Skip to main content

Vibrational Excitation I: The Quantal Treatment

  • Chapter
Atom - Molecule Collision Theory

Abstract

The close-coupling treatment of excitation of vibration by collision is formally the same as that for rotational excitation described in Chapter 8. The expansion of the wave function contains, in addition to the rotational wave functions, the vibrational wave functions of the noninteracting systems. The potential integral becomes more complicated and has more subscripts. The radial wave function has more subscripts and there are a larger number of coupled equations to consider. Still the form of the system of coupled equations is the same as it was for pure rotational excitation, and the methods described in Chapter 8 may be used for solving these systems also. There are, however, differences which arise in vibrational transition problems under certain circumstances and these will be discussed; and the methods described in Chapter 8 may be used for solving these problems will be pointed out later.

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

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. J. Schaefer and W.A. Lester, Jr., Theoretical study of inelastic scattering of H2 by Li+ on SCF and CI potential energy surfaces, J. Chem. Phys. 62, 1913–1924 (1975).

    Article  CAS  Google Scholar 

  2. H. Rabitz, Effective potentials in molecular collisions, J. Chem. Phys. 57, 1718–1725 (1972).

    Article  CAS  Google Scholar 

  3. H. Rabitz, Effective Hamiltonians in molecular collisions, in Modern Theoretical Chemistry, Part A, W.H. Miller, editor, Plenum Press, New York (1976), pp. 33–80.

    Google Scholar 

  4. G. Pfeffer, The calculation of the scattering of lithium ions from nitrogen molecules Ph.D. Thesis, University of Illinois, Urbana, Illinois (1977).

    Google Scholar 

  5. J.M. Bowman and S.C. Leasure, Sudden rotational calculations of atom-molecule scattering, J. Chem. Phys. 66, 288–295 (1977); Erratum: J. Chem. Phys. 66, 4724 (1977).

    Article  Google Scholar 

  6. R.W. Hamming, Numerical Methods for Scientists and Engineers, McGraw-Hill, New York (1962).

    Google Scholar 

  7. D. Secrest, Theory of angular momentum decoupling approximations for rotational transitions in scattering, J. Chem. Phys. 62, 710–719 (1975).

    Article  CAS  Google Scholar 

  8. L. Monchick and S. Green, Validity of central field approximations in molecular scattering: Low energy CO-He collisions, J. Chem. Phys. 63, 2000–2009 (1975).

    Article  CAS  Google Scholar 

  9. P.G. Burke and H.M. Schey, Elastic scattering of low-energy electrons by atomic hydrogen, Phys. Rev. 126, 147–162 (1962).

    Article  CAS  Google Scholar 

  10. M. A. Brandt and D.G. Truhlar, Importance of long-range forces and short-range forces in electron scattering: Elastic scattering by N2 at 10 and 30 eV, Chem. Phys. Lett. 23, 48–52 (1973).

    Article  CAS  Google Scholar 

  11. M.A. Brandt, Topics in quantum mechanical scattering theory with application to electron-nitrogen-molecule scattering, Masters Thesis, University of Minnesota, Minneapolis, Minnesota (1975).

    Google Scholar 

  12. A. Erdély, Asymptotic Expansions, Dover, New York (1956).

    Google Scholar 

  13. A.L. Scherzinger, Inelastic scattering of dissociable molecules, Ph.D. Thesis, University of Illinois, Urbana, Illinois (1977).

    Google Scholar 

  14. J.C. Light, Quantum calculations in chemically reactive systems, in Methods of Computational Physics, B. Alder, S. Fernbach, and M. Rotenberg, editors, Vol. 10, Academic Press, New York (1971), pp. 111 - 142.

    Google Scholar 

  15. J.C. Light and R.B. Walker, An R matrix approach to the solution of coupled equations for atom-molecule reactive scattering, J. Chem. Phys. 65, 4272–4282 (1976).

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1979 Plenum Press, New York

About this chapter

Cite this chapter

Secrest, D. (1979). Vibrational Excitation I: The Quantal Treatment. In: Bernstein, R.B. (eds) Atom - Molecule Collision Theory. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2913-8_11

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-2913-8_11

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-2915-2

  • Online ISBN: 978-1-4613-2913-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics