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Effective Hamiltonians in Molecular Collisions

  • Chapter
Dynamics of Molecular Collisions

Part of the book series: Modern Theoretical Chemistry ((MTC,volume 1))

Abstract

Considerable progress has recently been made in the measurement of phenomena dependent on molecular collisions.(1_3) In some cases individual inelastic cross sections have been measured. Both vibrational and rotational states are involved in many experiments. It is anticipated that further detailed experimental studies will be forthcoming. The availability of such new experimental data has stimulated a serious effort to find theoretical methods capable of describing and possibly predicting observable phenomena. The development of effective Hamiltonian (EH) theory is a direct outgrowth of these efforts. The achievement of practical theoretical methods for describing molecular collisions has been an elusive goal over the years. It is the general aim of EH methods to achieve such practicality within a quantum mechanical framework. Other chapters in this two-volume work and elsewhere in the literature describe various other approaches to this problem. It is perhaps in the combining of these various approaches that the most significant progress will be made.

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References

  1. R. G. Gordon, W. Klemperer, and J. I. Steinfeld, Vibrational and rotational relaxation, Annu. Rev. Phys. Chem. 19, 215–250 (1968).

    Article  CAS  Google Scholar 

  2. H. Rabitz, Rotation and rotation-vibration pressure-broadened lineshapes, Annu. Rev. Phys. Chem. 25, 155–177 (1974).

    Article  CAS  Google Scholar 

  3. E. Weitz and G. Flynn, Laser studies of vibrational and rotational relaxation in small molecules, Annu. Rev. Phys. Chem. 25, 275–315 (1974).

    Article  CAS  Google Scholar 

  4. D. M. Brink and G. R. Satchler, Angular Momentum, 2nd ed., Clarendon Press, Oxford (1968).

    Google Scholar 

  5. M. Verter and H. Rabitz, Sources of rotational cross section asymmetry σ (J→J+ΔJ)/σ(J→ J-ΔJ) in Molecule-Atom and Molecule-Molecule Systems, J. Chem. Phys. 61, 3707–3719 (1974).

    Article  CAS  Google Scholar 

  6. K. Takayanagi, The production of rotational and vibrational transitions in encounters between molecules, Adv. At. Mol. Phys. 1, 149–194 (1965).

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  8. G. Zarur and H. Rabitz, Effective potential formulation of molecule-molecule collisions with application to H2-H2, J. Chem. Phys. 60, 2057–2078 (1974).

    Article  CAS  Google Scholar 

  9. Shih-I Chu and A. Dalgarno, Approximation for the rotational excitation of molecules by atoms, J. Chem. Phys. 63, 2115–2118 (1975).

    Article  CAS  Google Scholar 

  10. Shih-I Chu and A. Dalgarno, The rotational excitation of carbon monoxide by hydrogen atom impact, Proc. R. Soc. London Ser. A 342, 191–207 (1975).

    Article  CAS  Google Scholar 

  11. M. Jacob and G. C. Wick, On the general theory of collisions for particles with spin, Ann. Phys. (NY) 7, 404–428 (1959).

    Article  Google Scholar 

  12. K. P. Lawley and J. Ross, Semiclassical theory of rotational excitation of a diatomic molecule by an atom, J. Chem. Phys. 43, 2930–2942 (1965);

    Article  CAS  Google Scholar 

  13. K. P. Lawley and J. Ross, Semiclassical calculation of rotational excitation, J. Chem. Phys. 43, 2943–2950 (1965).

    Article  CAS  Google Scholar 

  14. R. T. Pack, Space-fixed vs. body-fixed axes in atom-diatomic molecule scattering. Sudden approximations, J. Chem. Phys. 60, 633–639 (1974).

    Article  CAS  Google Scholar 

  15. P. McGuire, Elastic and inelastic angular distribution in the j z -conserving coupled states approximation for molecular collisions, Chem. Phys. Lett. 23, 575–578 (1973).

