Theoretical Chemistry Accounts

, Volume 127, Issue 1–2, pp 1–17 | Cite as

Wavepacket quantum dynamics

  • Gabriel G. Balint-KurtiEmail author
Feature Article


The article reviews the use of wavepackets in molecular quantum dynamics. The basic theory concerned with their use in both reactive molecular scattering and photodissociation dynamics is outlined. The great advantage of using wavepackets is that the full S matrix for the scattering problem need not be evaluated, and the numerical effort can be concentrated on those initial molecular quantum states which are of interest. Wavepackets may be used within a time-dependent or a time-independent framework, both are discussed and compared. Some examples of calculations from both reactive scattering and photodissociation theory are given.


Wavepackets Quantum mechanics Molecular dynamics Molecular collisions Reactive scattering Photodissociation 



I would like to thank my many colleagues and friends who have collaborated with me over many years for their essential part in developing the methods outlined in this review and for performing many of the calculations used as illustrations. In particular I thank Marlies Hankel, Stephen K. Gray, Alex Brown, F. Javier Aoiz, Niyazi Bulut, Tianshu Zhu, Mohammad Noh Daud, Ezinvi Baloitcha, Richard N. Dixon, László Füsti-Molnár, Clay C. Marston, Alison Offer, George C. Schatz, Moshe Shapiro and Sean C. Smith.


  1. 1.
    Mazur J, Rubin RJ (1959) J Chem Phys 31:1395CrossRefGoogle Scholar
  2. 2.
    McCullough EA, Wyatt RE (1969) J Chem Phys 51:1253CrossRefGoogle Scholar
  3. 3.
    McCullough EA, Wyatt RE (1971) J Chem Phys 54:3578CrossRefGoogle Scholar
  4. 4.
    Zuhrt C, Kamal T, Zulicke L (1975) Chem Phys Lett 36:396CrossRefGoogle Scholar
  5. 5.
    Kellerhals NSE, Raff L (1976) J Chem Phys 64:818CrossRefGoogle Scholar
  6. 6.
    Agrawal PM, Raff LM (1981) J Chem Phys 74:5076CrossRefGoogle Scholar
  7. 7.
    Leforestier C (1984) Chem Phys 87:241CrossRefGoogle Scholar
  8. 8.
    Zhang ZH, Kouri DJ (1986) Phys Rev A 34:2687Google Scholar
  9. 9.
    Lester WA Jr (1976) In: Miller WH (ed) Modern theoretical chemistry, Vol 1. Plenum Press, New York, pp 1–32Google Scholar
  10. 10.
    Miller WH (1969) J Chem Phys 50:407CrossRefGoogle Scholar
  11. 11.
    Wolken JG, Miller WH, Karplus M (1972) J Chem Phys 56:4930CrossRefGoogle Scholar
  12. 12.
    Wolken JG, Karplus M (1974) J Chem Phys 60:351CrossRefGoogle Scholar
  13. 13.
    Schatz GC, Kuppermann A (1976) J Chem Phys 65:4642CrossRefGoogle Scholar
  14. 14.
    Schatz GC, Kuppermann A (1976) J Chem Phys 65:4668CrossRefGoogle Scholar
  15. 15.
    Mielke SL, Lynch GC, Truhlar DG, Schwenke DW (1994) J Phys Chem 98:8000CrossRefGoogle Scholar
  16. 16.
    Heller EJ (1978) J Chem Phys 68:2066CrossRefGoogle Scholar
  17. 17.
    Heller EJ (1978) J Chem Phys 68:3891CrossRefGoogle Scholar
  18. 18.
    Kulander KC, Heller EJ (1978) J Chem Phys 69:2439CrossRefGoogle Scholar
  19. 19.
    Heller EJ (1981) Accounts Chem Res 14:368CrossRefGoogle Scholar
  20. 20.
    Lee S-Y, Heller EJ (1982) J Chem Phys 76:3035CrossRefGoogle Scholar
  21. 21.
    Ben-Nun M, Quenneville J, Martinez T (2000) J Phys Chem A 104:5161CrossRefGoogle Scholar
  22. 22.
    Virshup AM, Punwong C, TVP, Lindquist BA, Ko C, Martinez T (2009) J Phys Chem B 113:3280CrossRefGoogle Scholar
  23. 23.
    Chen X, Batista VS (2006) J Chem Phys 125:124313CrossRefGoogle Scholar
  24. 24.
    Justin K, Wu Y, BJ-L, Batista VS (2009) Israel J Chem 49:187CrossRefGoogle Scholar
  25. 25.
    Iyengar SS, Sumner I, Jakowski J (2008) Phys J Chem B 112:7601CrossRefGoogle Scholar
  26. 26.
    Iyengar SS (2009) Internat J Quant Chem 109:3798CrossRefGoogle Scholar
  27. 27.
    Feit M, JAF Jr, Steiger A (1982) J Comp Phys 47:412Google Scholar
  28. 28.
    Feit MD, Fleck JJA (1983) J Chem Phys 78:301CrossRefGoogle Scholar
  29. 29.
    Kosloff D, Kosloff R (1983) J Comp Phys 52:35CrossRefGoogle Scholar
  30. 30.
    Kosloff R (1988) J Phys Chem 92:2087CrossRefGoogle Scholar
  31. 31.
    Tal-Ezer H, Kosloff R (1984) J Chem Phys 81:3967CrossRefGoogle Scholar
  32. 32.
    Kosloff D, Kosloff R (1986) J Comp Phys 63:363CrossRefGoogle Scholar
  33. 33.
    Kouri DJ, Mowrey RC (1987) J Chem Phys 86:2087CrossRefGoogle Scholar
  34. 34.
    Balint-Kurti GG, Dixon RN, Marston CC (1992) Internat Rev Phys Chem 11:317CrossRefGoogle Scholar
  35. 35.
    Jackson B (1995) Annu Rev Phys Chem 46:251CrossRefGoogle Scholar
  36. 36.
    Balint-Kurti GG (2003) Adv Chem Phys 128:249CrossRefGoogle Scholar
  37. 37.
    Meyer H-D, Worth GA (2003) Theoret Chem Acct 109:251CrossRefGoogle Scholar
  38. 38.
    Althorpe SC (2004) Int Rev Phys Chem 23:219CrossRefGoogle Scholar
  39. 39.
    Balint-Kurti GG, Brown A (2004) In: Lagana A, Lendvay G (eds) Theory of chemical reaction dynamics; Proceedings of the Nato advanced research workshop on the theory of dynamics of elementary chemical reactions. Kluwer Academic Publishers, New York, pp 149–185, ISBN 1-4020-2055-4Google Scholar
