Saddle-node bifurcations in the LiNC/LiCN molecular system: Classical aspects and quantum manifestations

Borondo, F.; Zembekov, A. A.; Benito, R. M.

doi:10.1063/1.472351

Cited by 40 publications

(27 citation statements)

References 79 publications

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“…This represents an additional source of uncertainity in the RRKM calculations performed here, although full derivation of the molecular energy levels is a complex issue. 29,30 4.4. General Comments.…”

Section: + No Ab Initio Resultsmentioning

confidence: 99%

The Gas-Phase Kinetics of Reactions of Alkali Metal Atoms with Nitric Oxide

et al. 1999

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Time-resolved atomic resonance absorption spectroscopy was employed, with flash-photolysis generation of atomic potassium and sodium at 734 K, to investigate the kinetics of K + NO + Ar and Na + NO + Ar. The low-pressure limit recombination rate constants are (1.0 ( 0.2) × 10 -31 and (1.9 ( 0.5) × 10 -32 cm 6 molecule -2 s -1 , respectively. Mainly ionic, triplet state adducts are predicted. RRKM modeling yielded K-NO and Na-NO bond dissociation enthalpies of 104 and 66 kJ mol -1 , which compare well with UQCISD(T)/6-311+ G(2d) ab initio values of 81 and 68 kJ mol -1 , respectively. For Li + NO +Ar, the predicted binding energy is 134 kJ mol -1 , which yields a predicted rate constant of 1.4 × 10 -31 cm 6 molecule -2 s -1 .

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Section: + No Ab Initio Resultsmentioning

confidence: 99%

The Gas-Phase Kinetics of Reactions of Alkali Metal Atoms with Nitric Oxide

et al. 1999

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“…However, SN bifurcations are also found above the barriers of isomerization/dissociation [Farantos, 1996]. There is evidence that they result from the unstable periodic orbits originated from the saddle point and the Newhouse wild hyperbolic set [Newhouse, 1979;Borondo et al, 1996;Contopoulos et al, 1996]. These periodic orbits seem to have no connection to any main family and they appear abruptly like the cubic polynomial type.…”

Section: Application To the 1 B 2 -State Of Ozonementioning

confidence: 99%

REACTION PATHS AND ELEMENTARY BIFURCATIONS TRACKS: THE DIABATIC ¹B₂-STATE OF OZONE

Farantos

Zhu

et al. 2006

Int. J. Bifurcation Chaos

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Bifurcations of equilibrium points and periodic orbits are common in nonlinear dynamical systems when some parameters change. The vibrational motions of a molecule are nonlinear, and the bifurcation phenomena are seen in spectroscopy and chemical reactions. Bifurcations may lead to energy localization in specific bonds, and thus, they have important consequences for elementary chemical reactions, such as isomerization and dissociation/association. In this article we investigate how elementary bifurcations, such as saddle-node and pitchfork bifurcations, appear in small molecules and show their manifestations in the quantum mechanical frequencies and in the topology of wave functions. We present the results of classical and quantum mechanical calculations on a new (diabatic) potential energy surface of ozone for the 1 B 2 state. This excited electronic state of ozone is pertinent for the absorption of the harmful UV radiation from the sun. We demonstrate that regular localized overtone states, which extend from the bottom of the well up to the dissociation or isomerization barrier, are associated with families of periodic orbits emanated from elementary bifurcations.

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“…Many authors [37][38][39][40][41] compared the quantum and classical dynamics to understand the vibrational wave functions and proved the benefit of the classical analyses. Although the periodic orbit analysis is one of the most common and powerful tool, we adopted the Poincarè SOS, taking advantage of the 2D model, in order to characterize 2D trajectories.…”

Section: Two-dimensional Analysesmentioning

confidence: 99%

Regularity in highly excited vibrational dynamics of NOCl (X 1A′): Quantum mechanical calculations on a new potential energy surface

Yamashita

Kato

2003

The Journal of Chemical Physics

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Calculation of the structure, potential energy surface, vibrational dynamics, and electric dipole properties for the Xe:HI van der Waals complex Ab initio potential energy surfaces, total absorption cross sections, and product quantum state distributions for the low-lying electronic states of N 2 O A new potential energy surface ͑PES͒ of NOCl in the ground electronic state (X 1 AЈ) is constructed based on multireference configuration interaction calculations. Almost all the vibrational eigenstates up to the dissociation threshold are obtained using filter diagonalization method with the present PES. The vibrational excitation energies are in good agreement with the experimental values. The nearest neighbor level spacing distribution shows that the vibrational structure is regarded as regular up to the dissociation threshold. The distribution of radiative coupling elements also supports the regularity. It is further found out that the NO stretching mode is strongly decoupled from the other modes. Taking advantage of this result, the two-dimensional ͑2D͒ analyses are carried out with the NO distance fixed. The 2D wave functions have clear nodal patterns even near the dissociation threshold, indicating that the 2D quantum dynamics is regular as in the three-dimensional case. Comparing the 2D classical dynamics with the 2D wave functions, quasiperiodic trajectories closely related to the corresponding quantum dynamics are extracted. Although it is generally believed that the phase space becomes fully chaotic with approaching to the dissociation threshold, two stable islands of regular motion still remain even at this energy region.

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Saddle-node bifurcations in the LiNC/LiCN molecular system: Classical aspects and quantum manifestations

Cited by 40 publications

References 79 publications

The Gas-Phase Kinetics of Reactions of Alkali Metal Atoms with Nitric Oxide

The Gas-Phase Kinetics of Reactions of Alkali Metal Atoms with Nitric Oxide

REACTION PATHS AND ELEMENTARY BIFURCATIONS TRACKS: THE DIABATIC ¹B₂-STATE OF OZONE

Regularity in highly excited vibrational dynamics of NOCl (X 1A′): Quantum mechanical calculations on a new potential energy surface

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Saddle-node bifurcations in the LiNC/LiCN molecular system: Classical aspects and quantum manifestations

Cited by 40 publications

References 79 publications

The Gas-Phase Kinetics of Reactions of Alkali Metal Atoms with Nitric Oxide

The Gas-Phase Kinetics of Reactions of Alkali Metal Atoms with Nitric Oxide

REACTION PATHS AND ELEMENTARY BIFURCATIONS TRACKS: THE DIABATIC 1B2-STATE OF OZONE

Regularity in highly excited vibrational dynamics of NOCl (X 1A′): Quantum mechanical calculations on a new potential energy surface

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REACTION PATHS AND ELEMENTARY BIFURCATIONS TRACKS: THE DIABATIC ¹B₂-STATE OF OZONE