    Article  CAS  Google Scholar 

  16. P. McGuire, Coupled-states approach for elastic and for rotationally and vibrationally inelastic atom-molecule collisions, J. Chem. Phys. 62, 525–534 (1975).

    Article  CAS  Google Scholar 

  17. P. McGuire, Convergence of the elastic and the inelastic collisions cross sections in the coupled-states and the close-coupling methods, Chem. Phys. 8, 231–238 (1975).

    Article  CAS  Google Scholar 

  18. P. McGuire and D. J. Kouri, Quantum mechanical close coupling approach to molecular collisions. j z -Conserving coupled states approximation, J. Chem. Phys. 60, 2488–2499 (1974).

    Article  CAS  Google Scholar 

  19. D. J. Kouri, On the decoupling of angular momenta in molecular collisions, Chem. Phys. Lett. 31, 599–601 (1975).

    Article  CAS  Google Scholar 

  20. M. Tamir and M. Shapiro, The approximate conservation of P-helicity in rotational excitation: A new decoupling scheme, Chem. Phys. Lett. 31, 166–171 (1975).

    Article  CAS  Google Scholar 

  21. R. B. Walker and J. C. Light, Body-fixed equations for atom-molecule scattering: Exact and centrifugal decoupling methods, Chem. Phys. 7, 84–93 (1975).

    Article  CAS  Google Scholar 

  22. L. Biolsi and C. F. Curtiss, Molecular collisions. VII. Nuclear spin and statistics effects, J. Chem. Phys. 48, 4508–4516 (1968).

    Article  CAS  Google Scholar 

  23. H. Klar, Angular-momentum decomposition of nonrelativistic multichannel scattering, Nuovo Cimento 4A, 529–534 (1971).

    Google Scholar 

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

    Article  CAS  Google Scholar 

  25. A. F. Wagner and V. McKoy, Quantum mechanical calculations of rotational-vibrational scattering in homonuclear diatom-atom collisions, J. Chem. Phys. 58, 2604–2620 (1973).

    Article  CAS  Google Scholar 

  26. G. Englot and H. Rabitz, Dimensionality control of coupled scattering equations using partitioning techniques, Chem. Phys. 4, 458–466 (1974).

    Article  CAS  Google Scholar 

  27. G. Fisanick Englot and H. Rabitz, Dimensionality control of coupled scattering equations using partitioning techniques: The case of two molecules, Phys. Rev. A 10, 2187–2205 (1974).

    Article  Google Scholar 

  28. M. L. Goldberger and K. M. Watson, Collision Theory, John Wiley & Sons, Inc., New York (1964).

    Google Scholar 

  29. R. D. Levine, Quantum Mechanics of Molecular Rate Processes, Clarendon Press, Oxford (1969).

    Google Scholar 

  30. M. Rotenberg, Optical potential for the rotational excitation of diatomic molecules by atoms, Phys. Rev. A 4, 220–225 (1971).

    Article  Google Scholar 

  31. R. A. White, A. Altenberger-Siczek, and J. C. Light, Optical potentials in time-dependent quantum theory, J. Chem. Phys. 59, 200–205 (1973).

    Article  CAS  Google Scholar 

  32. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover Publications, Inc., New York (1965).

    Google Scholar 

  33. S. Tarr and H. Rabitz, unpublished results (1975).

    Google Scholar 

  34. T. Adachi and T. Kotani, An impact parameter representation of the scattering problem, Prog. Theor. Phys. 39, 430–452, 785–816 (1968).

    Article  CAS  Google Scholar 

  35. M. Razavy, Impact parameter representation of the scattering amplitude, Can. J. Phys. 49, 1885–1898 (1971).

    Article  Google Scholar 

  36. A. N. Kamal and L. K. Chavda, Impact-parameter representations in potential scattering, Phys. Rev. D 5, 994–1001 (1972).

    Article  Google Scholar 

  37. M. M. Islam, Impact parameter description of high energy scattering, Lect. Theor. Phys. XB, 97–156 (1967).

    Google Scholar 

  38. H. Rabitz, Impact parameter methods with effective potentials for inelastic molecular collisions, J. Chem. Phys. 58, 3975–3987 (1973).

    Article  CAS  Google Scholar 

  39. G. Fisanick-Englot and H. Rabitz, Studies of inelastic molecular collisions using impact parameter methods. I. Model calculations, J. Chem. Phys. 62, 1409–1424 (1975).

    Article  CAS  Google Scholar 

  40. G. Fisanick-Englot and H. Rabitz, Studies of inelastic molecular collisions using impact parameter methods. II. Exact and high-energy approximate calculations, J. Chem. Phys. 62, 2747–2759 (1975).

    Article  CAS  Google Scholar 

  41. G. Fisanick-Englot and H. Rabitz, Studies of inelastic molecular collisions using impact parameter methods. III. Line shape functions, J. Chem. Phys. 63, 1547–1554 (1975).

    Article  CAS  Google Scholar 

  42. T. P. Tsien and R. T. Pack, Rotational excitation in molecular collisions: A strong coupling approximation, Chem. Phys. Lett. 6, 54–56 (1970);

    Article  CAS  Google Scholar 

  43. T. P. Tsien and R. T. Pack, Rotational excitation in molecular collisions. Corrections to a strong coupling approximation, Chem. Phys. Lett. 6, 400–402 (1970).

    Article  CAS  Google Scholar 

  44. T. P. Tsien and R. T. Pack, Rotational excitation in molecular collisions. A many-state test of the strong coupling approximation, Chem. Phys. Lett. 8, 579–581 (1971).

    Article  CAS  Google Scholar 

  45. T. P. Tsien, G. A. Parker, and R. T. Pack, Rotationally inelastic molecular scattering. Computational tests of some simple solutions of the strong coupling, J. Chem. Phys. 59, 5373–5381 (1973).

    Article  CAS  Google Scholar 

  46. R. T. Pack, Relations between some exponential approximations in rotationally inelastic molecular collisions, Chem. Phys. Lett. 14, 393–395 (1972).

    Article  CAS  Google Scholar 

  47. G. Zarur and H. Rabitz, Rotationally inelastic scattering with effective potentials, J. Chem. Phys. 59, 943–951 (1973).

    Article  CAS  Google Scholar 

  48. H. Rabitz and G. Zarur, Vibration-rotation inelasticity in He-H2, J. Chem. Phys. 61, 5076–5084 (1974).

    Article  CAS  Google Scholar 

  49. H. Rabitz and G. Zarur, Vibration-rotation relaxation in He-H2, J. Chem. Phys. 62, 1425–1434 (1975).

    Article  CAS  Google Scholar 

  50. M. H. Alexander, Effective potential study of rotationally-vibrationally inelastic collisions between He and H2, J. Chem. Phys. 61, 5167–5181 (1974).

    Article  CAS  Google Scholar 

  51. M. H. Alexander, Potential surface dependence of cross section and rate constants for the vibrational relaxation of H2 in collisions with 4He, Chem. Phys. 8, 86–98 (1975).

    Article  CAS  Google Scholar 

  52. P. McGuire and J. P. Toennies, A priori low-temperature vibrational relaxation rates for He-H2, J. Chem. Phys. 62, 4623–4627 (1975).

    Article  CAS  Google Scholar 

  53. Shih-I Chu and A. Dalgarno, Angular distributions in the elastic scattering and rotational excitation of molecular hydrogen by atomic hydrogen, Astrophys. J. 199, 637–664 (1975).

    Article  CAS  Google Scholar 

  54. D. J. Kouri and P. McGuire, A coupled-states approximation study of Li+-H2 collisions, Chem. Phys. Lett. 29, 414–417 (1974).

    Article  CAS  Google Scholar 

  55. S. Green, Accuracy of decoupling approximations for rotational excitation: Low energy Co-He collisions, Chem. Phys. Lett. 38, 293–296 (1976).

    Article  CAS  Google Scholar 

  56. M. Verter and H. Rabitz, Vibrational and rotational inelasticity in He-Co, J. Chem. Phys. 64, 2939–2952 (1975).

    Article  Google Scholar 

  57. S. C. Mehrotra and J. E. Boggs, A semiclassical, nonperturbative approach to collision induced transitions between rotational levels for the N2-Ar system, J. Chem. Phys. 63, 4618–4621 (1975).

    Article  CAS  Google Scholar 

  58. S. Green, Comment on the accuracy of Rabitz’ effective potential approximation for rotational excitation by collisions, J. Chem. Phys. 62, 3568–3570 (1975).

    Article  CAS  Google Scholar 

  59. S. Green, Rotational excitation in H2-H2 collisions: Close-coupling calculations, J. Chem. Phys. 62, 2271–2277 (1975).

    Article  CAS  Google Scholar 

  60. H. Rabitz and H. Lam, Mechanisms of rotational relaxation in hydrogen, J. Chem. Phys. 63, 3532–3542 (1975).

    Article  CAS  Google Scholar 

  61. Shih-I Chu, Effective potential study of the rotational excitation of HD by collision with H2, J. Chem. Phys. 62, 4089–4100 (1975).

    Article  CAS  Google Scholar 

  62. S. C. Mehrotra and J. E. Boggs, A semiclassical, nonperturbative approach to the description of molecular collisions, J. Chem. Phys. 62, 1453–1459 (1975).

    Article  CAS  Google Scholar 

  63. S. Tarr, J. Sampson and H. Rabitz, Model studies of vibrational and rotational inelastic collisions, J. Chem. Phys. 64, 5291 (1976).

    Article  CAS  Google Scholar 

  64. S. Green, Rotational excitation of symmetric-top molecules by collisions with atoms: Close coupling, coupled states, and effective potential calculations for NH3-He, J. Chem. Phys. 64, 3463–3473 (1976).

    Article  CAS  Google Scholar 

  65. A. B. Elkowitz and R. E. Wyatt, J z conserving approximation for the hydrogen exchange reaction, Mol. Phys. 31, 189–201 (1976).

    Article  CAS  Google Scholar 

  66. A. E. DePristo and M. H. Alexander, An L-dominant simplification of the close-coupled equations for collisions between atomic and diatomic molecules, J. Chem. Phys. 63, 3552–3559 (1975).

    Article  CAS  Google Scholar 

  67. S. Augustin and H. Rabitz, Effective Hamiltonian methods for the semiclassical treatment of molecular collisions, J. Chem. Phys. 64, 4821 (1976).

    Article  CAS  Google Scholar 

  68. S. Tarr, H. Rabitz, D. Fitz, and R. Marcus, unpublished work (1976).

    Google Scholar 

  69. P. McGuire, Validity of the coupled states approximated for molecular collisions, Chem. Phys. 13, 81–94 (1976).

    Article  CAS  Google Scholar 

  70. D. Kouri, T. Heil, Y. Shimoni, On the energy dependence of the j z -conserving coupled states approximation, unpublished (1976).

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Chemistry, Princeton University, Princeton, New Jersey, USA

    Herschel Rabitz

Authors
  1. Herschel Rabitz
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Editor information

Editors and Affiliations

  1. University of California, Berkeley, USA

    William H. Miller

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© 1976 Plenum Press, New York

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Rabitz, H. (1976). Effective Hamiltonians in Molecular Collisions. In: Miller, W.H. (eds) Dynamics of Molecular Collisions. Modern Theoretical Chemistry, vol 1. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-8867-2_2

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  • DOI: https://doi.org/10.1007/978-1-4615-8867-2_2

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4615-8869-6

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