Skip to main content
SpringerLink
Log in

Vibrational Energy Transfer

  • Chapter
Dynamics of Molecular Collisions

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

Abstract

The theory of energy transfer in molecular collisions is of importance for the understanding of a great variety of physical problems.(1–7) In many of these problems we are interested in determining probabilities of energy transfer between the translational motion and one or more of the internal motions of the molecules. There has been much work done in recent years on the calculation of vibrational transition probabilities and inelastic scattering cross sections in which vibrational and/or rotational states are excited. Such collisions are a characteristic process in a simple molecular gas in the temperature range from 100° to 5000°K. Electronic transitions during collision will take place to a significant extent only at higher temperatures. For a gas in thermal equilibrium, individual molecules are constantly gaining or losing energy through collisions, but the total energy is unchanged. If conditions of equilibrium are suddenly changed, the gas finds itself seeking a new state of equilibrium; the rate of adjustment is governed directly by the collision efficiency, which measures the amount of energy either gained or lost per collision. At large separations, the colliding molecules attract slightly so their electron cloud overlapping is not important. However, as they approach each other to close range, where the overlapping of electron clouds is appreciable, repulsive forces are set up.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
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. K. F. Herzfeld and T. A. Litovitz, Absorption and Dispersion of Ultrasonic Waves, Academic Press, Inc., New York (1959), Chap. 7.

    Google Scholar 

  2. T. L. Cottrell and J. C. McCoubrey, Molecular Energy Transfer in Gases, Butterworth & Co. (Publishers) Ltd., London (1961), Chap. 6.

    Google Scholar 

  3. K. F. Herzfeld, Fundamental physics of matter, in: Thermodynamics and Physics of Matter, F. D. Rossini, ed., Princeton University Press, Princeton, N. J. (1965), Sec. H, pp. 111–239.

    Google Scholar 

  4. N. F. Mott and H. S. W. Massey, The Theory of Atomic Collisions, 3rd ed., Oxford University Press, Inc., New York (1965).

    Google Scholar 

  5. B. Stevens, “Collisional Activation in Gases,” in: International Encyclopedia of Physical Chemistry and Chemical Physics, Vol. 3, Topic 19, Pergamon Press, Inc., Elmsford, N. Y. (1967).

    Google Scholar 

  6. G. M. Burnett and A. M. North (eds.), Transfer and Storage of Energy by Molecules, Vol. 2, John Wiley & Sons, Inc. (Interscience Division), New York (1969).

    Google Scholar 

  7. D. Rapp and T. Kassal, The theory of vibrational energy transfer between simple molecules in nonreactive collisions, Chem. Rev. 69, 61–102 (1969).

    CAS  Google Scholar 

  8. H. K. Shin, A collision model for the vibrational relaxation of hydrogen fluoride at low temperatures, Chem. Phys. Lett. 26, 450 (1974).

    CAS  Google Scholar 

  9. B. Widom, Relaxation of string oscillator, J. Chem. Phys. 28, 918–925 (1958).

    CAS  Google Scholar 

  10. B. H. Mahan, Collinear collision chemistry. I. A simple model for inelastic and reactive collision dynamics, J. Chem. Educ. 41, 308–311 (1974)

    Google Scholar 

  11. B. H. Mahan, Collinear collision chemistry. II. Energy disposition in reactive collisions, J. Chem. Educ. 41, 377–380 (1974).

    Google Scholar 

  12. D. Rapp, Complete classical theory of vibrational energy exchange, J. Chem. Phys. 32, 735–737 (1960).

    CAS  Google Scholar 

  13. J. C. Slater and N. H. Frank, Mechanics, McGraw-Hill Book Company, New York (1947).

    Google Scholar 

  14. B. H. Mahan, Refined impulse approximation for the collisional excitation of the classical anharmonic oscillator, J. Chem. Phys. 52, 5221–5225 (1970).

    CAS  Google Scholar 

  15. D. Rapp, Quantum Mechanics, Holt, Rinehart and Winston, Inc., New York (1971), Chap. 21 and 22.

    Google Scholar 

  16. N. Rosen and C. Zener, Double Stern-Gerlach experiment and related collision phenomena, Phys. Rev. 40, 502–507 (1932).

    CAS  Google Scholar 

  17. D. Rapp and T. E. Sharp, Vibrational energy transfer in molecular collisions involving large transition probabilities, J. Chem. Phys. 38, 2641–2648 (1963).

