Skip to main content

Vibrational Predissociation: Quasiclassical Tunneling Through Classical Chaotic Sea

  • Conference paper
Theory of Chemical Reaction Dynamics

Part of the book series: NATO Science Series II: Mathematics, Physics and Chemistry ((NAII,volume 145))

  • 1233 Accesses

Abstract

Vibrational predissociation (VP) of van der Waals complexes occurs via an isolated resonance. An isolated resonance possesses no classical counterpart. And yet, classical calculations of the decay yield the rates that are sometimes not too different from the quantum rates. We resolve this puzzle by addressing the following points: i) Quantum theory of VP: accurate and perturbative approaches; ii) Quasiclassical theory of VP: Landau method and recovery of VP transition probabilities from the correspondence principle transition probabilities; iii) Classical theory of VP: diffusional description of long-time chaotic dynamics.

We calculate the ratio of the classical to quantum VP rates, determine the conditions when the rates of quantum dynamical tunneling is close to the classical diffusional rates across the chaotic sea and establish a classical counterpart of quantum perturbation approach.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baer, T. and W. L. Hase, (1996) Unimolecular Reaction Dynamics, Oxford University Press, Oxford.

    Google Scholar 

  2. Landau L. D. and Lifshitz, E. M., (1977) Quantum Mechanics, Pergamon Press, Oxford.

    Google Scholar 

  3. Moiseyev, N. (1998) Quantum theory of resonances: calculating energies, widths and cross-sections by complex scaling, Phys. Rep., 302, 211–293.

    Article  CAS  Google Scholar 

  4. Nikitin, E.E., Noda, C. and Zare, R.N. (1993) On the quasiclassical calculation of fundamental and overtone intensities, J. Chem. Phys., 98, 47–59.

    Article  Google Scholar 

  5. Karni, Y., and Nikitin, E.E., (1994) Recovery of the Landau matrix elements from the classical Fourier components:one-dimensional dissociating oscillator, (1994) J.Chem. Phys., 100, 2027–2033.

    CAS  Google Scholar 

  6. Nikitin, E.E. and Pitaevskii, L. (1994) Calculation of the Landau quasi-classical exponent from the Fourier components of classical functions, Phys.Rev., A49, 695–703.

    Google Scholar 

  7. Noid, D.W., Gray, S.K. and Rice S.A., (1986) Fractal behavior in classical collisional energy transfer J.Chem.Phys. 84, 2649–2652.

    Article  CAS  Google Scholar 

  8. Gray, S.K., Rice, S.A. and Noid, D.W. (1986) The classical mechanics of vibrational predissociation: A model based study of phase space structure and its influence on fragmentation rates, J.Chem.Phys. 84, 3745–3752.

    CAS  Google Scholar 

  9. Davis, M.J. and Gray, S.K. (1986) Unimolecular reactions and phase space bottlenecks, J.Chem.Phys. 84, 5389–5411.

    Article  CAS  Google Scholar 

  10. Gray, S.K., Rice, S.A. and Davis, M.J. (1986) Bottlenecks to unimolecular reactions and alternative form for classical RRKM Theory, J.Phys.Chem. 90, 3470–3482.

    Article  CAS  Google Scholar 

  11. Karni, Y. and Nikitin, E.E. (1996) Vibrational predissociation: quasiclassical tunneling and classical diffusion, Mol.Phys. 89, 1327–1343.

    CAS  Google Scholar 

  12. Dashevskaya, E. I. Litvin, I., Nikitin, E. E. and Troe, J. (2001) Classical diffusion model of vibrational predissociation of van der Waals complexes: II. Comparison with trajectory calculations and analytical approximations, Phys. Chem. Chem. Phys., 3, 2315–2324.

    Article  CAS  Google Scholar 

  13. Gray, S.K. (1987) A periodically forced oscillator model of van der Waals fragmentation: Classical and quantum dynamics, J.Chem.Phys. 87, 2051–2061.

