ion reactions. Theoretical work correlating the CH bond strengths in hydrocarbons with their H-abstraction rate coefficient by OH radicals showed 361,362 that many terpenoids have weakly bonded H-atoms, in particular H-atoms whose abstraction leads to allylor superallyl-resonance stablized alkyl product radicals. At the same time, other H-atoms were found to be deactivated 362 towards Habstraction due to unexpected lack of stabilisation of the product radical. A particularly important example for bicyclic terpenes are the H-atoms on the bridgeheads connecting two fused ring systems where geometric constraints prevent rehybridization from an sp 3 to an sp 2 orbital arrangement in the product radical. The correlations observed between the bond strength and H-abstraction rate then led to the development of predictive correlations, dependent on the type of H-atom abstracted, that allow facile prediction of the abstraction rate, and improve the agreement between SARs and experiment for specific compounds. 362 These SARs have since been used extensively in the construction of complete degradation schemes for terpenoids, such as -pinene, 363–367 -pinene 368 or pinonaldehyde, 369 with often excellent agreement with available environmental chamber data. 5. Peroxy Radical Chemistry 5.1. Peroxy Radicals in Atmospheric Chemistry and Combustion Peroxy radicals play a central role in the oxidation of organic compounds in the troposphere. Carbon centered radicals, R  , formed by H-abstraction by OH or OH addition to a double bond, react

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Theoretical Chemical Kinetics in Tropospheric Chemistry: Methodologies and Applications

We review a theory for coupled many-nonlinear oscillator systems that describes quantum ergodicity and energy flow in molecules. The theory exploits the isomorphism between quantum energy flow in Fock space, that is, vibrational state space, and single-particle quantum transport in disordered solid-state systems. The quantum ergodicity transition in molecules is thereby analogous to the Anderson transition in disordered solids. The theory reviewed here, local random matrix theory (LRMT), describes the nature of the quantum ergodicity transition, statistical properties of vibrational eigenstates, and quantum energy flow through the vibrational states of molecules. Predictions of LRMT have been observed in computational studies of coupled nonlinear oscillator systems, which are summarized here. We also review applications of LRMT to molecular spectroscopy and chemical reaction rate theory, including adoption of LRMT in theories that predict rates of conformational change of molecules taking place at energie...

Quantum ergodicity and energy flow in molecules

Novel experimental techniques and computational methods have provided new insight into the behavior of reactive intermediates in solution. The results of these studies show that some of the earlier ideas about how reactive intermediates ought to behave in solution were incomplete or even incorrect. This Perspective summarizes the new experimental and computational methods and draws attention to the shortcomings that their application has brought to light in previous models. Key areas needing further research are highlighted.

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The study of reactive intermediates in condensed phases

The phenomenon of roaming in chemical reactions has now become both commonly observed in experiment and extensively supported by theory and simulations. Roaming occurs in highly-excited molecules when the trajectories of atomic motion often bypass the minimum energy pathway and produce reaction in unexpected ways from unlikely geometries. The prototypical example is the unimolecular dissociation of formaldehyde (H2CO), in which the "normal" reaction proceeds through a tight transition state to yield H2 + CO but for which a high fraction of dissociations take place via a "roaming" mechanism in which one H atom moves far from the HCO, almost to dissociation, and then returns to abstract the second H atom. We review below the theories and simulations that have recently been developed to address and understand this new reaction phenomenon.

Theories and simulations of roaming.

The time-dependent geometrical separatrices governing state transitions in field-induced ketene isomerization are constructed using the method of Lagrangian descriptors. We obtain the stable and unstable manifolds of time-varying transition states as dynamic phase space objects governing configurational changes when the ketene molecule is subjected to an oscillating electric field. The dynamics of the isomerization reaction are modeled through classical trajectory studies on the Gezelter–Miller potential energy surface and an approximate dipole moment model which is coupled to a time-dependent electric field. We obtain a representation of the reaction geometry, over varying field strengths and oscillation frequencies, by partitioning an initial phase space into basins labeled according to which product state is reached at a given time. The borders between these basins are in agreement with those obtained using Lagrangian descriptors, even in regimes exhibiting chaotic dynamics. Major outcomes of this work are: validation and extension of a transition state theory framework built from Lagrangian descriptors, elaboration of the applicability for this theory to periodically- and aperiodically-driven molecular systems, and prediction of regimes in which isomerization of ketene and its derivatives may be controlled using an external field.

Deconstructing field-induced ketene isomerization through Lagrangian descriptors.

A model Hamiltonian for the reaction CH 4+→ CH 3+ + H, parametrized to exhibit either early or late inner transition states, is employed to investigate the dynamical characteristics of the roaming mechanism. Tight/loose transition states and conventional/roaming reaction pathways are identified in terms of time-invariant objects in phase space. These are dividing surfaces associated with normally hyperbolic invariant manifolds (NHIMs). For systems with two degrees of freedom NHIMS are unstable periodic orbits which, in conjunction with their stable and unstable manifolds, unambiguously define the (locally) non-recrossing dividing surfaces assumed in statistical theories of reaction rates. By constructing periodic orbit continuation/bifurcation diagrams for two values of the potential function parameter corresponding to late and early transition states, respectively, and using the total energy as another parameter, we dynamically assign different regions of phase space to reactants and products as well as ...

Roaming dynamics in ion-molecule reactions: Phase space reaction pathways and geometrical interpretation

We re-examine the prototypical roaming reaction—hydrogen atom roaming in formaldehyde decomposition—from a phase space perspective. Specifically, we address the question “why do trajectories roam, rather than dissociate through the radical channel?” We describe and compute the phase space structures that define and control all possible reactive events for this reaction, as well as provide a dynamically exact description of the roaming region in phase space. Using these phase space constructs, we show that in the roaming region, there is an unstable periodic orbit whose stable and unstable manifolds define a conduit that both encompasses all roaming trajectories exiting the formaldehyde well and shepherds them toward the H2···CO well.

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Phase Space Structures Explain Hydrogen Atom Roaming in Formaldehyde Decomposition.

We investigate the fragmentation dynamics of an atomic chain under tensile stress. We have classified the location, stability type (indices), and energy of all equilibria for the general n-particle chain, and have highlighted the importance of saddle points with index >1. We show that for an n = 2-particle chain under tensile stress the index 2 saddle plays a central role in organizing the dynamics. We apply normal form theory to analyze phase space structure and dynamics in a neighborhood of the index 2 saddle. We define a phase dividing surface (DS) that enables us to classify trajectories passing through a neighborhood of the saddle point using the values of the integrals associated with the normal form. We also generalize our definition of the dividing surface and define an extended dividing surface (EDS), which is used to sample and classify all trajectories that pass through a phase space neighborhood of the index 2 saddle at total energies less than that of the saddle. Classical trajectory simulations are used to study fragmentation patterns for the n = 2 chain under tension. That is, we investigate the relative probability for breaking one bond versus concerted fission of several (two, in this case) bonds. Initial conditions for trajectories are obtained by sampling the EDS at constant energy. We sample trajectories at fixed energies both above and below the energy of the saddle. The fate of trajectories (single versus multiple bond breakage) is explored as a function of the location of the initial condition on the EDS, and a connection made to the work of Chesnavich on collision-induced dissociation. A significant finding is that we can readily identify trajectories that exhibit bond healing. Such trajectories pass outside the nominal (index 1) transition state for single bond dissociation, but return to the potential well region, possibly several times, before ultimately dissociating.

Bond breaking in a Morse chain under tension: Fragmentation patterns, higher index saddles, and bond healing

A model Hamiltonian for the reaction CH$_4^+ \rightarrow$ CH$_3^+$ + H, parametrized to exhibit either early or late inner transition states, is employed to investigate the dynamical characteristics of the roaming mechanism. Tight/loose transition states and conventional/roaming reaction pathways are identified in terms of time-invariant objects in phase space. These are dividing surfaces associated with normally hyperbolic invariant manifolds (NHIMs). For systems with two degrees of freedom NHIMS are unstable periodic orbits which, in conjunction with their stable and unstable manifolds, unambiguously define the (locally) non-recrossing dividing surfaces assumed in statistical theories of reaction rates. By constructing periodic orbit continuation/bifurcation diagrams for two values of the potential function parameter corresponding to late and early transition states, respectively, and using the total energy as another parameter, we dynamically assign different regions of phase space to reactants and products as well as to conventional and roaming reaction pathways. The classical dynamics of the system are investigated by uniformly sampling trajectory initial conditions on the dividing surfaces. Trajectories are classified into four different categories: direct reactive and non reactive trajectories,which lead to the formation of molecular and radical products respectively, and roaming reactive and non reactive orbiting trajectories, which represent alternative pathways to form molecular and radical products. By analysing gap time distributions at several energies we demonstrate that the phase space structure of the roaming region, which is strongly influenced by non-linear resonances between the two degrees of freedom, results in nonexponential (nonstatistical) decay.

Peter R C Collins

Papers

Roaming dynamics in ion-molecule reactions: Phase space reaction pathways and geometrical interpretation

Phase Space Structures Explain Hydrogen Atom Roaming in Formaldehyde Decomposition.

Bond breaking in a Morse chain under tension: Fragmentation patterns, higher index saddles, and bond healing

Roaming dynamics in ion-molecule reactions: phase space reaction pathways and geometrical interpretation