Skip to main content

Calculations on Collinear Reactions Using Hyperspherical Coordinates

  • Chapter
The Theory of Chemical Reaction Dynamics

Part of the book series: NATO ASI Series ((ASIC,volume 170))

Abstract

A number of new effects in reaction dynamics discovered by theoretical investigations using hyperspherical coordinates, e.g.

vibrational adiabaticity oscillating reactivity resonances and their mode specific decay vibrational bonding

are presented and discussed with respect to their experimental consequences. Finally it is shown that the important class of organic SN2-reactions may be investigated in an approximate collinear treatment using a combination of molecular structure and reaction dynamics theory.

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 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover 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.

Similar content being viewed by others

References

  1. T.H. Gronwall, Annals. Math. 33 (1932) 279 T.H. Gronwall, Phys. Rev. 51 (1937) 655 J.H. Bartlett, Phys. Rev. 51 (1937) 661 P.M. Morse and H. Feshbach, “Methods of Theoretical Physics”, (McGraw-Hill, 1953), p. 1729

    Article  Google Scholar 

  2. U. Fano, Rep. Prog. Phys. 46 (1983) 97 and Ref. therein CD. Liu and J.H. Macek, Phys. Rev. A30 (1984) 2161 and Ref. therein C.H. Greene and C.W. Clark, Phys. Rev. A30 (1984) 2161 and Ref. therein H. Klar, in “Electronic and Atomic Collisions”, eds. J. Eichler, I.V. Hertel and N. Stolterfoht (Elsevier, 1984), p. 767 and Ref. therein

    Article  Google Scholar 

  3. R.C. Whitten and J.S. Sims, Phys. Rev. A9 (1974) 1586 C.H. Greene, Phys. Rev. A26 (1982) 2974

    Google Scholar 

  4. R.E. Clapp, Phys. Rev. 76 (1949) 873 L.H. Delves, Nucl. Phys. 9 (1959) 391; 20 (1960) 275

    Article  CAS  Google Scholar 

  5. F.T. Smith, Phys. Rev. 120 (1960) 1058 F.T. Smith, in “Kinetic Processes in Gases and Plasmas”, ed. A.R. Hochstim (Academic Press, 1969), p. 321.

    Article  Google Scholar 

  6. R.D. Levine and R.B. Bernstein, Chem. Phys. Letters 11 (1971) 552 C. Rebick and R.D. Levine, J. Chem. Phys. 58 (1973) 3942

    Article  CAS  Google Scholar 

  7. M. Tamir, U. Halavee and R.D. Levine, Chem. Phys. Letters 25 (1974) 38

    Article  CAS  Google Scholar 

  8. A. Kuppermann, Chem. Phys. Letters 32 (1975) 374 R.A. Marcus, Faraday Symp. Chem. Soc. 10 (1975) 60

    Article  CAS  Google Scholar 

  9. C.W. Clark and J. Siegel, J. Phys. B 13 (1980) L 31 Vo Ky Lan, M. Le Dourneuf and J.M. Launay, in “Electron-Atom and Electron-Molecule Collisions”, ed. J. Hinze (Plenum Press, 1983), p. 161

    Article  Google Scholar 

  10. C.H. Greene and Ch. Jungen, Abstract of Papers, 11th Int. Conf. Physics of Electronic and Atomic Collision, ed. S. Datz (Gattingburg, Tennesse, USA, 1981), p. 1019 J.G. Frey, Chem. Phys. Letters 102 (1983) 421

    Google Scholar 

  11. A. Kuppermann, J.A. Kaye and J.P. Dwyer, Chem. Phys. Letters 74 (1980) 257

    Article  CAS  Google Scholar 

  12. G. Hauke, J. Manz and J. Römelt, J. Chem. Phys. 73 (1980) 5040 J. Römelt, Chem. Phys. Letters 74 (1980) 263

    Article  CAS  Google Scholar 

  13. G.L. Hofacker, Z. Naturforsch. A18 (1963) 607 R.A. Marcus, J. Chem. Phys. 45 (1966) 4432, 4600

    Google Scholar 

  14. J. Manz, Chem. Phys. Letters 15 (1972) 136

    Article  CAS  Google Scholar 

  15. D.J. Diestler, in “Atom-Molecule Collision Theory”, ed. R.B. Bernstein (Plenum Press, 1979), p. 655

    Google Scholar 

  16. M. Baer, J. Chem. Phys. 62 (1975) 305

    Article  CAS  Google Scholar 

  17. J. Manz, Comment on At. Mol. Phys. (1985), in press

    Google Scholar 

  18. F.T. Smith, J. Chem. Phys. 31 (1959) 1352

    Article  CAS  Google Scholar 

  19. U.K. Babamov and R.A. Marcus, J. Chem. Phys. 74 (1981) 1790

    Article  CAS  Google Scholar 

  20. J.M. Launay and M. Le Dourneuf, J. Phys. B 15 (1982) L 455

    Article  Google Scholar 

  21. F. Mrugala and J. Römelt, to be published

    Google Scholar 

  22. D.K. Bondi and J.N.L. Connor, Chem. Phys. Letters 92 (1982) 570 D.K. Bondi and J.N.L. Connor, J. Chem. Phys., in press

