Advertisement

Quantum Rate Theory: A Path Integral Centroid Perspective

  • Eitan Geva
  • Seogjoo Jang
  • Gregory A. Voth

Abstract

The dynamics of many important processes that take place in condensed phase hosts can be described in terms of rate kinetics, with well-defined rate constants. The calculation of such rate constants from first principles has presented theoretical chemistry with an ongoing challenge. Nonequilibrium statistical mechanics provides a framework within which one can derive explicit expressions for those rate constants, via either linear response theory or Fermi’s golden rule. In both cases, one finds that the rate constants are given in terms of equilibrium correlation functions [1, 2, 3, 4, 5, 6]. Those correlation functions can be evaluated with relative ease from classical molecular dynamics (MD) simulations, even for complex anharmonic many-body systems such as molecular liquids and biopolymers. However, classical mechanics is not valid in the case of many important processes, such as electron and proton transfer and vibrational relaxation. In those cases, one needs to compute the quantummechanical correlation functions. A numerically exact calculation of the latter lies far beyond the reach of currently available computer resources, due to the exponential scaling of the computational effort with the number of degrees of freedom [7, 8]. The challenge therefore lies in finding ways to compute quantum mechanical rate constants which are based on either bypassing the explicit simulation of the quantum dynamics (e.g., transition state theory (TST)), or by using reliable and computationally feasible approximate techniques for computing quantitatively accurate quantum mechanical correlation functions.

Keywords

Correlation Function Lithium Atom Transition State Theory Time Correlation Function Transition State Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    T. Yamamoto, J. Chem. Phys., 33, 281, 1960.MathSciNetADSCrossRefGoogle Scholar
  2. [2]
    A.G. Redfield, Adv. Mag. Reson., 1, 1, 1965.Google Scholar
  3. [3]
    B.J. Berne and G.D. Harp, Adv. Chem. Phys., 17, 63, 1970.CrossRefGoogle Scholar
  4. [4]
    D.A. McQuarrie, Statistical Mechanics (Harper and Row, New York, 1976).Google Scholar
  5. [5]
    R. Kubo, M. Toda, and N. Hashitsume, Statistical Physics II — Nonequilibrium Statistical Mechanics, (Springer-Verlag, Berlin, 1983).Google Scholar
  6. [6]
    W.T. Pollard, A.K. Felts, and R.A. Friesner, Adv. Chem. Phys. XCIII, 77, 1996.CrossRefGoogle Scholar
  7. [7]
    N. Makri, Annu. Rev. Phys. Chem., 50, 167, 1999.ADSCrossRefGoogle Scholar
  8. [8]
    P. Jungwirth and R.B. Gerber, Chem. Rev, 99, 1583, 1999.CrossRefGoogle Scholar
  9. [9]
    R.P. Feynman and A.R. Hibbs, Quantum Mechanics and Path Integrals (McGrawHill Book Company, New York, 1965).MATHGoogle Scholar
  10. [10]
    R.P. Feynman, Statistical Mechanics (Addison-Wesley Publishing Company, New York, 1972).Google Scholar
  11. [11]
    H. Kleinert, Path Integrals in Quantum Mechanics, Statistics, and Polymer Physics (World Scientific, Singapore, 1995).MATHGoogle Scholar
  12. [12]
    U. Weiss, Series in Modern Condensed Matter Physics Vol. 2: Quantum Dissipative Systems (World Scientific, Singapore, 1993).Google Scholar
  13. [13]
    W.H. Miller, J. Phys. Chem. A, 105, 2942, 2001.CrossRefGoogle Scholar
  14. [14]
    B.J. Berne and D. Thirumalai, Annu. Rev. Phys. Chem., 37, 401, 1986.ADSCrossRefGoogle Scholar
  15. [15]
    D.M. Ceperley, Rev. Mod. Phys., 67, 279, 1995.ADSCrossRefGoogle Scholar
  16. [16]
    R. Giachetti and V. Tognetti, Phys. Rev. Lett., 55, 912, 1985.MathSciNetADSCrossRefGoogle Scholar
  17. [17]
    R.P. Feynman and H. Kleinert, Phys. Rev. A, 34, 5080, 1986.MathSciNetADSCrossRefGoogle Scholar
  18. [18]
    W.H. Miller, J. Chem. Phys., 61, 1823, 1974.ADSCrossRefGoogle Scholar
  19. [19]
    M.J. Gillan, Phys. Rev. Lett., 58, 563, 1987.ADSCrossRefGoogle Scholar
  20. [20]
    M.J. Gillan, J. Phys. C, 20, 3621, 1987.ADSCrossRefGoogle Scholar
  21. [21]
    G.A. Voth, D. Chandler, and W.H. Miller, J. Chem. Phys., 91, 7749, 1989.ADSCrossRefGoogle Scholar
  22. [22]
    G.A. Voth, Chem. Phys. Lett., 170, 289, 1990.ADSCrossRefGoogle Scholar
  23. [23]
    R.P. McRae, G.K. Schenter, B.C. Garrett, G.R. Haynes, G.A. Voth, and G.C. Schatz, J. Chem. Phys., 97, 7392, 1992.ADSCrossRefGoogle Scholar
  24. [24]
    G.A. Voth, J. Phys. Chem., 97, 8365, 1993.CrossRefGoogle Scholar
  25. [25]
    G.A. Voth, Adv. Chem. Phys., 93, 135, 1996.CrossRefGoogle Scholar
  26. [26]
    N. Fisher and H.C. Andersen, J. Phys. Chem., 100, 1137, 1996.CrossRefGoogle Scholar
  27. [27]
    E. Pollak and J. Liao, J. Chem. Phys., 108, 2733, 1998.ADSCrossRefGoogle Scholar
  28. [28]
    S. Jang and G.A. Voth, J. Chem. Phys., 112, 8747, 2000.ADSCrossRefGoogle Scholar
  29. [29]
    J.L. Liao and E. Pollak, Chem. Phys., 268, 295, 2001.ADSCrossRefGoogle Scholar
  30. [30]
    P. Pechukas, in Dynamics of molecular collisions, Part 2 (Plenum Press, N.Y, 1976), p. 269.Google Scholar
  31. [31]
    J. Cao and G.A. Voth, J. Chem. Phys., 100, 5093, 1994.ADSCrossRefGoogle Scholar
  32. [32]
    J. Cao and G.A. Voth, J. Chem. Phys., 100, 5106, 1994.ADSCrossRefGoogle Scholar
  33. [33]
    J. Cao and G.A. Voth, J. Chem. Phys., 101, 6157, 1994.ADSCrossRefGoogle Scholar
  34. [34]
    J. Cao and G.A. Voth, J. Chem. Phys., 101, 6168, 1994.ADSCrossRefGoogle Scholar
  35. [35]
    J. Cao and G.A. Voth, J. Chem. Phys., 101, 6184, 1994.ADSCrossRefGoogle Scholar
  36. [36]
    S. Jang and G.A. Voth, J. Chem. Phys., 111, 2357, 1999.ADSCrossRefGoogle Scholar
  37. [37]
    S. Jang and G.A. Voth, J. Chem. Phys., 111, 2371, 1999.ADSCrossRefGoogle Scholar
  38. [38]
    Q. Shi and E. Geva, J. Chem. Phys., 118, 8173, 2003.ADSCrossRefGoogle Scholar
  39. [39]
    D.R. Reichman, P.-N. Roy, S. Jang, and G.A. Voth, J. Chem. Phys., 113, 919, 2000.ADSCrossRefGoogle Scholar
  40. [40]
    E. Geva, Q. Shi, and G.A. Voth, J. Chem. Phys., 115, 9209, 2001.ADSCrossRefGoogle Scholar
  41. [41]
    Q. Shi and E. Geva, J. Chem. Phys., 119, 9030, 2003.ADSCrossRefGoogle Scholar
  42. [42]
    A. Calhoun, M. Pavese, and G.A. Voth, Chem. Phys. Lett., 262, 415, 1996.ADSCrossRefGoogle Scholar
  43. [43]
    U.W. Schmitt and G.A. Voth, J. Chem. Phys., 111, 9361, 1999.ADSCrossRefGoogle Scholar
  44. [44]
    S. Jang, Y Pak, and G.A. Voth, J. Phys. Chem. A, 103, 10289, 1999.CrossRefGoogle Scholar
  45. [45]
    M. Pavese and G.A. Voth, Chem. Phys. Lett., 249, 231, 1996.ADSCrossRefGoogle Scholar
  46. [46]
    K. Kinugawa, P.B. Moore, and M.L. Klein, J. Chem. Phys., 106, 1154, 1997.ADSCrossRefGoogle Scholar
  47. [47]
    K. Kinugawa, P.B. Moore, and M.L. Klein, J. Chem. Phys., 109, 610, 1998.ADSCrossRefGoogle Scholar
  48. [48]
    K. Kinugawa, Chem. Phys. Lett., 292, 454, 1998.ADSCrossRefGoogle Scholar
  49. [49]
    M. Pavese, D.R. Bernard, and G.A. Voth, Chem. Phys. Lett., 300, 93, 1999.ADSCrossRefGoogle Scholar
  50. [50]
    S. Miura, S. Okazaki, and K. Kinugawa, J. Chem. Phys., 110, 4523, 1999.ADSCrossRefGoogle Scholar
  51. [51]
    F.J. Bermejo, K. Kinugawa, C. Cabrillo, S.M. Bennington, B. Fak, M.T. Fernandez-Diaz, P. Verkerk, J. Dawidowski, and R. Fernandez-Pirea, Phys. Rev. Lett., 84, 5359, 2000.ADSCrossRefGoogle Scholar
  52. [52]
    J. Poulsen and P.J. Rossky, J. Chem. Phys., 115, 8014, 2001.ADSCrossRefGoogle Scholar
  53. [53]
    J. Poulsen, S.R. Keiding, and P.J. Rossky, Chem. Phys. Lett., 336, 488, 2001.ADSCrossRefGoogle Scholar
  54. [54]
    J. Poulsen and P.J. Rossky, J. Chem. Phys., 115, 8024, 2001.ADSCrossRefGoogle Scholar
  55. [55]
    J.B. Anderson, Adv. Chem. Phys., 91, 381, 1995.CrossRefGoogle Scholar
  56. [56]
    M. Messina, G.K. Schenter, and B.C. Garrett, J. Chem. Phys., 98, 8525, 1993.ADSCrossRefGoogle Scholar
  57. [57]
    M. Messina, G.K. Schenter, and B.C. Garrett, J. Chem. Phys., 99, 8644, 1993.ADSCrossRefGoogle Scholar
  58. [58]
    G.K. Schenter, M. Messina, and B.C. Garret, J. Chem. Phys., 99, 1674, 1993.ADSCrossRefGoogle Scholar
  59. [59]
    E. Pollak, J. Chem. Phys., 103, 973, 1995.ADSCrossRefGoogle Scholar
  60. [60]
    N. Chakrabarti, T.C. Jr., and B. Roux, Chem. Phys. Lett., 293, 209, 1998.Google Scholar
  61. [61]
    R. Ramirez, J. Chem. Phys., 107, 3550, 1997.ADSCrossRefGoogle Scholar
  62. [62]
    J. Cao and G.A. Voth, J. Chem. Phys., 105, 6856, 1996.ADSCrossRefGoogle Scholar
  63. [63]
    I. Affleck, Phys. Rev. Lett., 46, 388, 1981.MathSciNetADSCrossRefGoogle Scholar
  64. [64]
    S. Jang, C.D. Schwieters, and G.A. Voth, J. Phys. Chem. A, 103, 9527, 1999.CrossRefGoogle Scholar
  65. [65]
    W.H. Miller, S.D. Schwartz, and J.W. Tromp, J. Chem. Phys., 79, 4889, 1983.ADSCrossRefGoogle Scholar
  66. [66]
    W.H. Miller, J. Phys. Chem. A, 102, 793, 1998.CrossRefGoogle Scholar
  67. [67]
    I. Navrotskaya, Q. Shi, and E. Geva, Isr. J. Chem., 42, 225, 2002.CrossRefGoogle Scholar
  68. [68]
    Q. Shi and E. Geva, J. Chem. Phys., 116, 3223, 2002.ADSCrossRefGoogle Scholar
  69. [69]
    Y.-C. Sun and G.A. Voth, J. Chem. Phys., 98, 7451, 1993.ADSCrossRefGoogle Scholar
  70. [70]
    S.W. Rick, D.L. Lynch, and J.D. Doll, J. Chem. Phys., 99, 8183, 1993.ADSCrossRefGoogle Scholar
  71. [71]
    T.R. Mattsson and G. Wahnström, Phys. Rev. B, 56, 14944, 1997.ADSCrossRefGoogle Scholar
  72. [72]
    M.J. Murphy, G.A. Voth, and A.L.R. Bug, J. Phys. Chem. B, 101, 491, 1997.CrossRefGoogle Scholar
  73. [73]
    S. Jang and G.A. Voth, J. Chem. Phys., 108, 4098, 1998.ADSCrossRefGoogle Scholar
  74. [74]
    S. Jang, S. Jang, and G.A. Voth, J. Phys. Chem. A, 103, 9512, 1999.CrossRefGoogle Scholar
  75. [75]
    U.W. Schmitt and G.A. Voth, Israeli J. Chem., 39, 483, 1999.Google Scholar
  76. [76]
    U.W. Schmitt and G.A. Voth, Chem. Phys. Lett., 329, 36, 2000.ADSCrossRefGoogle Scholar
  77. [77]
    J. Lobaugh and G.A. Voth, J. Chem. Phys., 100, 3039, 1994.ADSCrossRefGoogle Scholar
  78. [78]
    J. Lobaugh and G.A. Voth, J. Chem. Phys., 104, 2056, 1996.ADSCrossRefGoogle Scholar
  79. [79]
    I. Feierberg and V. Luzhkov and J. Åqvist, J. Bio. Chem., 275, 22657, 2000.Google Scholar
  80. [80]
    R. Iftimie and J. Schofield, J. Chem. Phys., 115, 5891, 2001.ADSCrossRefGoogle Scholar
  81. [81]
    K. Hinsen and B. Roux, J. Chem. Phys., 106, 3567, 1997.ADSCrossRefGoogle Scholar
  82. [82]
    M.E. Tuckerman and D. Marx, Phys. Rev. Lett., 86, 4946, 2001.ADSCrossRefGoogle Scholar
  83. [83]
    M. Celli, D. Colognesi, and M. Zoppi, Phys. Rev. E, 66, 021202, 2002.ADSCrossRefGoogle Scholar
  84. [84]
    A. Nakayama and N. Makri, J. Chem. Phys., 119, 8592, 2003.ADSCrossRefGoogle Scholar
  85. [85]
    E. Rabani, D.R. Reichman, G. Krylov, and B.J. Berne, Proc. Natl. Acad. Sci. USA, 99, 1129, 2002.MATHADSCrossRefGoogle Scholar
  86. [86]
    D.R. Reichman and E. Rabani, J. Chem. Phys., 116, 6279, 2002.ADSCrossRefGoogle Scholar
  87. [87]
    E. Rabani and D.R. Reichman, J. Chem. Phys., 120, 2004.Google Scholar
  88. [88]
    E. Rabani and D.R. Reichman, Europhys. Lett., 60, 656, 2002.ADSCrossRefGoogle Scholar
  89. [89]
    K. Carneiro, M. Nielsen, and J.P. McTague, Phys. Rev. Lett., 30, 481, 1973.ADSCrossRefGoogle Scholar
  90. [90]
    M. Mukherjee, F.J. Bermejo, B. Fak, and S.M. Bennington, Europhys. Lett., 40, 153, 1997.ADSCrossRefGoogle Scholar
  91. [91]
    F.J. Bermejo, F.J. Mompean, M. Garcia-Hernandez, J.L. Martinez, D. Martin-Marero, A. Chahid, G. Senger, and M.L. Ristig, Phys. Rev. B, 47, 15097, 1993.ADSCrossRefGoogle Scholar
  92. [92]
    F.J. Bermejo, B. Fax, S.M. Bennington, R. Fernandez-Perea, C. Cabrillo, J. Dawidowski, M.T. Fernandez-Diaz, and P. Verkerk, Phys. Rev. B, 60, 15154, 1999.ADSCrossRefGoogle Scholar
  93. [93]
    Y. Yonetani and K. Kinugawa, J. Chem. Phys., 119, 9651, 2003.ADSCrossRefGoogle Scholar
  94. [94]
    M. Mukherjee, F.J. Bermejo, S.M. Bennington, and B. Fak, Phys. Rev. B, 57, 11031, 1998.ADSCrossRefGoogle Scholar
  95. [95]
    T.D. Hone and G.A. Voth, J. Chem. Phys., (Submitted).Google Scholar
  96. [96]
    D.W. Oxtoby, Adv. Chem. Phys., 47 (Part 2), 487, 1981.CrossRefGoogle Scholar
  97. [97]
    D.W. Oxtoby, Annu. Rev. Phys. Chem., 32, 77, 1981.ADSCrossRefGoogle Scholar
  98. [98]
    D.W. Oxtoby, J. Phys. Chem., 87, 3028, 1983.CrossRefGoogle Scholar
  99. [99]
    J. Chesnoy and G.M. Gale, Adv. Chem. Phys., 70 (part 2), 297, 1988.CrossRefGoogle Scholar
  100. [100]
    R.M. Stratt and M. Maroncelli, J. Phys. Chem., 100, 12981, 1996.CrossRefGoogle Scholar
  101. [101]
    T. Elsaesser and W. Kaiser, