102,106,107,119,121 is unlikely to lead to an accurate description of decay dynamics at longer times.…”

“…177,178 While the use of dividing surfaces ͑transition states͒ defined in configuration space is quite familiar in the field of reaction rate theory, 93,179 carrying out these steps in phase space, as opposed to configuration space, remains less familiar in practice. 99,121 In the present paper we show how the expression for the microcanonical rate of reaction described above can be evaluated using the phase space approach to reaction dynamics developed in a recent series of papers. 148,149,[153][154][155][156][157][158][159] Moreover, we analyze in detail the properties of the gap time distribution previously obtained for HCN isomerization using the phase space reaction rate theory.…”

“…Methods for defining approximate intramolecular bottlenecks and reactive dividing surfaces have been devised. [115][116][117][118][119][120][121] Although the Arnold web of resonances provides a useful framework for mapping and analyzing evolution of phase points in near-integrable multimode systems, 86,122 so-called Arnold diffusion 86,123 has become a convenient but often ill-defined catchall term employed to describe a variety of possibly distinct phase space transport mechanisms in N Ն 3 DoF systems. 124 The possible role of "Arnold diffusion" in multimode molecular systems has been studied in IVR ͑Refs.…”

Index k saddles and dividing surfaces in phase space with applications to isomerization dynamics

“…In this case the standard phase space picture can be applied to analyze isomerizations, with reactant regions identified in the usual way. There are 2 symmetry related NHIMs, and for each isomerization reaction either a 2-state (RRKM) or 3-state (Gray-Rice 80,81 ) model can be used to describe the isomerization kinetics for each pair of wells.…”

“…In this case there are 4 relevant NHIMs. A standard RRKM model could presumably be be used to analyze the kinetics (flux over saddles), or a 5-state generalized Gray-Rice model can be applied 80,81 . In the latter case, there are 4 reactant regions (wells) with boundaries consising of broken separatrices, and a 5th region lying outside the reactant region.…”