    Article  CAS  Google Scholar 

  23. C.L. Shoemaker, N. AbuSalbi and D.J. Kouri, J. Chem. Phys. 87 (1983) 5389

    Article  CAS  Google Scholar 

  24. J. Manz and J. Römelt, Chem. Phys. Letters 77 (1981) 172 J.A. Kaye and A. Kuppermann, Chem. Phys. Letters 78 (1981) 546; 115 (1985) 158

    Article  CAS  Google Scholar 

  25. J. Römelt, Chem. Phys. Letters 87 (1982) 259

    Article  Google Scholar 

  26. V. Aquilanti, G. Grossi and A. Lagana, Chem. Phys. Letters 93 (1982) 174, 179 V. Aquilanti, S. Cavalli, G. Grossi and A. Laganà, J. Mol. Struc. 93 (1983) 319; 107 (1984) 95

    Article  CAS  Google Scholar 

  27. V.K. Babamov, V. Lopez and R.A. Marcus, J. Chem. Phys. 78 (1983) 5621; 80 (1984) 1812; Chem. Phys. Letters 101 (1983) 507

    Article  CAS  Google Scholar 

  28. C. Hiller, J. Manz, W.H. Miller and J. Römelt, J. Chem. Phys. 78 (1983) 3850

    Article  CAS  Google Scholar 

  29. M. Born and J.R. Oppenheimer, Ann. Physik 84 (1927) 457

    Article  CAS  Google Scholar 

  30. J.H. van Vleck, J. Chem. Phys. 4 (1936) 327

    Article  Google Scholar 

  31. J. Römelt, Chem. Phys. 79 (1983) 197

    Article  Google Scholar 

  32. D.K. Bondi, J.N.L. Connor, J. Manz and J. Römelt, Mol. Phys. 50 (1983) 467

    Google Scholar 

  33. N.B.H. Jonathan, P.M.Sellers and A.J. Stace, Mol. Phys. 43 (1981) 215

    Article  CAS  Google Scholar 

  34. J.A. Kaye and A. Kuppermann, Chem. Phys. Letters 77 (1981) 573. Manz and J. Römelt, Chem. Phys. Letters 81 (1981) 179

    Article  CAS  Google Scholar 

  35. E. Pollak, J. Chem. Phys. 78 (1983) 1228

    Article  CAS  Google Scholar 

  36. N. AbuSalbi, S.-H. Kim, D.J. Kouri and M. Baer, Chem. Phys. Letters 112 (1984) 502 D.C. Clary, Mol. Phys. 53 (1984) 3 E. Pollak, M. Baer, N. AbuSalbi and D.J. Kouri, Chem. Phys., in press

    Google Scholar 

  37. M. Baer, J. Chem. Phys. 62 (1975) 305

    Article  CAS  Google Scholar 

  38. R.D. Levine and R.B. Bernstein, in “Molecular Reaction Dynamics” (Clarendon Press, 1974)

    Google Scholar 

  39. N. AbuSalbi, D.J. Kouri, M. Lopez, U.K. Babamov and R.A. Marcus, Chem. Phys. Letters 103 (1984) 458

    Article  CAS  Google Scholar 

  40. P.V. Coveney, M.S. Child and J. Römelt, to be published

    Google Scholar 

  41. J. Manz and H.H.R. Schor, Chem. Phys. Letters 107 (1984) 549.L. Gertitschke, J. Manz, J. Römelt and H.H.R. Schor, J. Chem. Phys. 83 (1985) 208 J. Manz, J. Römelt and H.H.R. Schor, to be published

    Article  CAS  Google Scholar 

  42. J.A. Kaye and A. Kuppermann, Chem. Phys. Letters 92 (1982) 579

    Article  Google Scholar 

  43. E.E. Nikitin, in “Theory of Elementary Atomic and Molecular Processes” (Oxford Univ. Press, 1974)

    Google Scholar 

  44. J.P. Sung and D.W. Setser, Chem. Phys. Letters 48 (1977) 413 P. Beadle, M.R. Dunn, N.B.H. Jonathan, J.P. Liddy and J.C. Naylor, J. Chem. Soc. Faraday Trans. 2, 74 (1978) 2170 K. Tamagake, D.W. Setser and J.P. Sung, J. Chem. Phys. 73 (1980) 2203 L.S. Dzelzkalns and F. Kaufmann, J. Chem. Phys. 79 (1983) 3836

    Article  CAS  Google Scholar 

  45. E. Würzberg and P.L. Houston, J. Chem. Phys. 72 (1980) 5915 J.W. Hepburn, K. Liu, R.G. Macdonald, F.J. Northrup and J.C. Polanyi, J. Chem. Phys. 75 (1981) 3353

    Article  Google Scholar 

  46. C.C. Mei and C.B. Moore, J. Chem. Phys. 67 (1977) 3936, 70 (1979) 1759

    Article  CAS  Google Scholar 

  47. B.C. Barrett, D.W. Schwenke, R.T. Skodje, D. Thirumalai, I.C. Thompson and D.G. Truhlar, in “Resonances in Electron-Molecule Scattering, van der Waals Complexes and Reactive Chemical Dynamics”, ed. D.G. Truhlar (Plenum Press, 1984), p. 421

    Google Scholar 

  48. T. Carrington Jr., J.C. Polanyi and J.R. Wolf, in “Physics of Electronic and Atomic Collisions”, ed. S. Datz (North Holland, 1982), p. 393 and Ref. therein H.R. Mayne, R.A. Poinier and J.C. Polanyi, J. Chem. Phys. 80 (1984) 4025 W. Kamke, B. Kamke, I. Hertel and A. Gallagher, J. Chem. Phys. 80 (1984) 4879

    Google Scholar 

  49. R.H. Bisseling, R. Kosloff, J. Manz and H.H.R. Schor, Ber. Bunsenges. Phys. Chem. 89 (1985) 270 R.H. Bisseling, R. Kosloff and J. Manz, J. Chem. Phys., in press R.H. Bisseling, R. Kosloff, J. Manz and J. Rbmelt, to be published

    CAS  Google Scholar 

  50. N. Rosen, J. Chem. Phys. 1 (1933) 319 E. Thiele and D.J. Wilson, J. Chem. Phys. 35 (1961) 1256 R.M. Hedges Jr. and W.P. Reinhardt, Chem. Phys. tetters 91 (1982) 241; J. Chem. Phys. 78 (1983) 3964

    Article  CAS  Google Scholar 

  51. M.S. Child and T. Halonen, Adv. Chem. Phys. 57 (1984) 1 and Refs. therein

    Google Scholar 

  52. K.C. Kulander, J. Chem. Phys. 79 (1983) 1279

    Article  CAS  Google Scholar 

  53. K.C. Kulander, J. Manz and H.H.R. Schor, J. Chem.Phys., in press J. Manz and H.H.R. Schor, Chem. Phys. Letters 107 (1984) 542

    Google Scholar 

  54. G. Hose and H.S. Taylor, J. Chem. Phys. 76 (1982) 5356 Phys. Rev. Letters 51 (1983) 947 G. Hose, H.S. Taylor and Y.Y. Bai, J. Chem. Phys. 80 (1984) 4363

    Article  CAS  Google Scholar 

  55. T.C. Thompson and D.G. Truhlar, Chem. Phys. Letters 101 (1983) 235 V. Lopez and R.A. Marcus, Chem. Phys. Letters 93 (1982) 232 K.N. Swamy and W.L. Hase, J. Chem. Phys. 82 (1985) 123 H. Shyldkrot and M. Shapiro, J. Chem. Phys. 79 (1983) 5927

    Article  CAS  Google Scholar 

  56. M.D. Feit and J.A. Fleck Jr., J. Chem. Phys. 78 (1983) 301

    Article  CAS  Google Scholar 

  57. J. Manz, R. Meyer, E. Pollak and J. Römelt, Chem. Phys. Letters 93 (1982) 184

    Article  CAS  Google Scholar 

  58. E. Pollak, in “Intramolecular Dynamics”, eds. J. Jortner and B. Pullmann (D. Reidel, 1982), p. 1

    Google Scholar 

  59. D.C. Clary and J.N.L. Connor, Chetn. Phys. Letters 94 (1983) 81 E. Pollak, Chem. Phys. Letters 94 (1983) 85 J. Manz, R. Meyer and J. Römelt, Chem. Phys. Letters 96 (1983) 607

    Article  CAS  Google Scholar 

  60. J. Manz, R. Meyer, E. Pollak, J. Römelt and H.H.R. Schor, Chem. Phys. 83 (1984) 333 J. Manz, R. Meyer and H.H.R. Schor, J. Chem. Phys. 80 (1984) 1562 D.C. Clary and J.N.L. Connor, J. Phys. Chem. 88 (1984) 2758

    Article  CAS  Google Scholar 

  61. E. Pollak, Comment on At. Mol. Phys. 15 (1984) 73 J. Römelt and E. Pollak, in “Resonances in Electron-Molecule Scattering, van der Waals Complexes and Reactive Chemical Dynamics”, ed. D.G. Truhlar (Plenum Press, 1984), p. 353 J. Manz and J. Römelt, Nachr. Chem. Techn. Lab. 33 (1985) 210

    CAS  Google Scholar 

  62. B.S. Ault and J. Manz, Chem. Phys. Letters, in press

    Google Scholar 

  63. A. Kupperman, in “Potential Energy Surfaces and Dynamics Calculations”, ed. D.G. Iruhlar (Plenum Press, 1981), p. 375

    Google Scholar 

  64. B.R. Johnson, J. Chem. Phys. 73 (1983) 1906, 1916

    Article  Google Scholar 

  65. R.T. Pack, Chem. Phys. Letters 108 (1984) 333

    Article  CAS  Google Scholar 

  66. H. Mishra and J. Linderberg, Mol. Phys. 50 (1983) 91 M. Mishra, J. Linderberg and Y. Öhrn, Chem. Phys. Letters 111 (1984) 439

    Article  CAS  Google Scholar 

  67. A. Kuppermann, private communication

    Google Scholar 

  68. C.K. Ingold, “Structure and Mechanism in Organic Chemistry” (Cornell Univ. Press, 1953)

    Google Scholar 

  69. P. Walden, Chem. Ber. 29 (1896) 133; 30 (1897) 3146

    Article  Google Scholar 

  70. S.D. Peyerimhoff and J. Römelt, Phys. Bl. 40 (1984) 300 H. Dohmann and J. Römelt, to be published

    CAS  Google Scholar 

  71. e.g. K. Muller and L.D. Brown, Iheor. Chim. Acta (Berl.) 53 (1979) 75 and Refs. therein

    Article  Google Scholar 

  72. K. Morokuma, S. Kato, K. Kitaura, S. Obara, K. Ohta and M. Hanamura, in “Proceedings of the 4th Int. Congress of Quantum Chemistry”, eds. P.-0. Löwdin and B. Pullmann (D. Reidel Publ. Comp., 1983), p. 221

    Google Scholar 

  73. C. Leforestier, J. Chem. Phys. 68 (1978) 4406

    Article  CAS  Google Scholar 

  74. K. Ishida, K. Morokuma and A. Kormonicki, J. Chem. Phys. 66 (1977) 2153

    Article  CAS  Google Scholar 

  75. J. Linderberg, in “Intramolecular Dynamics”, eds. J. Jortner and B. Pullmann (D. Reidel, 1982), p. 325 J. Linderberg, in “Proceedings of the 4th Int. Congress on Quantum Chemistry”, eds. P.-0. Löwdin and B. Pullmann (D. Reidel, 1983) p. 7 J. Avery, B. Christensen-Dalsgaard, P.S. Larsen and Shen Hengyi, Intern. J. Quant. Chem. S 18 (1984) 321

    Google Scholar 

  76. T. Carrington Jr. and W.H. Miller, J. Chem. Phys. 81 (1984) 3942

    Article  CAS  Google Scholar 

  77. Potential Energy Surfaces and Dynamics Calculations”, ed. D.G. Truhlar (Plenum Press, 1981) and Ref. therein

    Google Scholar 

  78. R.J. Buenker, G. Hirsch, S.D. Peyerimhoff, P.J. Bruna, J. Römelt, M. Bettendorff and C. Petrongolo, in “Studies in Physical and Theoretical Chemistry”, Vol. 21 (Elsevier Publ. Comp., 1982), p. 81 and Refs. therein

    Google Scholar 

  79. B.C. Garrett and D.G. Truhlar, Theor. Chem.: Adv. Persp. 6A (1981) 215 J.M. Launay and M.L. Dourneuf, poster presented at Molec V, Jerusalem 03.-07.09.1984

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1986 D. Reidel Publishing Company

About this chapter

Cite this chapter

Römelt, J. (1986). Calculations on Collinear Reactions Using Hyperspherical Coordinates. In: Clary, D.C. (eds) The Theory of Chemical Reaction Dynamics. NATO ASI Series, vol 170. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4618-7_4

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-4618-7_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-8552-6

  • Online ISBN: 978-94-009-4618-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics