scholarly journals Bifurcation of Dividing Surfaces Constructed from a Pitchfork Bifurcation of Periodic Orbits in a Symmetric Potential Energy Surface with a Post-Transition-State Bifurcation

2021 ◽  
Vol 31 (14) ◽  
Author(s):  
M. Katsanikas ◽  
M. Agaoglou ◽  
S. Wiggins
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Periodic Orbits ◽  
Lower Energy ◽  
Degrees Of Freedom ◽  
Energy Surface ◽  
Pitchfork Bifurcation ◽  
High Energy ◽  
Symmetric Potential ◽  
The Family

In this work, we analyze the bifurcation of dividing surfaces that occurs as a result of a pitchfork bifurcation of periodic orbits in a two degrees of freedom Hamiltonian System. The potential energy surface of the system that we consider has four critical points: two minima, a high energy saddle and a lower energy saddle separating two wells (minima). In this paper, we study the structure, the range, and the minimum and maximum extent of the periodic orbit dividing surfaces of the family of periodic orbits of the lower saddle as a function of the total energy.

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.

Triangulation of the Lowest Energy Sheet for Jahn-Teller Potential Energy Surfaces

1986 ◽  
Vol 41 (3) ◽  
pp. 532-534
Author(s):  
Ariel Fernández
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Potential Energy Surfaces ◽  
Lower Energy ◽  
Energy Surface ◽  
Teller Effect ◽  
Jahn Teller ◽  
Jahn Teller Effect ◽  
Energy Surfaces

The topology of the lower energy sheet for the Potential Energy Surface corresponding to the dynamic Jahn-Teller effect is obtained by means of homological techniques.

Connection between the Upper and Lower Energy Regions of the Potential Energy Surface of the Ground Electronic State of the HSO2 System

2012 ◽  
Vol 116 (29) ◽  
pp. 7677-7685 ◽  
Author(s):  
Gabriel N. Freitas ◽  
Juan D. Garrido ◽  
Maikel Y. Ballester ◽  
Marco Antonio Chaer Nascimento
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Electronic State ◽  
Lower Energy ◽  
Energy Surface ◽  
Ground Electronic State

Water models based on a single potential energy surface and different molecular degrees of freedom

2005 ◽  
Vol 122 (22) ◽  
pp. 224509 ◽  
Author(s):  
Humberto Saint-Martin ◽  
Jorge Hernández-Cobos ◽  
Iván Ortega-Blake
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Degrees Of Freedom ◽  
Energy Surface ◽  
Water Models ◽  
Single Potential

Potential energy surface for high-energy N + N2 collisions

2021 ◽  
Author(s):  
Zoltán Varga ◽  
Donald G. Truhlar
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Energy Surface ◽  
Molecular Simulations ◽  
High Energy ◽  
Molecular Collisions ◽  
Physical Insight ◽  
Insight Into

Potential energy surface calculations yield physical insight into the structure of intermediates and the dynamics of molecular collisions, and they are the first step toward molecular simulations that provide physical...

Phase transition at N = 92 in 158Dy

2016 ◽  
Vol 25 (10) ◽  
pp. 1650076 ◽  
Author(s):  
J. B. Gupta
Keyword(s):  
Phase Transition ◽  
Potential Energy ◽  
Potential Energy Surface ◽  
Single Particle ◽  
Degrees Of Freedom ◽  
Energy Surface ◽  
Transition Rates ◽  
Microscopic Approach ◽  
Shape Phase Transition

Beyond the shape phase transition from the spherical vibrator to the deformed rotor regime at [Formula: see text], the interplay of [Formula: see text]- and [Formula: see text]-degrees of freedom becomes important, which affects the relative positions of the [Formula: see text]- and [Formula: see text]-bands. In the microscopic approach of the dynamic pairing plus quadrupole model, a correlation of the strength of the quadrupole force and the formation of the [Formula: see text]- and [Formula: see text]-bands in [Formula: see text]Dy is described. The role of the potential energy surface is illustrated. The [Formula: see text] transition rates in the lower three [Formula: see text]-bands and the multi-phonon bands with [Formula: see text] and [Formula: see text] are well reproduced. The absolute [Formula: see text] [Formula: see text] serves as a good measure of the quadrupole strength. The role of the single particle Nilsson orbits is also described.

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