Skip to main content

Derivative Coupling Elements in Electronically Adiabatic Representations and Their Use in Scattering Calculations

  • Conference paper
Energy Storage and Redistribution in Molecules

Abstract

The Born-Oppenheimer electronically adiabatic basis provides the most convenient representation for obtaining molecular-structure and potential-energy-surface information for systems of chemical interest. In this representation the electronic Hamiltonian is diagonal, and the adiabatic energies may be defined and calculated accurately by the variational principle. For systems in which the adiabatic states are well separated in energy, the nuclear motion at chemical energies can be treated adequately using a single adiabatic potential energy surface. For systems in which the coupling of electronic states is important, the coupling can be included consistently in this representation through matrix elements of nuclear-motion derivative operators.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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. B. C. Garrett and D. G. Truhlar, The coupling of electronically adiabatic states in atomic and molecular collisions, in: “Theoretical Chemistry: Advances and Perspectives”, Vol. 6A, D. Henderson, ed., Academic Press, New York (1981), p. 215.

    Google Scholar 

  2. D. R. Bates, H. S. W. Massey, and A. L. Stewart, Inelastic collisions between atoms. I. General theoretical considerations, Proc. Roy. Soc. Lond., Ser. A 216: 437 (1953).

    Article  MATH  Google Scholar 

  3. See, e.g., R. D. Piacentini and A. Salin, Molecular treatment of the He2+-H collisions, J. Phys. B 7:1666 (1974); C. Harel and A. Salin, Charge exchange in collisions of highly ionized ions and atoms, J. Phys. B 10: 3511 (1977).

    Article  ADS  Google Scholar 

  4. R. T Pack and J. O. Hirschfelder, Separation of rotational coordinates from the N-electron diatomic Schrftdinger equation, J. Chem. Phys. 49: 4009 (1968).

    Article  MathSciNet  ADS  Google Scholar 

  5. B. C. Garrett, M. J. Redmon, D. G. Truhlar, and C. F. Melius, Ab initio treatment of electronically inelastic K 4- H collisions using a direct integration method for the solutionof the coupled-channel scattering equations in electronically adiabatic representations, J. Chem. Phys. 74: in press.

    Google Scholar 

  6. D. R. Bates and R. McCarroll, Electron capture in slow collisions, Proc. Roy. Soc. Lond., Ser. A 245: 175 (1958).

    Article  ADS  MATH  Google Scholar 

  7. M. H. Mittleman and H. Tai, Low energy atom-atom scattering: Corrections to the He-He interaction, Phys. Rev. A 8: 1880 (1973).

    Article  ADS  Google Scholar 

  8. W. R. Thorson and J. B. Delos, Theory of near-adiabatic collisions. II. Scattering coordinate method, Phys. Rev. A 18: 135 (1978).

    Article  ADS  Google Scholar 

  9. A time-independent quantum mechanical formulation proposed by M. E. Riley is presented in reference 1. A semiclassical formulation is given by S. K. Knudson and W. R. Thorson, Lyman -α excitation and resonant charge exchange in slow H+-H(1s) collisions, Can. J. Phys. 48: 313 (1970).

    Article  ADS  Google Scholar 

  10. J. C. Y. Chen, V. H. Ponce, and K. M. Watson, Translational factors in eikonal approximation and their effect on channel couplings, J. Phys. B 6: 965 (1973).

    Article  ADS  Google Scholar 

  11. V. SethuRaman, W. R. Thorson, and C. F. Lebeda, Impact ionization in the proton-H-atom system. V. Final cross section calculations, Phys. Rev. A 8:1316 (1973); W. R. Thorson and J. B. Delos, Theory of near-adiabatic collisions. I. Electron trans-lation factor method, Phys. Rev. A 18: 117 (1978).

    Article  ADS  Google Scholar 

  12. C. F. Melius and W. A. Goddard III, The theoretical description of an asymmetric nonresonant charge transfer process: Li + Na+ ⇄ Li+ + Na, the two state approximation, Chem. Phys. Lett. 15: 524 (1972).

    Article  ADS  Google Scholar 

  13. C. F. Melius and W. A. Goddard III, Charge-transfer process using the molecular-wavefunction approach: The asymmetric charge transfer and excitation in Li + Na+ and Na + Li+, Phys. Rev. A 10: 1541 (1974).

    Article  ADS  Google Scholar 

  14. C. F. Melius, The H+ + H- neutralization process using the molecular wavefunction approach, Bull. Amer. Phys. Soc. 19: 1199 (1974).

    Google Scholar 

  15. C. F. Melius, R. W. Numrich, and D. G. Truhlar, Calculations of potential energy curves for the ground states of NaH+ and KH+ and Π state of NaH and KH, J. Phys. Chem. 83: 1221 (1979).

    Article  Google Scholar 

  16. R. W. Numrich and D. G. Truhlar, The mixing of ionic and covalent configurations for NaH, KH, and MgH+. Potential energy curves and couplings between molecular states, J. Phys. Chem. 79: 2745 (1975).

    Article  Google Scholar 

  17. R. W. Numrich and D. G, Truhlar, Detailed study of the interaction of covalent and ionic states in collisions of Na and K with H, J. Phys. Chem. 82: 168 (1978).

    Article  Google Scholar 

  18. E. J. Shipsey, J. C. Browne, and R. E. Olson, Theoretical charge-exchange cross sections for B+3 + He and C+4 + He collisions, Phys. Rev. A 15: 2166 (1977).

    Article  ADS  Google Scholar 

  19. See, e.g., S. Geltman, “Topics in Atomic Collision Theory”, Academic Press, New York (1969), section 21; J. E. Bayfield, E. E. Nikitin, and A. I. Reznikov, Semiclassical scattering matrix for two-state exponential model, Chem. Phys. Lett. 19: 471 (1973).

    Article  ADS  Google Scholar 

  20. See, e.g., P. L. DeVries and T. F. George, Quantum mechanical theory of a structured atom-diatom collision system: A + BC(1Σ), J. Chem. Phys. 67:1293 (1977); F. Rebentrost and W. A. Lester, Nonadiabatic effects in the collision of F(2P) with H2(1Σ +g ). III. Scattering theory and coupled-channel computations, J. Chem. Phys. 67: 3367 (1977).

    Article  ADS  Google Scholar 

  21. A. Riera and A. Salin, Limitations on the use of the perturbed stationary-state methods for the description of slow atom- atom collisions, J. Phys. B 9: 2877 (1976).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1983 Plenum Press, New York

About this paper

Cite this paper

Garrett, B.C., Truhlar, D.G., Melius, C.F. (1983). Derivative Coupling Elements in Electronically Adiabatic Representations and Their Use in Scattering Calculations. In: Hinze, J. (eds) Energy Storage and Redistribution in Molecules. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3667-9_22

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-3667-9_22

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-3669-3

  • Online ISBN: 978-1-4613-3667-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics