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

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.

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.

scholarly journals NORMALIZATION OF CLASSICAL HAMILTONIAN SYSTEMS WITH TWO DEGREES OF FREEDOM

2020 ◽  
pp. 348-355
Author(s):  
Ирина Николаевна Беляева ◽  
Игорь Константинович Кириченко ◽  
Олег Дмитриевич Пташный ◽  
Наталья Николаевна Чеканова ◽  
Татьяна Александровна Ярхо
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Hamiltonian Systems ◽  
Gaussian Curvature ◽  
Degrees Of Freedom ◽  
Energy Surface ◽  
Integrable Case ◽  
Arbitrary Parameter ◽  
Two Degrees Of Freedom ◽  
Negative Gaussian Curvature

В работе исследовано семейство гамильтоновых систем с двумя степенями свободы. Расчетами сечений Пуанкаре показано, что при произвольных значениях параметров функции Гамильтона система является неинтегрируемой и в ней реализуется динамический хаос. Найдено, что для трех наборов параметров рассматриваемая система является интегрируемой, однако в одном интегрируемом случае при этих же значениях параметров на поверхности потенциальной энергии имеется область с отрицательной гауссовой кривизной, в то же время в двух других случаях интегрируемости при соответствующих значениях параметров областей с отрицательной гауссовой кривизной не имеется. Таким образом, наличие областей с отрицательной гауссовой кривизной на поверхности потенциальной энергии не достаточно для развития в системе глобального хаоса. Получена классическая нормальная форма для произвольных значений параметров. The family of the Hamiltonian systems with two degrees of freedom was investigated. The calculations of the Poincaré sections show that with arbitrary values of the parameters of the Hamilton function, the system is non-integrable and dynamic chaos is realized in it. For the three parameter sets, the system in question was found to be integrable, but shows that in one integrable case on the potential energy surface (PES) there are regions with the negative Gaussian curvature. It was found that in one integrable case for the same values of the parameters, the potential energy surface has a region with the negative Gaussian curvature. At the same time, in the other two cases, the domains with negative Gaussian curvature are not integrable for the corresponding values of the parameters. Thus, the presence of regions with negative Gaussian curvature on the potential energy surface is not enough for the development of the global chaos in the system. The classical normal form for arbitrary parameter values is obtained.

An accurate, global, ab initio potential energy surface for the H + 3 molecule

2000 ◽  
Vol 98 (5) ◽  
pp. 261-273 ◽  
Author(s):  
Oleg L. Polyansky, Rita Prosmiti, Wim Kl
Keyword(s):  
Potential Energy ◽  
Potential Energy Surface ◽  
Ab Initio ◽  
Energy Surface
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