Skip to main content

Dimensionality Reduction Methods for Rotovibrational Cross Section Calculations

  • Chapter
The Transfer of Molecular Energies by Collision: Recent Quantum Treatments

Part of the book series: Lecture Notes in Chemistry ((LNC,volume 11))

  • 93 Accesses

Abstract

In the previous Chapter we established the fundamental theory describing physical and chemical aspects, on a microscopic level, of the elastic and inelastic collisions between molecules in their ground electronic states. The whole formulation of that theory was given by quantum mechanics based on the Schrödinger equation and it was made clear that the most systematic approximations used to provide possible numerical treatments involve the expansion of the total wavefunction for the system under study in terms of a unperturbed basis set of known, exact or nearly exact, functions.

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

Access this chapter

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. A. E. De Pristo and M. H. Alexander, chem. Phys., 19, 181 (1977).

    Article  Google Scholar 

  2. A. E. De Pristo and M. H. Alexander, J. Chem. Phys., 63, 3552 (1975).

    Article  Google Scholar 

  3. P. McGuire, Chem. Phys. Lett., 23, 575 (1973).

    Article  CAS  Google Scholar 

  4. R. T. Pack, J. Chem. Phys., 60, 633 (1974).

    Article  CAS  Google Scholar 

  5. P. McGuire and D. J. Kouri, J. Chem. Phys., 60, 2488 (1974).

    Article  CAS  Google Scholar 

  6. P. McGuire, J. Chem. Phys., 62, 525 (1975).

    Article  CAS  Google Scholar 

  7. P. McGuire, Chem. Phys., 13, 81 (1976).

    Article  CAS  Google Scholar 

  8. G. A. Parker and R. T. Pack, J. Chem. Phys., 66, 2850 (1977).

    Article  CAS  Google Scholar 

  9. D. J. Kouri and Y. Shimoni, J. Chem. Phys., 67, 86 (1977).

    Article  Google Scholar 

  10. D. Secrest, J.Chem. Phys., 62, 710 (1975).

    Article  CAS  Google Scholar 

  11. V. Khare, J. Chem. Phys., 67, 3897 (1977).

    Article  CAS  Google Scholar 

  12. M. A. Brandt and D. G. Truhlar, Chem. Phys., 13, 461 (1976).

    Article  CAS  Google Scholar 

  13. M. Tamir and M. Shapiro, Chem. Phys. Lett., 31., 166 (1975).

    Article  CAS  Google Scholar 

  14. M. Jacob and G. C. Wick, Ann. Phys., 7, 404 (1959).

    Article  Google Scholar 

  15. M. Shapiro and M. Tamir, Chem. Phys. 13, 215 (1976).

    Article  CAS  Google Scholar 

  16. D. J. Kouri, Phys. Lett., 31, 599 (1975).

    CAS  Google Scholar 

  17. J. M. Launay, J. Phys. B., 9, 1823 (1976).

    Article  CAS  Google Scholar 

  18. Y. Shimoni and D. J. Kouri, J. Chem. Phys., 66, 2841 (1977).

    Article  CAS  Google Scholar 

  19. Y. Shimoni and D. J. Kouri, J. Chem. Phys., 65, 3372 (1976).

    Article  CAS  Google Scholar 

  20. Y. Shimoni and D. J. Kouri, J. Chem. Phys., 65, 3958 (1976).

    Article  CAS  Google Scholar 

  21. R. Schinke and P. McGuire, Chem. Phys., 128, 129 (1978).

    Article  Google Scholar 

  22. Y. Khare, D. J. Kouri and R. T. Pack. J. Chem. Phys. (1978).

    Google Scholar 

  23. D. J. Kouri, T. G. Heil and Y. Shimoni, J. Chem. Phys., 65, 226 (1976).

    Article  CAS  Google Scholar 

  24. V. Khare, D. J. Kouri, J. Chem. Phys. (1978).