    Article  CAS  Google Scholar 

  14. Dashevskaya, E. I., Litvin, I., Nikitin, E. E., Oref, I. and Troe, J. (2002) Classical diffusion model of vibrational predissociation of van der Waals complexes: III. Comparison with quantum calculations, Phys. Chem. Chem. Phys. 4, 3330–3340.

    Article  CAS  Google Scholar 

  15. Rosen, N. (1933) Lifetimes of unstable molecules, J.Chem.Phys., 1, 319–326.

    Article  CAS  Google Scholar 

  16. Beswick, J.A. and Jortner J., (1978) Vibrational predissociation of triatomic van der Waals molecules, J.Chem.Phys., 68, 2277–2297.

    CAS  Google Scholar 

  17. Beswick, J. A. and Jortner, J. (1978) Perpendicular vibrational predissociation of T-shaped van der Waals molecules, J. Chem. Phys., 69, 512–518.

    Article  CAS  Google Scholar 

  18. Beswick, J. A. and Jortner, J. (1981) Intramolecular dynamics of van der Waals molecules, Adv.Chem.Phys., 47, 363–506.

    CAS  Google Scholar 

  19. Karni, Y. and Nikitin, E.E. (1994) Vibrational predissociation rate from dynamics of the full collision: a test of the Landau method against the exact results, J.Chem.Phys., 100, 8065–8071.

    CAS  Google Scholar 

  20. Karni, Y. and Nikitin, E.E. (1995) Adiabatically corrected quasiclassical model for the vibrational predissociation of van der Waals complexes, Chem.Phys., 191, 235–246.

    Article  CAS  Google Scholar 

  21. Woodruff, S.B. and Thompson, D. (1979) A quasiclassical trajectory study of vibrational predissociation of van der Waals molecules: Collinear He..I2(B3Π), J.Chem.Phys. 71, 376–380.

    Article  CAS  Google Scholar 

  22. Dashevskaya, E.I., Litvin, I., Nikitin, E. E., Oref, I. and Troe, J. (2000) Classical diffusion model of vibrational predissociation of van der Waals complexes: I. Truncated mean first passage time approximation. Phys. Chem. Chem. Phys 2, 2251–2259.

    Article  CAS  Google Scholar 

  23. G.M. Zaslavskii, (1985), Chaos in Dynamical Systems, Harwood Academic Publishers.

    Google Scholar 

  24. Shalashilin, D.V. and Thompson, D.L. (1996) Intrinsic non-RRK behaviour: Classical trajectory, statistical theory, and diffusional theory studies of a unimolecular reaction, J.Chem.Phys. 105, 1833–1845.

    Article  CAS  Google Scholar 

  25. Shalashilin, D.V. and Thompson, D.L. (1997) Method for predicting IVR-limited unimolecular reaction rate coefficients, J.Chem.Phys. 107, 6204–6212.

    Article  CAS  Google Scholar 

  26. Guo, Y., Shalashilin, D. V., Krouse, J. A. and Thompson, D. L. (1999) Predicting nonstatistical unimolecular reaction rates using Kramers’ theory, J. Chem. Phys. 110, 5514–5520.

    CAS  Google Scholar 

  27. Guo, Y., Shalashilin, D. V., Krouse, J. A. and Thompson, D. L.(1999) Intramolecular dynamics diffusion theory approach to complex unimolecular reactions, J. Chem. Phys. 110, 5521–5525.

    CAS  Google Scholar 

  28. Guo, Y., Thompson, D. L. and Miller, W. (1999) Thermal and microcanonical rates of unimolecular reactions from an energy diffusion theory approach, J.Phys.Chem. A, 103, 10308–10311.

    CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Kluwer Academic Publishers

About this paper

Cite this paper

Nikitin, E., Troe, J. (2004). Vibrational Predissociation: Quasiclassical Tunneling Through Classical Chaotic Sea. In: Lagana, A., Lendvay, G. (eds) Theory of Chemical Reaction Dynamics. NATO Science Series II: Mathematics, Physics and Chemistry, vol 145. Springer, Dordrecht. https://doi.org/10.1007/1-4020-2165-8_18

Download citation

Publish with us

Policies and ethics