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Local modes of silane within the framework of stretching vibrational polyads

  • Molecular Physics and Chemical Physics
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Abstract.

We define stretching relative equilibria (RE) of silane and other similar tetrahedral molecules in terms of the dynamical polyad symmetry which assumes the resonance condition 1:1 between the two stretching vibrational modes ν1 and ν3 of the molecule. Exploiting symmetry and topology arguments and reducing the dimension of the classical mechanical system, we find these RE. One of them, with local symmetry C3v and minimal energy within a polyad, corresponds to the local modes. We give the upper energy limit of the local mode localization within a polyad.

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References

  • J.T. Muckerman, M.S. Child, Chem. Phys. Lett. 153, 477 (1988)

    Article  ADS  Google Scholar 

  • I.N. Kozin, D.A. Sadovskií, B.I. Zhilinskií, Spectrochim. Acta A 61, 2867 (2005)

    Article  Google Scholar 

  • L. Halonen, M.S. Child, Comp. Phys. Communs. 51, 173 (1988)

    Article  ADS  Google Scholar 

  • M.S. Child, Qing-shi Zhu, Chem. Phys. Lett. 184, 41 (1991)

    Article  ADS  Google Scholar 

  • M. Chevalier, A. De Martino, F. Michelot, J. Mol. Spectrosc. 131, 382 (1988)

    Article  ADS  Google Scholar 

  • C. Leroy, F. Michelot, J. Mol. Spectrosc. 151, 71 (1992)

    Article  ADS  Google Scholar 

  • C. Leroy, F. Michelot, V. Boujut, J. Mol. Spectrosc. 173, 333 (1995)

    Article  ADS  Google Scholar 

  • K. Stefanski, E. Pollak, J. Chem. Phys. 87, 1079 (1987)

    Article  ADS  Google Scholar 

  • L. Xiao, M.E. Kellman, J. Chem. Phys. 90, 6086 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  • Z.-M. Lu, M.E. Kellman, J. Chem. Phys. 107, 1 (1997)

    Article  ADS  Google Scholar 

  • A. Weinstein, Invent. Math. 20, 47 (1973)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  • J. Montaldi, R.M. Roberts, I. Stewart, Phil. Trans. R. Soc. Lond. A 325, 237 (1988)

    MATH  ADS  MathSciNet  Google Scholar 

  • J. Montaldi, M. Roberts, I. Stewart, Nonlinearity 3, 695 (1990)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  • J. Montaldi, M. Roberts, I. Stewart, Nonlinearity 3, 730 (1990)

    ADS  Google Scholar 

  • D.A. Sadovskií, N.G. Fulton, J.R. Henderson, J. Tennyson, B.I. Zhilinskií, J. Chem. Phys. 99, 906 (1993)

    Article  ADS  Google Scholar 

  • K. Efstathiou, D.A. Sadovskií, B.I. Zhilinskií, SIAM J. Appl. Dyn. Syst. (SIADS) 3, 261 (2004)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • K. Efstathiou, D.A. Sadovskií, Nonlinearity 17, 415 (2004)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  • Ch. Van Hecke, D.A. Sadovskií, B.I. Zhilinskií, V. Boudon, Eur. Phys. J. D 17, 13 (2001)

    Article  ADS  Google Scholar 

  • G. Dhont, D.A. Sadovskií, B.I. Zhilinskií, V. Boudon, J. Mol. Spectrosc. 201, 95 (2000)

    Article  ADS  Google Scholar 

  • Vl.I. Arnol'd, Matematicheskie Metody Klassicheskoí Mekhaniki (Nauka, Moscow, 1974), in Russian; Mathematical Methods of Classical Mechanics, translated by K. Vogtmann, A. Weinstein, 2nd edn., ser. Graduated Texts in Mathematics 60 (Springer-Verlag, New York, 1989)

  • Vl.I. Arnol'd, V.V. Kozlov, A.I. Neíshtadt, Mathematical Aspects of Classical and Celestial Mechanics , Dynamical Systems III, Encyclopedia of Mathematical Sciences 3 (Springer-Verlag, Berlin, 1988)

  • B.I. Zhilinskií, Chem. Phys. 137, 1 (1989)

    Article  ADS  Google Scholar 

  • D.A. Sadovskií, B.I. Zhilinskií, Phys. Rev. A 48, 1035 (1993)

    Article  ADS  Google Scholar 

  • K. Efstathiou, D.A. Sadovskií, R.H. Cushman, Proc. Roy. Soc. Lond. A 459, 2997 (2003)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  • X.-G. Wang, E.L. Sibert, J. Chem. Phys. 113, 5384 (2000)

    Article  ADS  Google Scholar 

  • J.-P. Champion, M. Loëte, G. Pierre, in Spectroscopy of the Earth's Atmosphere and Interstellar Medium, edited by K.N. Rao, A. Weber (Academic Press, San Diego, 1992)

  • Ch. Wenger, J.-P. Champion, J. Quant. Spectrosc. Radiat. Transfer 59 471 (1998)

    Google Scholar 

  • Spherical Top Data System (STDS): a computer package for simulation of spherical top spectra, available from url http://icb.u-bourgogne.fr/OMR/SMA/SHTDS/STDS.html

  • J.C. Hilico et al., J. Mol. Spectrosc. 168, 455 (1994)

    Article  Google Scholar 

  • J. Williamson, Amer. J. Math. 58, 141 (1936); J. Williamson, Amer. J. Math. 59, 599 (1937)

    Article  MATH  MathSciNet  Google Scholar 

  • L. Halonen, J. Chem. Phys. 106, 831 (1997)

    Article  ADS  Google Scholar 

  • M. Halonen, L. Halonen, H. Burger, W. Jerzembeck, J. Chem. Phys. 108, 9285 (1998)

    Article  ADS  Google Scholar 

  • J.J. Duistermaat, Comm. Pure Appl. Math. 33, 687 (1980)

    MATH  MathSciNet  Google Scholar 

  • R.H. Cushman, L. Bates, Global aspects of classical integrable systems (Birkhauser, Basel, 1997)

  • K. Efstathiou, M. Joyeux, D.A. Sadovskií, Phys. Rev. A 69, 032504 (2004)

    Article  ADS  Google Scholar 

  • R.H. Cushman, H.R. Dullin, A. Giacobbe, D.D. Holm, M. Joyeux, P. Lynch, D.A. Sadovskií, B.I. Zhilinskií, Phys. Rev. Lett. 93, 024302 (2004)

    Article  ADS  Google Scholar 

  • B.P. Winnewisser, M. Winnewisser, I.R. Medvedev, M. Behnke, F.C. De Lucia, S.C. Ross, J. Koput, Phys. Rev. Lett. 95, 243002 (2005)

    Article  ADS  Google Scholar 

  • Ch. Van Hecke, D.A. Sadovskií, B.I. Zhilinskií, Eur. Phys. J. D 7, 199 (1999)

    Article  ADS  Google Scholar 

  • E.B. Wilson Jr, J.C. Decius, P.C. Cross, Molecular Vibrations (McGraw-Hill, New York, 1955)

  • G. Amat, H.H. Nielsen, G. Tarrago, Rotation-vibrations of polyatomic molecules (Dekker, New York, 1971)

  • M.R. Aliev, J.K.G. Watson, Higher-order effects in the vibration-rotation spectra of semirigid molecules , in Molecular Spectroscopy: Modern Research, edited by K.N. Rao (Academic Press, New York, 1985), Vol. 3, p. 1.

  • T. Lukka, L. Halonen, J. Chem. Phys. 101, 8380 (1994)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Institut Carnot de Bourgogne, UMR 5209 CNRS-Université de Bourgogne, 9 avenue Alain Savary, B.P. 47870, 21078, Dijon, France

    H. Crogman & V. Boudon

  2. Université du Littoral, Département de physique, 59140, Dunkerque, France

    D. A. Sadovskií

Authors
  1. H. Crogman
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  2. V. Boudon
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  3. D. A. Sadovskií
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Correspondence to D. A. Sadovskií.

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Crogman, H., Boudon, V. & Sadovskií, D. Local modes of silane within the framework of stretching vibrational polyads. Eur. Phys. J. D 42, 61–72 (2007). https://doi.org/10.1140/epjd/e2007-00011-3

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  • DOI: https://doi.org/10.1140/epjd/e2007-00011-3

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