  40. 40.
    Chu T-S, Zhang Y, Han K-L (2006) Int Rev Phys Chem 25:201CrossRefGoogle Scholar
  41. 41.
    Balint-Kurti GG (2008) Internat Rev Phys Chem 27:507CrossRefGoogle Scholar
  42. 42.
    Goldstein H (1950) Classical mechanics. Addison-Wesley Publishing Co., ReadingGoogle Scholar
  43. 43.
    Dirac PAM (1958) The principles of quantum mechanics, 4th ed. Clarendon Press, OxfordGoogle Scholar
  44. 44.
    Marston CC, Balint-Kurti GG (1990) J Chem Phys, Phys Chem Chem Phys 91Google Scholar
  45. 45.
    Balint-Kurti GG, Dixon RN, Marston CC (1990) J Chem Soc Faraday Trans 86:1741CrossRefGoogle Scholar
  46. 46.
    Hankel M, Balint-Kurti GG, Gray SK (2001) J Phys Chem 105:2330Google Scholar
  47. 47.
    Hankel M, Smith SC, Allan RJ, Gray SK, Balint-Kurti GG (2006) J Chem Phys 125:164303CrossRefGoogle Scholar
  48. 48.
    Huang Y, Zhou W, Kouri DJ, Hoffman DK (1993) Chem Phys Lett 206:96CrossRefGoogle Scholar
  49. 49.
    Kouri D, Arnold M, Hoffman D (1993) Chem Phys Lett 203:166CrossRefGoogle Scholar
  50. 50.
    Hoffman DK, Huang Y, Zhu W, Kouri DJ (1994) J Chem Phys 101:1242CrossRefGoogle Scholar
  51. 51.
    Zhu W, Huang Y, Kouri DJ, Arnold M, Hoffman DK (1994) Phys Rev Lett 72:1310CrossRefGoogle Scholar
  52. 52.
    Kouri DJ, Huang Y, Zhu W, Hoffman DK (1994) J Chem Phys 100:3662CrossRefGoogle Scholar
  53. 53.
    Kouri DJ, Hoffman DK (1995) Few-Body Syst 18:203CrossRefGoogle Scholar
  54. 54.
    Kouri DJ, Zhou W, Huang Y, Hoffman DK (1996). In: Wyatt RE, Zhang JZH (eds) Dynamics of molecules and chemical reactions. Dekker, New YorkGoogle Scholar
  55. 55.
    Althorpe SC, Kouri DJ, Hoffman DK, Moiseyev N (1997) Chem Phys 217:289CrossRefGoogle Scholar
  56. 56.
    Gray SK, Balint-Kurti GG (1998) J Chem Phys 108:950CrossRefGoogle Scholar
  57. 57.
    Gray SK (1992) J Chem Phys 96:6543CrossRefGoogle Scholar
  58. 58.
    Gray SK, Verosky J (1994) J Chem Phys 100:5011CrossRefGoogle Scholar
  59. 59.
    Gray SK, Manolopoulos D (1996) J Chem Phys 104:7099CrossRefGoogle Scholar
  60. 60.
    Mandelshtam VA, Taylor HS (1995) J Chem Phys 103:2903CrossRefGoogle Scholar
  61. 61.
    Vibók Á, Balint-Kurti GG (1992) J Phys Chem 96:8712CrossRefGoogle Scholar
  62. 62.
    Vibók Á, Balint-Kurti GG (1992) J Chem Phys 96:7615CrossRefGoogle Scholar
  63. 63.
    Chen R, Guo H (1996) J Chem Phys 105:3569CrossRefGoogle Scholar
  64. 64.
    Mandelshtam VA, Taylor HS (1995) J Chem Phys 102:7390CrossRefGoogle Scholar
  65. 65.
    Jang HW, Light JC (1995) J Chem Phys 102:3262CrossRefGoogle Scholar
  66. 66.
    Kroes G-J, Neuhauser D (1996) J Chem Phys 105:8690CrossRefGoogle Scholar
  67. 67.
    Chen R, Guo H (1996) Chem Phys Lett 261:605CrossRefGoogle Scholar
  68. 68.
    Kroes G-J, van Hemert MC, Billing GD, Neuhauser D (1997) Phys Rev Lett 78:3583CrossRefGoogle Scholar
  69. 69.
    Guo H, Seideman T (1999) Phys Chem Chem Phys 1:1265CrossRefGoogle Scholar
  70. 70.
    Lin SY, Guo H, (2005) J Chem Phys 122:074304CrossRefGoogle Scholar
  71. 71.
    Neuhauser D (1990) J Chem Phys 93:2611CrossRefGoogle Scholar
  72. 72.
    Neuhauser D (1990) J Chem Phys 93:7836CrossRefGoogle Scholar
  73. 73.
    Huang Y, Iyengar SS, Kouri DJ, Hoffman DK (1996) J Chem Phys 105:927CrossRefGoogle Scholar
  74. 74.
    Neuhauser D, Judson RS, Baer M, Kouri DJ (1997) J Chem Soc Faraday Trans 93:727CrossRefGoogle Scholar
  75. 75.
    Althorpe SC (2001) J Chem Phys 114:1601CrossRefGoogle Scholar
  76. 76.
    Neuhauser D, Baer M, Judson RS, Kouri DJ (1990) J Chem Phys 93:312CrossRefGoogle Scholar
  77. 77.
    Neuhauser D (1992) Chem Phys Letts 200:173CrossRefGoogle Scholar
  78. 78.
    Meijer AJHM, Goldfield EM, Gray SK, Balint-Kurti GG (1998) Chem Phys Lett 293:270CrossRefGoogle Scholar
  79. 79.
    Hankel M, Smith SC, Gray SK, Balint-Kurti GG (2008) Comput Phys Commmun 179:569CrossRefGoogle Scholar
  80. 80.
    Balint-Kurti GG, Füsti-Molnár L, Brown A (2001) Phys Chem Chem Phys 3:702CrossRefGoogle Scholar
  81. 81.
    Balint-Kurti GG, Shapiro M (1981) Chem Phys 61:137CrossRefGoogle Scholar
  82. 82.
    Edmonds AR (1960) Angular momentum in quantum mechanics. Princeton University Press, PrincetonGoogle Scholar
  83. 83.
    Zare RN (1988) Angular momentum. Wiley, New YorkGoogle Scholar
  84. 84.
    Balint-Kurti GG (1975) In: Buckingham AD, Coulson CA (eds) International review of science, series II, Vol. 1. Butterworth, London, pp 286–326Google Scholar
  85. 85.
    A mistake has been found in the formulae of appendix B of Ref. 36. The correct formulae are given in appendix A of this paperGoogle Scholar
  86. 86.
    Qu ZW, Zhu H, Grebenshchikov SY, Schinke R (2005) J Chem Phys 123:074305CrossRefGoogle Scholar
  87. 87.
    Gray SK, Balint-Kurti GG, Schatz GC, Lin JJ, Liu X, Harich S, Yang X (2000) J Chem Phys 113:7330CrossRefGoogle Scholar
  88. 88.
    Gray SK, Goldfield EM, Schatz GC, Balint-Kurti GG (1999) Phys Chem Chem Phys 1:1141CrossRefGoogle Scholar
  89. 89.
    Chu T-S, Han K-L, Hankel M, Balint-Kurti GG, Kuppermann A, Abrol R (2009) J Chem Phys 130:144301CrossRefGoogle Scholar
  90. 90.
    Jambrina PG, Aoiz FJ, Bulut N, Smith SC, Balint-Kurti GG, Hankel M (2010) Phys Chem Chem Phys 12:1102CrossRefGoogle Scholar
  91. 91.
    Brown A, Balint-Kurti GG (2000) J Chem Phys 113:1870CrossRefGoogle Scholar
  92. 92.
    Brown A, Balint-Kurti GG (2000) J Chem Phys 113:1879CrossRefGoogle Scholar
  93. 93.
    Nee JB, Suto M, Lee LC (1985) J Phys B 18:L293CrossRefGoogle Scholar
  94. 94.
    Zhang J, Riehn CW, Dulligan M, Wittig C (1996) J Chem Phys 104:7027CrossRefGoogle Scholar
  95. 95.
    Daud MN, Balint-Kurti GG, Brown A (2005) J Chem Phys 122:054305CrossRefGoogle Scholar
  96. 96.
    Teule JM, Groenenboom GC, Neyer DW, Chandler DW, Janssen MHM (2000) Chem Phys Lett 320:177CrossRefGoogle Scholar
  97. 97.
    Hanisco TF, Kummel AC (1993) J Phys Chem 97:7242CrossRefGoogle Scholar
  98. 98.
    Baloïtcha E, Balint-Kurti GG (2005) J Chem Phys 123:014306CrossRefGoogle Scholar
  99. 99.
    Baloïtcha E, Balint-Kurti GG (2008) J Chem Phys 128:089901CrossRefGoogle Scholar
  100. 100.
    Freeman DE, Yoshino K, Esmond JR, Parkinson WH (1984) Planet Space Sci 32:239CrossRefGoogle Scholar
  101. 101.
    Balint-Kurti GG, Orr-Ewing AJ, Beswick JA, Brown A, Vasyutinskii OS (2002) J Chem Phys 116:10760CrossRefGoogle Scholar
  102. 102.
    Rakitzis TP, Samartzis PC, Toomes RL, Kitsopoulos TN, Brown A, Balint-Kurti GG, Vasyutinskii OS, Beswick JA (2003) Science 300:1936CrossRefGoogle Scholar
  103. 103.
    Brown A, Balint-Kurti GG, Vasyutinskii OS (2004) J Phys Chem 108:7790Google Scholar
  104. 104.
    Kuznetsov VV, Vasyutinskii OS (2005) J Chem Phys 123:034307CrossRefGoogle Scholar
  105. 105.
    Balint-Kurti GG, Vasyutinskii OS (2009) J Phys Chem 113:14281Google Scholar
  106. 106.
    Hankel M, Balint-Kurti GG, Gray SK (2003) Int J Quant Chem 92:205CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Centre for Computational Chemistry, School of ChemistryUniversity of BristolBristolUK

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