    Google Scholar 

  25. R. T. Pack, J.Chem. Phys., 66, 1557 (1977).

    Article  CAS  Google Scholar 

  26. P. McGuire and H. Kruger, J. Chem. Phys., 63, 1090 (1975).

    Article  CAS  Google Scholar 

  27. M. H. Alexander and P. J. McGuire, J. Chem. Phys., 64, 452 (1976).

    Article  CAS  Google Scholar 

  28. P. McGuire and J. P. Toennics, J.Chem. Phys., 62, 4623 (1975).

    Article  CAS  Google Scholar 

  29. M. H. Alexander and P. McGuire, Chem. Phys., 12, 31 (1976).

    Article  CAS  Google Scholar 

  30. M. Alexander, Chem. Phys. Lett., 38, 417 (1976).

    Article  CAS  Google Scholar 

  31. S. I. Chu and A. Dalgarno, Proc. Roy Soc. (London) A342, 191 (1975).

    Google Scholar 

  32. S. I. Chu and A. Dalgarno, J. Chem. Phys., 63, 2115 (1975).

    Article  CAS  Google Scholar 

  33. S. Green and P. Thaddeus, Astrophys. 205, 266 (1976).

    Article  Google Scholar 

  34. S. Green, Chem. Phys. Lett. 38, 293 (1976).

    Article  CAS  Google Scholar 

  35. B. J. Garrison et al. Astrophys. J. Lett., 200, L175 (1975).

    Article  CAS  Google Scholar 

  36. S. Green and L. Monchick, J. Chem. Phys., 63, 4198 (1975).

    Article  CAS  Google Scholar 

  37. L. Monchick and S. Green, J. Chem. Phys., 63, 2000 (1975).

    Article  CAS  Google Scholar 

  38. U. Buck and P. McGuire, (to be published).

    Google Scholar 

  39. S. Green, J. Chem. Phys., 64, 3463 (1976).

    Article  CAS  Google Scholar 

  40. S. Green and L. Monchick, J. Chem. Phys., 66, 3085 (1977).

    Article  Google Scholar 

  41. L. D. Thomas et al., Chem. Phys., 27, 237 (1978).

    Article  CAS  Google Scholar 

  42. D. J. Kouri and P. McGuire, Chem. Phys. Lett., 29, 414 (1974).

    Article  CAS  Google Scholar 

  43. M. H. Alexander, J. Chem. Phys., 66, 4608 (1977).

    Article  CAS  Google Scholar 

  44. P. McGuire, Chem. Phys., 8, 231 (1975).

    Article  CAS  Google Scholar 

  45. L. Monchick, J. Chem. Phys., 67, 4626 (1977).

    Article  CAS  Google Scholar 

  46. J. H. Ferziger and M. G. Kaper, Mathe-atical Theory of Transport processes in gases (N. Holland, Amsterdam, 1972).

    Google Scholar 

  47. L. Monchick, Physics of Fluids, 7, 882 (1964).

    Article  CAS  Google Scholar 

  48. W. Wielsen and R. G. Gordon, J. Chem. Phys., 58, 4149 (1973).

    Article  Google Scholar 

  49. H. Rabitz, Ann. Rev. Phys. Chem., 25, 155 (1974).

    Article  CAS  Google Scholar 

  50. S. Green, J. Chem. Phys., 62, 3568 (1975).

    Article  CAS  Google Scholar 

  51. L. Monchick and D. J. Kouri, J. Chem. Phys. (1978).

    Google Scholar 

  52. D. M. Chase, Phys. Rev. 104, 838 (1956).

    Article  CAS  Google Scholar 

  53. K. Takayanagi, Progr. Theoret. Phys. Suppl. 25 40 (1963).

    Article  Google Scholar 

  54. K. M. Kramer and R. B. Bernstein, J. Chem. Phys., 40, 200 (1964).

    Article  CAS  Google Scholar 

  55. R. D. Levine, Chem. Phys. Lett., 4, 211 (1969).

    Article  CAS  Google Scholar 

  56. E. S. Chang and A. Temkin, Phys. Rev. Lett., 28, 203 (1972).

    Article  Google Scholar 

  57. N. Chandra and F. A. Gianturco, Chem. Phys. Lett., 24 326 (1974).

    Article  CAS  Google Scholar 