    CAS  Google Scholar 

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

    Google Scholar 

  19. J. D. Jackson and N. F. Mott, Energy exchange between inert gas atoms and a solid surface, Proc. R. Soc. London Sec. A 137, 703–717 (1932).

    CAS  Google Scholar 

  20. C. Zener, Interchange of translational, rotational, and vibrational energy in molecular collisions, Phys. Rev. 37, 556–569 (1964).

    Google Scholar 

  21. D. Rapp, Vibrational energy exchange in quantum and classical mechanics, J. Chem. Phys. 40, 2813–2818 (1964).

    CAS  Google Scholar 

  22. J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids, John Wiley & Sons, Inc., New York (1964), pp. 1110–1112,

    Google Scholar 

  23. J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids, John Wiley & Sons, Inc., New York (1964), pp. 1200.

    Google Scholar 

  24. G. Herzberg, Spectra of Diatomic Molecules, Van Nostrand Reinhold Company, New York (1950), Table 39.

    Google Scholar 

  25. D. Secrest and B. R. Johnson, Exact quantum-mechanical calculation of a collinear collision of a particle with a harmonic oscillator, J. Chem. Phys. 45, 4556–4570 (1966).

    CAS  Google Scholar 

  26. J. D. Kelley and M. Wolfsberg, Comparison of approximate translational-vibrational energy transfer formulas with exact classical calculations, J. Chem. Phys. 44, 324–338 (1966).

    CAS  Google Scholar 

  27. L. Brillouin, The undulatory mechanics of Schrödinger, C. R. Acad. Sci. Ser. B 183, 24–27 (1926)

    Google Scholar 

  28. L. Brillouin, Note on undulatory mechanics J. Phys. (Paris) 7, 353–368 (1926).

    Google Scholar 

  29. G. Wentzel, A generalization of the quantum conditions for the purposes of wave mechanics, Z Phys. 38, 518–529 (1926).

    Google Scholar 

  30. H. A. Kramers, Wave mechanics and semi-numerical quantisation, Z. Phys. 39, 828–840 (1926).

    Google Scholar 

  31. H. Jeffreys, On certain approximate solutions of linear differential equations of the second order, Proc. London Math. Soc. 23 (2), 428–438 (1923).

    Google Scholar 

  32. E. C. Kemble, Quantum Mechanics, Dover Publications, Inc., New York (1958), Sec. 21.

    Google Scholar 

  33. L. Landau and E. M. Lifshitz, Quantum Mechanics, Addison-Wesley Publishing Company, Inc., Reading, Mass. (1965), Chap. 7.

    Google Scholar 

  34. B. Widom, Some aspects of the theory of vibrational transition probabilities in molecular collisions, Discuss. Faraday Soc. 33, 37–43 (1962).

    CAS  Google Scholar 

  35. L. Landau, Theory of energy transfer, Phys. Z. Sowjetunion 2, 46–51 (1932).

    CAS  Google Scholar 

  36. L. Landau and E. Teller, Zur Theorie der Schalldispersion, Phys. Z. Sowjetunion 10, 34–43 (1936).

    Google Scholar 

  37. D. Rapp, Vibrational energy exchange in quantum and classical mechanics, Lockheed Aircraft Corp. Technical Report. 6–90–61–14 (July, 1960).

    Google Scholar 

  38. H. K. Shin, Dependence of the probability of vibrational deexcitation on interaction potentials, J. Chem. Phys. 42, 59–62 (1965)

    CAS  Google Scholar 

  39. H. K. Shin, Temperature dependence of intermolecular energy transfer in polar molecules, J. Am. Chem. Soc. (Debye issue) 90, 3025–3029 (1968).

    CAS  Google Scholar 

  40. A. Erdélyi, Asymptotic Expansions, Dover Publications, Inc., New York (1956).

    Google Scholar 

  41. N. G. de Bruijn, Asymptotic Methods in Analysis, North-Holland Publishing Company, Amsterdam (1961).

    Google Scholar 

  42. H. K. Shin, WKB calculation of vibrational transition probabilities in molecular collisions, J. Chem. Phys. 48, 3644–3651 (1968).

    CAS  Google Scholar 

  43. H. K. Shin, Temperature dependence of vibrational transition probabilities for O2, N2, CO, and Cl2 in the region below 300% J. Chem. Phys. 57, 1363–1364 (1972).

    CAS  Google Scholar 

  44. B. Hartmann and Z. I. Slawsky, Vibrational relaxation with a Lennard-Jones potential, J. Chem. Phys. 47, 2491–2494 (1967).

    CAS  Google Scholar 

  45. K. Takayanagi, On the inelastic collision between molecules, II, Prog. Theor. Phys. 8, 497–508 (1952); Vibrational and rotational transitions in molecular collisions, Prog. Theor. Phys. Suppl. 25, (1963).

    CAS  Google Scholar 

  46. H. K. Shin, Excitation of molecular vibration on collision. Role of the high-order angular momenta, J. Chem. Phys. 46, 744–754 (1967).

    CAS  Google Scholar 

  47. M. Salkoff and E. Bauer, Excitation of molecular vibration on collision, J. Chem. Phys. 29, 26–31 (1958).

    CAS  Google Scholar 

  48. R. N. Schwartz, Z. I. Slawsky, and K. F. Herzfeld, Calculation of vibrational relaxation times in gases, J. Chem. Phys. 20, 1591–1599 (1952).

    CAS  Google Scholar 

  49. R. N. Schwartz and K. F. Herzfeld, Vibrational relaxation times of gases: Three-dimensional treatment, J. Chem. Phys. 22, 767–773 (1954).

    CAS  Google Scholar 

  50. R. Marriott, Molecular collision cross sections and vibrational relaxation in carbon dioxide, Proc. Phys. Soc. London 84, 877–888 (1964).

    CAS  Google Scholar 

  51. A. Messiah, Quantum Mechanics, Vol. 1, North-Holland Publishing Company, Amsterdam (1968), Chap. 12.

    Google Scholar 

  52. I.I. Gol’dman and V. D. Krivchenkov, Problems in Quantum Mechanics, Addison-Wesley Publishing Company, Inc., Reading, Mass. (1961), p. 103.

    Google Scholar 

  53. H. K. Shin, Vibrational excitation of diatomic molecules in high energy ion-molecule collisions, Chem. Phys. Lett. 5, 137–142 (1970).

    CAS  Google Scholar 

  54. H. K. Shin, Vibrational transitions in atom + diatomic systems: Use of the Lennard-Jones potential, J. Phys. Chem. 77, 1666–1673 (1973).

    CAS  Google Scholar 

  55. E. Kerner, Note on the forced and damped oscillator in quantum mechanics, Can. J. Phys. 36, 371–377 (1958).

    Google Scholar 

  56. C. E. Treanor, Vibrational energy transfer in high-energy collisions, J. Chem. Phys. 43, 532–538 (1965).

    CAS  Google Scholar 

  57. P. Pechukas and J. C. Light, On the exponential form of time-displacement operators in quantum mechanics, J. Chem. Phys. 44, 3897–3912 (1966).

    Google Scholar 

  58. H. K. Shin, Probability of vibrational excitations in high energy collisions, Chem. Phys. Lett. 3, 125–127 (1969).

    CAS  Google Scholar 

  59. H. K. Shin, Steric factor in vibrational-translational energy transfer, J. Chem. Phys. 46, 3688–3689 (1967).

    CAS  Google Scholar 

  60. H. K. Shin, Effect of molecular orientation on vibrational-translational energy transfer, J. Chem. Phys. 47, 3302–3311 (1967).

    CAS  Google Scholar 

  61. K. F. Herzfeld, Deactivation of the vibration during the collision of two diatomic molecules, Z. Phys. 156, 265–270 (1959).

    CAS  Google Scholar 

  62. H. K. Shin, Inelastic molecular collisions with a Lennard-Jones (12–6) interaction energy, J. Chem. Phys. 41, 2864–2868 (1964).

    CAS  Google Scholar 

  63. T. L. Cottrell and A. J. Matheson, Transition probability in molecular encounters. Part 5. Vibrational-rotational energy transfer, Trans. Faraday Soc. 58, 2336–2341 (1962).

    CAS  Google Scholar 

  64. C. B. Moore, Vibration-rotation energy transfer, J. Chem. Phys. 43, 2979–2986 (1965).

    CAS  Google Scholar 

  65. H. K. Shin, Deexcitation of molecular vibration on collision: Vibration-to-rotation energy transfer in hydrogen halides, J. Phys. Chem. 75, 1079–1090 (1971).

    CAS  Google Scholar 

  66. W. D. Breshears and P. F. Bird, Densitometric measurement of the vibrational relaxation of HCl and DC1 in shock waves, J. Chem. Phys. 50, 333–336 (1969)

    CAS  Google Scholar 

  67. W. D. Breshears and P. F. Bird, Vibrational relaxation of shock-heated Cl2: Effects of CO, HCl, and DC1, J. Chem. Phys. 51, 3660–3665 (1969).

    CAS  Google Scholar 

  68. H. K. Shin, Vibration-rotation-translation energy transfer in HF + HF and DF + DF collisions, Chem. Phys. Lett. 10, 81–85 (1971).

    CAS  Google Scholar 

  69. H. K. Shin, Vibration-to-rotation energy transfer in hydrogen fluoride: Effects of the dipole-dipole and hydrogen-bond interactions, J. Chem. Phys. 59, 879–884 (1973).

    CAS  Google Scholar 

  70. J. F. Bott and N. Cohen, Shock-tube studies of HF vibrational relaxation, J. Chem. Phys. 55, 3698–3706 (1971).

    CAS  Google Scholar 

  71. J. F. Bott and N. Cohen, Shock-tube study of DF vibrational relaxation, J. Chem. Phys. 58, 934–940 (1973).

    CAS  Google Scholar 

  72. R. C. Millikan and D. R. White, Vibrational energy exchange between N2 and CO. The vibrational relaxation of nitrogen, J. Chem. Phys. 39, 98–101 (1963).

    CAS  Google Scholar 

  73. Y. Sato, S. Tsuchiya, and K. Kuratani, Shock-wave study of vibrational energy exchange between diatomic molecules, J. Chem. Phys. 50, 1911–1919 (1969).

    CAS  Google Scholar 

  74. H. K. Shin, Excitation of molecular vibration on collision: Oriented nonlinear encounters, J. Phys. Chem. 73, 4321–4328 (1969).

    CAS  Google Scholar 

  75. H. K. Shin, Vibration-to-vibration energy transfer in near-resonant collisions, J. Chem. Phys. 60, 1064–1070 (1974).

    CAS  Google Scholar 

  76. T. I. McLaren and J. P. Appleton, Shock-tube measurements of the vibration-vibration energy exchange probability for the CO-N2 system, Eighth International Shock Tube Symposium, London, No. 27 (1971).

    Google Scholar 

  77. C. W. von Rosenberg, K. N. C. Bray, and N. H. Pratt, Shock-tube vibrational relaxation measurements: N2 relaxation by H2O and the CO-N2 V-V rate, J. Chem. Phys. 56, 3230–3237 (1972).

    Google Scholar 

  78. D. F. Starr, J. K. Hancock, and W. H. Green, Vibrational deactivation of carbon monoxide by hydrogen and nitrogen from 100 to 650°K, J. Chem. Phys. 61, 5421–5425 (1974).

    CAS  Google Scholar 

  79. J. C. Stephenson and E. R. Mosburg, Vibrational energy transfer in CO from 100 to 300°K, J. Chem. Phys. 60, 3562–3566 (1974).

    CAS  Google Scholar 

  80. S. Glasstone, K. J. Laidler, and H. Eyring, The Theory of Rate Processes, McGraw-Hill Book Company, New York, (1941), pp. 100–103.

    Google Scholar 

  81. D. W. Jepsen and J. O. Hirschfelder, Idealized theory of the recombinations of atoms by three-body collisions, J. Chem. Phys. 30, 1032–1044 (1959).

    CAS  Google Scholar 

  82. R. J. Rubin, Classical model for the study of isotope effects in energy exchange and particle exchange reactions, J. Chem. Phys. 40, 1069–1077 (1964).

    CAS  Google Scholar 

  83. H. K. Shin, Classical model for free radical formation, J. Phys. Chem. 68, 3410–3413 (1964).

    CAS  Google Scholar 

  84. H. K. Shin, Vibrational energy transfer for an impulsive BC + A collision, Chem. Phys. Lett. 4, 297–301 (1969)

    CAS  Google Scholar 

  85. H. K. Shin, Idealized model for the reactive collision AB + C → A + BC, Chem. Phys. Lett. 5, 232–236 (1970).

    CAS  Google Scholar 

  86. D. Secrest, Linear collision of a classical harmonic oscillator with a particle at high energies, J. Chem. Phys. 51, 421–425 (1969).

    CAS  Google Scholar 

  87. M. P. Hanson and M. Blomme, Relation of the string oscillator, J. Chem. Phys. 50, 4324–4335 (1969).

    CAS  Google Scholar 

  88. M. P. Hanson and L. G. Werbelow, Collinear collisions of an atom and string oscillator, J. Chem. Phys. 58, 3669–3674 (1973).

    CAS  Google Scholar 

  89. C. Rebick, R. D. Levine, and R. B. Bernstein, Energy requirements and energy disposal: Reaction probability matrices and a computational study of a model system, J. Chem. Phys. 60, 4977–4989 (1974).

    CAS  Google Scholar 

  90. J. F. Bott and N. Cohen, HF vibrational relaxation by F atoms, J. Chem. Phys. 55, 5124–5125 (1971).

    CAS  Google Scholar 

  91. W. C. Solomon, J. A. Blauer, F. C. Jaye, and J. G. Hnat, The vibrational excitation of hydrogen fluoride behind incident shock waves, Int. J. Chem. Kinet. 3, 215–222 (1971).

    CAS  Google Scholar 

  92. D. L. Thompson, Monte Carlo classical trajectory calculation of the rates of F-atom vibrational relaxation of HF and DF, J. Chem. Phys. 57, 4164–4169 (1972).

    CAS  Google Scholar 

  93. H. K. Shin, Temperature dependence of the probability of vibrational energy transfer between HF and F, Chem. Phys. Lett. 14, 64–69 (1972).

    CAS  Google Scholar 

  94. R. L. Wilkins, Monte Carlo calculations of reaction rates and energy distributions among reaction products. IV. F + HF(v) → HF(v) + F and F + DF(v) → DF(v’) + F, J. Chem. Phys. 59, 698–704 (1973).

    CAS  Google Scholar 

  95. E. A. Mason and J. T. Vanderslice in: Atomic and Molecular Processes (D. R. Bates, ed.), pp. 663–695, Academic Press, Inc., New York (1962).

    Google Scholar 

  96. S. O. Colgate, J. E. Jordan, I. Admur, and E. A. Mason, Scattering of high-velocity neutral particles. XVI. Ar-Ar, Ar-He, and Ar-H2, J. Chem. Phys. 51, 968–973 (1969).

    CAS  Google Scholar 

  97. F. P. Tully and Y. T. Lee, Intermolecular potentials from crossed beam differential elastic scattering measurements. VI. Atoms and diatomic molecules. Ar + N2, Ar 4- O2, Kr + N2, and Kr + O2, J. Chem. Phys. 57, 866–869 (1972).

    CAS  Google Scholar 

  98. M. Krauss and F. H. Mies, Interaction potential between He and H2, J. Chem. Phys. 42, 2703–2708 (1965).

    CAS  Google Scholar 

  99. M. D. Gordon and D. Secrest, Helium-atom-hydrogen-molecule potential surface employing the LCAO-MO-SCF and CI methods, J. Chem. Phys. 52, 120–131 (1970).

    CAS  Google Scholar 

  100. W. A. Lester, Jr., Interaction potential between Li+ and H2: I. Region appropriate for rotational excitation, J. Chem. Phys. 53, 1511–1515 (1970)

    CAS  Google Scholar 

  101. W. A. Lester, Jr., Analytical expression for the interaction potential between Li and HF, J. Chem. Phys. 53, 1611–1612 (1970)

    CAS  Google Scholar 

  102. W. A. Lester, Jr., Interaction potential between Li+ and H2: II. Region appropriate for vibrational excitation, J. Chem. Phys. 54, 3171–3179 (1970).

    Google Scholar 

  103. P. C. Crosby and T. F. Moran, Vibrational excitation in collisions involving oxygen ion beams, J. Chem. Phys. 52, 6157–6165 (1970).

    Google Scholar 

  104. F. Petty and T. F. Moran, Vibrationally inelastic low-energy CO+-Ar collisions, Phys. Rev. A 5, 266–276 (1972).

    Google Scholar 

  105. D. A. Micha and M. Rotenberg, Impact parameter dependence of vibrational excitation cross sections for H2+He collisions, Chem. Phys. Lett. 6, 79–82 (1970).

    CAS  Google Scholar 

  106. H. K. Shin, Idealized collision model for reactive scattering: Energy dependence of the cross section for CH3I+K→CH3 + KI, Chem. Phys. Lett. 34, 546–551 (1975)

    CAS  Google Scholar 

  107. H. K. Shin, Energy dependence of the cross section for CH3I+K→CH3 + KI near threshold, Chem. Phys. Lett. 38, 253–256 (1976).

    CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Chemistry, University of Nevada, Reno, Nevada, USA

    Hyung Kyu Shin

Authors
  1. Hyung Kyu Shin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of California, Berkeley, USA

    William H. Miller

Rights and permissions

Reprints and permissions

Copyright information

© 1976 Plenum Press, New York

About this chapter

Cite this chapter

Shin, H.K. (1976). Vibrational Energy Transfer. 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_4

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-8867-2_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4615-8869-6

  • Online ISBN: 978-1-4615-8867-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation