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Title: Dimension reduction for extracting geometrical structure of multidimensional phase space: Application to fast energy exchange in the reaction O({sup 1}D)+N{sub 2}O{yields}NO+NO

Abstract

One of the most fundamental problems in studying general Hamiltonian systems with many degrees of freedom is to extract a low-dimensional subsystem including the essential dynamics. In this paper, a new partial normal form (PNF) method is developed to reduce the number of coupling terms in the Hamiltonian and to simplify the dynamics analyses. The PNF method allows one to decouple many unimportant bath modes as well as the reactive mode from the system by assessing the significance of the coupling terms. The method is applied to the chemical reaction O({sup 1}D)+N{sub 2}O{yields}NO+NO, which was found to exhibit efficient energy exchange between the two NO stretching modes despite the short lifetime of the reaction intermediate [S. Kawai et al., J. Chem. Phys. 124, 184315 (2006)]. Through the analysis of the two-dimensional PNF Hamiltonian subsystem, it is found that the motion of the subsystem preserves the 'normal mode picture' of the symmetric and antisymmetric NO stretching modes despite its high energy. Then the vibrational energy, initially localized in the newly formed NO bond, is transferred to the reactants' NO bond through the beating between the symmetric and antisymmetric stretching modes. The preservation of the normal mode picture and the short periodmore » of the beating explain the fast energy exchange between the two NO bonds. This successful application proves that the PNF method can extract the essential small subspace from many-degrees-of-freedom Hamiltonian systems.« less

Authors:
; ; ; ; ; ;  [1];  [2];  [2];  [2];  [2]
  1. Department of Chemistry, Graduate School of Science, Kyoto University, Kitashirakawa-Oiwakecho, Sakyo-ku, Kyoto 606-8502 (Japan)
  2. (Japan)
Publication Date:
OSTI Identifier:
20982128
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevA.75.022714; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; ATOM-MOLECULE COLLISIONS; COUPLING; DEGREES OF FREEDOM; HAMILTONIANS; LIFETIME; NITROGEN OXIDES; OXYGEN; PHASE SPACE; REACTION INTERMEDIATES; REACTION KINETICS; TWO-DIMENSIONAL CALCULATIONS

Citation Formats

Kawai, Shinnosuke, Fujimura, Yo, Kajimoto, Okitsugu, Yamashita, Takefumi, Li, Chun-Biu, Komatsuzaki, Tamiki, Toda, Mikito, Department of Basic Science, Graduate School of Arts and Sciences, University of Tokyo, Komaba, Tokyo 153-8902, Nonlinear Science Laboratory, Department of Earth and Planetary Sciences, Faculty of Science, Kobe University, Nada, Kobe 657-8501, Nonlinear Science Laboratory, Department of Earth and Planetary Sciences, Faculty of Science, Kobe University, Nada, Kobe 657-8501, Japan and Department of Theoretical Studies, Institute for Molecular Science, Myodaiji, Okazaki 444-8585, and Department of Physics, Faculty of Science, Nara Women's University, Nara 630-8506. Dimension reduction for extracting geometrical structure of multidimensional phase space: Application to fast energy exchange in the reaction O({sup 1}D)+N{sub 2}O{yields}NO+NO. United States: N. p., 2007. Web. doi:10.1103/PHYSREVA.75.022714.
Kawai, Shinnosuke, Fujimura, Yo, Kajimoto, Okitsugu, Yamashita, Takefumi, Li, Chun-Biu, Komatsuzaki, Tamiki, Toda, Mikito, Department of Basic Science, Graduate School of Arts and Sciences, University of Tokyo, Komaba, Tokyo 153-8902, Nonlinear Science Laboratory, Department of Earth and Planetary Sciences, Faculty of Science, Kobe University, Nada, Kobe 657-8501, Nonlinear Science Laboratory, Department of Earth and Planetary Sciences, Faculty of Science, Kobe University, Nada, Kobe 657-8501, Japan and Department of Theoretical Studies, Institute for Molecular Science, Myodaiji, Okazaki 444-8585, & Department of Physics, Faculty of Science, Nara Women's University, Nara 630-8506. Dimension reduction for extracting geometrical structure of multidimensional phase space: Application to fast energy exchange in the reaction O({sup 1}D)+N{sub 2}O{yields}NO+NO. United States. doi:10.1103/PHYSREVA.75.022714.
Kawai, Shinnosuke, Fujimura, Yo, Kajimoto, Okitsugu, Yamashita, Takefumi, Li, Chun-Biu, Komatsuzaki, Tamiki, Toda, Mikito, Department of Basic Science, Graduate School of Arts and Sciences, University of Tokyo, Komaba, Tokyo 153-8902, Nonlinear Science Laboratory, Department of Earth and Planetary Sciences, Faculty of Science, Kobe University, Nada, Kobe 657-8501, Nonlinear Science Laboratory, Department of Earth and Planetary Sciences, Faculty of Science, Kobe University, Nada, Kobe 657-8501, Japan and Department of Theoretical Studies, Institute for Molecular Science, Myodaiji, Okazaki 444-8585, and Department of Physics, Faculty of Science, Nara Women's University, Nara 630-8506. Thu . "Dimension reduction for extracting geometrical structure of multidimensional phase space: Application to fast energy exchange in the reaction O({sup 1}D)+N{sub 2}O{yields}NO+NO". United States. doi:10.1103/PHYSREVA.75.022714.
@article{osti_20982128,
title = {Dimension reduction for extracting geometrical structure of multidimensional phase space: Application to fast energy exchange in the reaction O({sup 1}D)+N{sub 2}O{yields}NO+NO},
author = {Kawai, Shinnosuke and Fujimura, Yo and Kajimoto, Okitsugu and Yamashita, Takefumi and Li, Chun-Biu and Komatsuzaki, Tamiki and Toda, Mikito and Department of Basic Science, Graduate School of Arts and Sciences, University of Tokyo, Komaba, Tokyo 153-8902 and Nonlinear Science Laboratory, Department of Earth and Planetary Sciences, Faculty of Science, Kobe University, Nada, Kobe 657-8501 and Nonlinear Science Laboratory, Department of Earth and Planetary Sciences, Faculty of Science, Kobe University, Nada, Kobe 657-8501, Japan and Department of Theoretical Studies, Institute for Molecular Science, Myodaiji, Okazaki 444-8585 and Department of Physics, Faculty of Science, Nara Women's University, Nara 630-8506},
abstractNote = {One of the most fundamental problems in studying general Hamiltonian systems with many degrees of freedom is to extract a low-dimensional subsystem including the essential dynamics. In this paper, a new partial normal form (PNF) method is developed to reduce the number of coupling terms in the Hamiltonian and to simplify the dynamics analyses. The PNF method allows one to decouple many unimportant bath modes as well as the reactive mode from the system by assessing the significance of the coupling terms. The method is applied to the chemical reaction O({sup 1}D)+N{sub 2}O{yields}NO+NO, which was found to exhibit efficient energy exchange between the two NO stretching modes despite the short lifetime of the reaction intermediate [S. Kawai et al., J. Chem. Phys. 124, 184315 (2006)]. Through the analysis of the two-dimensional PNF Hamiltonian subsystem, it is found that the motion of the subsystem preserves the 'normal mode picture' of the symmetric and antisymmetric NO stretching modes despite its high energy. Then the vibrational energy, initially localized in the newly formed NO bond, is transferred to the reactants' NO bond through the beating between the symmetric and antisymmetric stretching modes. The preservation of the normal mode picture and the short period of the beating explain the fast energy exchange between the two NO bonds. This successful application proves that the PNF method can extract the essential small subspace from many-degrees-of-freedom Hamiltonian systems.},
doi = {10.1103/PHYSREVA.75.022714},
journal = {Physical Review. A},
number = 2,
volume = 75,
place = {United States},
year = {Thu Feb 15 00:00:00 EST 2007},
month = {Thu Feb 15 00:00:00 EST 2007}
}