  58. P. G. Burke, N. Chandra and F. A. Gianturco, J. Phys. B 5, 2212 (1972).

    Article  CAS  Google Scholar 

  59. M. Shugard and A. U. Hazi, Phys. Rev. A12, 1895 (1975).

    Google Scholar 

  60. P. G. Burke and L. T. Sinfailarn, J. Phys B 3, 641 (1970).

    Article  CAS  Google Scholar 

  61. R. J. Cross, J. Chem. Phys., 49, 1753 (1968).

    Article  CAS  Google Scholar 

  62. U. Buck and V. Khare, Chem. Phys. 26, 215 (1977).

    Article  CAS  Google Scholar 

  63. R. T. Pack, Chem. Phys. Lett., 14, 393 (1972).

    Article  CAS  Google Scholar 

  64. T. P. Tsien and R. T. Pach, Chem. Phys. Lett., 6, 54 (1970).

    Article  CAS  Google Scholar 

  65. C. F. Curtiss, J. Chem. Phys., 49, 1952 (1958).

    Article  Google Scholar 

  66. L. W. Hunter, J. Chem. Phys., 62, 2855 (1975).

    Article  CAS  Google Scholar 

  67. J. M. Bowman and S. C. Leasure, J. Chem. Phys., 66, 288 (1977).

    Article  CAS  Google Scholar 

  68. D. J. Kouri, T. G. Heil and Y. Shimoni, J. Chem. Phys., 65, 1462 (1976).

    Article  CAS  Google Scholar 

  69. M. A. Brandt and D. G. Truhlar, Chem. Phys. Lett., 23, 48 (1973).

    Article  CAS  Google Scholar 

  70. R. Goldflam, S. Green and D. J. Kouri, J. Chem. Phys., 67, 225 (1977).

    Article  CAS  Google Scholar 

  71. T. P. Tsien, G. A. Parker and R. J. Pack, J. Chem. Phys., 59, 5373 (1973).

    Article  CAS  Google Scholar 

  72. D. E. Fitz and P. McGuire, Chem. Phys. Lett., 44, 503 (1976).

    Article  CAS  Google Scholar 

  73. R. Goldflam, D. J. Kouri and S. Green, 67, 5661 (1977).

    Google Scholar 

  74. G. A. Parker and R. T. Pack, J. Chem. Phys., 68, 1585 (1978).

    Article  CAS  Google Scholar 

  75. L. Monchick and E. A. Mason, J. Chem. Phys., 35, 1676 (1961).

    Article  CAS  Google Scholar 

  76. L. Monchick and S. Green, J. Chem. Phys., 63, 4198 (1975).

    Article  Google Scholar 

  77. R. T. Pack, Chem. Phys. Lett., 55, 197 (1978).

    Article  CAS  Google Scholar 

  78. J. M. Bowman and S. C. Leasure, J. Chem. Phys., 66, 288 (1977).

    Article  CAS  Google Scholar 

  79. S. C. Leasure and J. M. Bowman, Chem. Phys. Lett., 48, 179 (1977).

    Article  CAS  Google Scholar 

  80. P. McGuire, J. Chem. Phys., 62, 525 (1975).

    Article  CAS  Google Scholar 

  81. F. A. Gianturco and U. Lamanna, Chem. Phys. Lett., 6, 326 (1970).

    Article  CAS  Google Scholar 

  82. R. Schinke and P. McGuire, Chem. Phys. 28, 129 (1978).

    Article  CAS  Google Scholar 

  83. A. Karo et al., Status Report, Argonne Nat. Laboratory (1974).

    Google Scholar 

  84. F. A. Gianturco and U. T. Lamanna, Chem. Phys. (1978).

    Google Scholar 

  85. M. Rabitz, J. Chem. Phys., 57, 1718 (1972).

    Article  CAS  Google Scholar 

  86. G. Zarur and H. Rabitz, J. Chem. Phys., 59, 943 (1973).

    Article  CAS  Google Scholar 

  87. H. Rabitz Modern Theoretical Chemistry, Vol. 1 pp. 33 (Plenum Press, N.Y. 1976).

    Google Scholar 

  88. H. Rabitz and G. Zarur, J. Chem. Phys. 61, 5076 (1974).

    Article  CAS  Google Scholar 

  89. H. Rabitz and G. Zarur, J. Chem. Phys. 62, 1425 (1975).

    Article  CAS  Google Scholar 

  90. M. H. Alexander, J. Chem. Phys., 61, 5167 (1974).

    Article  CAS  Google Scholar 

  91. M. H. Alexander, J. Chem. Phys., 8, 86 (1975).

    Article  CAS  Google Scholar 

  92. S. I. Chu and A. Dalgarno, Asptrophys. J. 199, 637 (1975).

    Article  CAS  Google Scholar 

  93. M. Verter and H. Rabitz, J. Chem. Phys., 64, 2939 (1975).

    Article  Google Scholar 

  94. S. Green, J. Chem. Phys., 62, 3568 (1975).

    Article  CAS  Google Scholar 

  95. G. Zarur and H. Rabitz, J. Chem. Phys., 60, 2057 (1974).

    Article  CAS  Google Scholar 

  96. S. I. Chu, J. Chem. Phys., 62, 4089 (1975).

    Article  CAS  Google Scholar 

  97. B. H. Choi and K. T. Tang, J. Chem. Phys., 64, 942 (1976).

    Article  CAS  Google Scholar 

  98. Y. Itikawa, J. Phys. Soc., 39, 1059 (1975).

    Article  CAS  Google Scholar 

  99. A. E. De Pristo and M. H. Alexander, J. Chem. Phys., 66, 1334 (1977).

    Article  Google Scholar 

  100. S. Augustin and H. Rabitz, J. Chem. Phys., 64, 4821 (1976).

    Article  CAS  Google Scholar 

  101. R. Ramaswamy and H. Rabitz, J. Chem. Phys., 66, 152 (1977).

    Article  CAS  Google Scholar 

  102. H. K. Shin, J. Chem.Phys., 46, 3688 (1967).

    Article  CAS  Google Scholar 

  103. F. M. Mies and K. Shuler, J. Chem. Phys., 37, 177 (1962).

    Article  CAS  Google Scholar 

  104. K. Takayanagi, Progr. Theor. Phys., (Kyoto), 8, 497 (1952).

    Article  CAS  Google Scholar 

  105. R. Marriott, Proc. Phys. Soc, 83, 159 (1964).

    Article  CAS  Google Scholar 

  106. F. A. Gianturco and U. T. Lamanna, Chem. Phys., 17, 255 (1976).

    Article  CAS  Google Scholar 

  107. F. A. Gianturco and R. Marriott, J. Phys. B 2, 1332 (1969).

    Article  CAS  Google Scholar 

  108. F. A. Gianturco and U. T. Lamanna, Chem. Phys. (1978).

    Google Scholar 

  109. F. A. Gianturco, U. T. Lamanna and I. Baraldi, J. Chim. Phys., 74, 437 (1977).

    CAS  Google Scholar 

  110. F. A. Gianturco and U. T. Lamanna, Chem. Phys. 3, 110 (1974).

    Article  CAS  Google Scholar 

  111. F. A. Gianturco and U. T. Lamanna, Chem. Phys., 25, 401 (1977).

    Article  CAS  Google Scholar 

  112. A. E. De Pristo and M. H. Alexander, J. Chem. Phys., 63, 5327 (1975).

    Article  Google Scholar 

  113. A. E. De Pristo and M. H. Alexander, J. Chem. Phys., 64, 3009 (1976).

    Article  Google Scholar 

  114. A. E. De Pristo and M. H. Alexander, J. Phys B, 9, L39 (1976).

    Article  Google Scholar 

  115. A. E. De Pristo and M. H. Alexander, J. Phys. B 9, 2713 (1976).

    Article  Google Scholar 

  116. A. E. De Pristo and M. H. Alexander, Chem. Phys. Lett., 44, 214 (1976).

    Article  Google Scholar 

  117. N. F. Mott and M. S. W. Massey, The Theory of atomic collisions, (Claredon Press Oxford, U.K. 1965).

    Google Scholar 

  118. A. M. Arthurs and A. Dalgarno, Proc. R. Soc. (London Ser.) A 256, 540 (1960).

    Article  Google Scholar 

  119. K. Takayanagi, Adv. At. Mol. Phys., 1, 149 (1965).

    Article  Google Scholar 

  120. C. F. Curtiss and A. Hardisson, J. Chem. Phys., 46, 2618 (1967).

    Article  CAS  Google Scholar 

  121. L. W. Hunter and C. F. Curtiss, J. Chem. Phys., 58, 3897 (1973).

    Article  CAS  Google Scholar 

  122. D. Russell and C. F. Curtiss, J. Chem. Phys., 59, 1974 (1973).

    Article  CAS  Google Scholar 

  123. G.C. Balint-Kurti, Int. Review of Science, Phys. Chem. Series 2, Vol. 1, pag. 283 (Butterworth, London, 1975).

    Google Scholar 

  124. K. Takayanagi, Sc. Rept. Saitama Univ. A3, 87 (1959).

    Google Scholar 

  125. R. B. Bernstein et al., Proc. Roy Soc. London Ser. A274, 427 (1963).

    Article  Google Scholar 

  126. I. C. Percival, Proc. Phys. Soc. (London) 76, 206 (1960).

    Article  Google Scholar 

  127. R. D. Levine, Mol. Phys., 22, 497 (1971).

    Article  CAS  Google Scholar 

  128. R. D. Levine and G. G. Balint-Kurti, Chem. Phys. Lett., 6, 101 (1970).

    Article  CAS  Google Scholar 

  129. M. J. Seaton, Proc. Phys. Soc. (London), 77, 174 (1961).

    Article  CAS  Google Scholar 

  130. M. Van Seggern and P. J. Toennies, Chem. Phys. Lett., 6, 101 (1970).

    Article  Google Scholar 

  131. G. G. Balint-Kurti and R. D. Levine, Chem. Phys. Lett., 7, 107 (1970).

    Article  CAS  Google Scholar 

  132. S. M. Tarr and H. Rabitz, J. Chem. Phys., 68, 642 (1978).

    Article  CAS  Google Scholar 

  133. R. B. Gerber, Chem. Phys., 16, 19 (1976).

    Article  CAS  Google Scholar 

  134. L. Eno and G. G. Balint-Kurti, Chem. Phys., 23, 295 (1977).

    Article  CAS  Google Scholar 

  135. L. Eno, G. G. Balint-Kurti, and R. Saktreger, Chem. Phys., 29, 453 (1978).

    Article  CAS  Google Scholar 

  136. F. H. Mies, J. Chem. Phys., 40, 523 (1964).

    Article  CAS  Google Scholar 

  137. J. B. Delas, W. R. Thorson and S. K. Khudson Phys. Rev. A6, 709 (1972).

    Google Scholar 

  138. W. M. Miller, Adv. Chem. Phys., 30, 77 (1975).

    Article  CAS  Google Scholar 

  139. D. L. Bunker, Methods Comp. Phys., 10, 287 (1971).

    CAS  Google Scholar 

  140. W. H. Miller, Adv. Chem. Phys., 25, 69 (1974).

    Article  Google Scholar 

  141. D. A. Micha, in Modem Theoret. Chem. Vol. 1 (W. M. Miller Ed., Plenum Press, N.Y. 1976).

    Google Scholar 

  142. D. J. Kouri, J. Chem. Phys., 48, 448 (1968).

    Google Scholar 

  143. G. Wolken Jr., J. Chem. Phys., 56, 259 (1972).

    Google Scholar 

  144. E. Ficocelli-Varracchio, Chem. Phys., 18, 37 (1976).

    Article  Google Scholar 

  145. E. Ficocelli-Varracchio, Mol. Phys., 30, 1117 (1975).

    Article  Google Scholar 

  146. R. B. Gerber, N. C. Zaritsky and U. Minglegrin, Mol. Phys. 35, 1247 (1978).

    Article  CAS  Google Scholar 

  147. N. C. Zaritsky and U. Minglegrin and R.B. Gerber, Mol. Phys. 35, 1269 (1978).

    Article  CAS  Google Scholar 

  148. e. g. see the recent review by M. Faubel and J. P. Toennies, Adv. At. Mol. Phys., 13, 229 (1977).

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1979 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Gianturco, F.A. (1979). Dimensionality Reduction Methods for Rotovibrational Cross Section Calculations. In: The Transfer of Molecular Energies by Collision: Recent Quantum Treatments. Lecture Notes in Chemistry, vol 11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-93122-2_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-93122-2_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09701-3

  • Online ISBN: 978-3-642-93122-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics