Deconstructing field-induced ketene isomerization through Lagrangian descriptors

2016 ◽  
Vol 18 (5) ◽  
pp. 4008-4018 ◽  
Author(s):  
Galen T. Craven ◽  
Rigoberto Hernandez
Keyword(s):  
Phase Space ◽  
Potential Energy ◽  
Potential Energy Surface ◽  
Energy Surface ◽  
Reaction Path ◽  
State Transitions ◽  
Lagrangian Descriptors

Phase space contours (shown in color) constructed using the method of Lagrangian descriptors resolve the separatrices governing state transitions on the reaction-path potential energy surface (shown in white) for field-induced ketene isomerization.

scholarly journals Reaction Path Description and Internal-Mode Dynamics of Molecular Rearrangement in HO2

1991 ◽  
Vol 11 (3-4) ◽  
pp. 199-203 ◽  
Author(s):  
Ch. Zuhrt ◽  
L. Zülicke ◽  
F. Schneider ◽  
X. Chapuisat
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Surface Topography ◽  
Exchange Reaction ◽  
Energy Surface ◽  
Reaction Path ◽  
Theoretical Models ◽  
Internal Mode ◽  
Molecular Rearrangement

After brief general remarks and definitions for the reaction path concept in view of formulating physically transparent and computationally feasible theoretical models, the HO2 system is studied for both the bimolecular exchange reaction and the intramolecular H transfer (isomerization). The analysis includes potential energy surface topography, reaction profiles and internal-mode dynamics.

scholarly journals Phase Space Structure and Transport in a Caldera Potential Energy Surface

2018 ◽  
Vol 28 (13) ◽  
pp. 1830042 ◽  
Author(s):  
Matthaios Katsanikas ◽  
Stephen Wiggins
Keyword(s):  
Phase Space ◽  
Potential Energy ◽  
Potential Energy Surface ◽  
Periodic Orbits ◽  
Central Region ◽  
Invariant Manifolds ◽  
Energy Surface ◽  
Unstable Periodic Orbits ◽  
Phase Space Transport ◽  
The Family

We study phase space transport in a 2D caldera potential energy surface (PES) using techniques from nonlinear dynamics. The caldera PES is characterized by a flat region or shallow minimum at its center surrounded by potential walls and multiple symmetry related index one saddle points that allow entrance and exit from this intermediate region. We have discovered four qualitatively distinct cases of the structure of the phase space that govern phase space transport. These cases are categorized according to the total energy and the stability of the periodic orbits associated with the family of the central minimum, the bifurcations of the same family, and the energetic accessibility of the index one saddles. In each case, we have computed the invariant manifolds of the unstable periodic orbits of the central region of the potential, and the invariant manifolds of the unstable periodic orbits of the families of periodic orbits associated with the index one saddles. The periodic orbits of the central region are, for the first case, the unstable periodic orbits with period 10 that are outside the stable region of the stable periodic orbits of the family of the central minimum. In addition, the periodic orbits of the central region are, for the second and third cases, the unstable periodic orbits of the family of the central minimum and for the fourth case the unstable periodic orbits with period 2 of a period-doubling bifurcation of the family of the central minimum. We have found that there are three distinct mechanisms determined by the invariant manifold structure of the unstable periodic orbits that govern the phase space transport. The first mechanism explains the nature of the entrance of the trajectories from the region of the low energy saddles into the caldera and how they may become trapped in the central region of the potential. The second mechanism describes the trapping of the trajectories that begin from the central region of the caldera, their transport to the regions of the saddles, and the nature of their exit from the caldera. The third mechanism describes the phase space geometry responsible for the dynamical matching of trajectories originally proposed by Carpenter and described in [Collins et al., 2014] for the two-dimensional caldera PES that we consider.

REDUCED GRADIENT METHODS AND THEIR RELATION TO REACTION PATHS

2003 ◽  
Vol 02 (03) ◽  
pp. 385-417 ◽  
Author(s):  
WOLFGANG QUAPP
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Energy Surface ◽  
Reaction Path ◽  
Gradient Methods ◽  
Theoretical Chemistry ◽  
Future Research ◽  
Branching Points ◽  
Reduced Gradient ◽  
Reduced Gradient Methods

The reaction path is an important concept in theoretical chemistry. We discuss different definitions, their merits as well as their drawbacks: IRC (steepest descent from saddle), reduced gradient following (RGF), gradient extremals, and some others. Many properties and problems are explained by two-dimensional figures. This paper is both a review and a pointer to future research. The branching points of RGF curves are valley-ridge inflection (VRI) points of the potential energy surface. These points may serve as indicators for bifurcations of the reaction path. The VRI points are calculated with the help of Branin's method. All the important features of the potential energy surface are independent of the coordinate system. Besides the theoretical definitions, we also discuss the numerical use of the methods.

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