We explore both classical and quantum dynamics of a model potential exhibiting a caldera: that is, a shallow potential well with two pairs of symmetry related index one saddles associated with entrance/exit channels. Classical trajectory simulations at several different energies confirm the existence of the "dynamical matching" phenomenon originally proposed by Carpenter, where the momentum direction associated with an incoming trajectory initiated at a high energy saddle point determines to a considerable extent the outcome of the reaction (passage through the diametrically opposing exit channel). By studying a "stretched" version of the caldera model, we have uncovered a generalized dynamical matching: bundles of trajectories can reflect off a hard potential wall so as to end up exiting predominantly through the transition state opposite the reflection point. We also investigate the effects of dissipation on the classical dynamics. In addition to classical trajectory studies, we examine the dynamics of quantum wave packets on the caldera potential (stretched and unstretched). These computations reveal a quantum mechanical analogue of the "dynamical matching" phenomenon, where the initial expectation value of the momentum direction for the wave packet determines the exit channel through which most of the probability density passes to product.
In this review we discuss the recently described roaming mechanism for chemical reactions from the point of view of nonlinear dynamical systems in phase space. The recognition of the roaming phenomenon shows the need for further developments in our fundamental understanding of basic reaction dynamics, as is made clear by considering some questions that cut across most studies of roaming: Is the dynamics statistical? Can transition state theory be applied to estimate roaming reaction rates? What role do saddle points on the potential energy surface play in explaining the behavior of roaming trajectories? How do we construct a dividing surface that is appropriate for describing the transformation from reactants to products for roaming trajectories? How should we define the roaming region? We show that the phase space perspective on reaction dynamics provides the setting in which these questions can be properly framed and answered. We illustrate these ideas by considering photodissociation of formaldehyde. The phase-space formulation allows an unambiguous description of all possible reactive events, which also allows us to uncover the phase space mechanism that explains which trajectories roam, as opposed to evolving toward a different reactive event.
The dynamics of the light initiated OH-overtone induced elimination reactions CH(2)FOH.(H(2)O)(n) + hnu--> HF + CH(2)O + n(H(2)O), n = 1-3, are studied using classical trajectory simulations where the ab initio potential energy surface is computed "on-the-fly". Hydrogen bonding to the water is found to lower the barrier to reaction by over 20 kcal mol(-1) and modifies the mechanism to a concerted multiple H-atom transfer process. The reaction process is found to occur on a rapid timescale, <100 fs, and involves the hydronium ion as an intermediate. An essential aspect of dynamics is the successful competition of reaction with energy dissipation through water evaporation from the cluster.
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.
We present a model of the surface kinetics of the dehydrogenation reaction of methanol on the Pd(111), Pt(111), and Ni(111) metal surfaces. The mechanism consists of 10 reversible dehydrogenation reactions that lead to the final products of CO and H2. The rate coefficients for each step are calculated using ab initio transition state theory that employs a new approach to obtain the symmetry factors. The potential energies and frequencies of the reagents and transition states are computed using plane wave DFT with the PW91 exchange correlation functional. The mechanism is investigated for low coverages using a global sensitivity analysis that monitors the response of a target function of the kinetics to the value of the rate coefficients. On Pd(111) and Ni(111), the reaction COH → CO + H is found to be rate limiting, and overall rates are highly dependent upon the decomposition time of the COH intermediate. Reactions at branches in the reaction network are also particularly important in the kinetics. A stochastic atom-following approach to pathway analysis is used to elucidate both the pathway probabilities in the kinetics and the dependence of the pathways on the values of the key rate coefficients of the mechanisms. On Pd(111) and Ni(111) there exists significant competition between the pathway containing the slow step and faster pathways that bypass the slow step. A discussion is given of the dependence of the model target’s probability density function on the chemical pathways.
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