Related papers: Obtaining time-dependent multi-dimensional dividin…
Transition state theory formally provides a simplifying approach for determining chemical reaction rates and pathways. Given an underlying potential energy surface for a reactive system, one can determine the dividing surface in phase space…
In chemical or physical reaction dynamics, it is essential to distinguish precisely between reactants and products for all time. This task is especially demanding in time-dependent or driven systems because therein the dividing surface (DS)…
Chemical reactions subjected to time-varying external forces cannot generally be described through a fixed bottleneck near the transition state barrier or dividing surface. A naive dividing surface attached to the instantaneous, but moving,…
Transition State Theory is a central cornerstone in reaction dynamics. Its key step is the identification of a dividing surface that is crossed only once by all reactive trajectories. This assumption is often badly violated, especially when…
Classical transition state theory (TST) is the cornerstone of reaction rate theory. It postulates a partition of phase space into reactant and product regions, which are separated by a dividing surface that reactive trajectories must cross.…
The accuracy of rate constants calculated using transition state theory depends crucially on the correct identification of a recrossing--free dividing surface. We show here that it is possible to define such optimal dividing surface in…
When a chemical reaction is driven by an external field, the transition state that the system must pass through as it changes from reactant to product -for example, an energy barrier- becomes time-dependent. We show that for periodic…
The framework of transition state theory (TST) provides a powerful way for analyzing the dynamics of physical and chemical reactions. While TST has already been successfully used to obtain reaction rates for systems with a single…
Chemical reaction rates must increasingly be determined in systems that evolve under the control of external stimuli. In these systems, when a reactant population is induced to cross an energy barrier through forcing from a temporally…
Transition State Theory overestimates reaction rates in solution because conventional dividing surfaces between reagents and products are crossed many times by the same reactive trajectory. We describe a recipe for constructing a…
A time-dependent no-recrossing dividing surface is shown to lead to a new criterion for identifying reactive trajectories well before they are evolved to infinite time. Numerical dynamics simulations of a dissipative anharmonic…
In this paper we develop new techniques for revealing geometrical structures in phase space that are valid for aperiodically time dependent dynamical systems, which we refer to as Lagrangian descriptors. These quantities are based on the…
In this paper we apply the method of Lagrangian descriptors to explore the geometrical structures in phase space that govern the dynamics of dissipative systems. We demonstrate through many classical examples taken from the nonlinear…
We develop the geometrical, analytical, and computational framework for reactive island theory for three degrees-of-freedom time-independent Hamiltonian systems. In this setting, the dynamics occurs in a 5-dimensional energy surface in…
Phase space structures such as dividing surfaces, normally hyperbolic invariant manifolds, their stable and unstable manifolds have been an integral part of computing quantitative results such as transition fraction, stability erosion in…
Heterogenous reactions typically consist of multiple elementary steps and their rate coefficients are of fundamental importance in elucidating the mechanisms and micro-kinetics of these processes. Transition-state theory (TST) for…
We formulate equations of time-dependent density functional theory (TDDFT) in the co-moving Lagrangian reference frame. The main advantage of the Lagrangian description of many-body dynamics is that in the co-moving frame the current…
The usual formulations of time-dependent mechanics start from a given splitting $Y=R\times M$ of the coordinate bundle $Y\to R$. From physical viewpoint, this splitting means that a reference frame has been chosen. Obviously, such a…
The time-dependent barrier passage of an anomalous damping system is studied via the generalized Langevin equation (GLE) with non-Ohmic memory damping friction tensor and corresponding thermal colored noise tensor describing a particle…
In this paper, we apply Lagrangian descriptors to study the invariant manifolds that emerge from the top of two barriers existing in the LiCN<->LiNC isomerization reaction. We demonstrate that the integration times must be large enough…