Related papers: Phase space structures causing the reaction rate d…
Recently the phase space structures governing reaction dynamics in Hamiltonian systems have been identified and algorithms for their explicit construction have been developed. These phase space structures are induced by saddle type…
In this article we present the influence of a Hamiltonian saddle-node bifurcation on the high-dimensional phase space structures that mediate reaction dynamics. To achieve this goal, we identify the phase space invariant manifolds using…
The transformation of a system from one state to another is often mediated by a bottleneck in the system's phase space. In chemistry these bottlenecks are known as \emph{transition states} through which the system has to pass in order to…
A geometrical model which captures the main ingredients governing atom-diatom collinear chemical reactions is proposed. This model is neither near-integrable nor hyperbolic, yet it is amenable to analysis using a combination of the recently…
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…
We examine the phase space structures that govern reaction dynamics in the absence of critical points on the potential energy surface. We show that in the vicinity of hyperbolic invariant tori it is possible to define phase space dividing…
Recent studies have found an unusual way of dissociation in formaldehyde. It can be characterized by a hydrogen atom that separates from the molecule, but instead of dissociating immediately it roams around the molecule for a considerable…
Chemical reactions involve the movement of charges, and this work presents a mathematical model for describing chemical reactions in electrolytes. The model is developed using an energy variational method that aligns with classical…
The quantum normal form approach to quantum transition state theory is used to compute the cumulative reaction probability for collinear exchange reactions. It is shown that for heavy atom systems like the nitrogen exchange reaction the…
Hamiltonian dynamical systems possessing equilibria of ${saddle} \times {centre} \times...\times {centre}$ stability type display \emph{reaction-type dynamics} for energies close to the energy of such equilibria; entrance and exit from…
Material balance equations describe the dynamics of the species in open reaction systems and contain information regarding reaction topology, kinetics and operation mode. For reaction systems, the state variables (the numbers of moles, or…
Quantum reactive scattering calculations for the hydrogen exchange reaction H + H$_2$($v=4$, $j=0$) $\to$ H + H$_2$($v'$, $j'$) and its isotopic analogues are reported for ultracold collision energies. Due to the unique properties…
We consider the existence of invariant manifolds in phase space governing reaction dynamics in situations where there are no saddle points on the potential energy surface in the relevant regions of configuration space. We point out that…
The crossing of a transition state in a multidimensional reactive system is mediated by invariant geometric objects in phase space: An invariant hyper-sphere that represents the transition state itself and invariant hyper-cylinders that…
We investigate the catalytic reactions model used in cell modeling. The reaction kinetic is defined through the energies of different species of molecules following random independent distribution. The related statistical physics model has…
In this article, we review the analytical and numerical approaches for computing the phase space structures in two degrees-of-freedom Hamiltonian systems that arise in chemical reactions. In particular, these phase space structures are the…
We study the effect of changes in the parameters of a two-dimensional potential energy surface on the phase space structures relevant for chemical reaction dynamics. The changes in the potential energy are representative of chemical…
The experimental emission probabilities of complex fragments by low energy compound nuclei and their dependence upon energy and atomic number are compared to the transition state rates. Intermediate-mass-fragment multiplicity distributions…
In this work, we analyze the evolution of the phase-space structures of KCN molecular system as a function of the vibrational energy using Lagrangian descriptors. For low energies, the motion is mostly regular around the absolute minimum of…
Standard models of reaction kinetics in condensed materials rely on the Boltzmann-Gibbs distribution for the population of reactants at the top of the free energy barrier separating them from the products. While energy dissipation and…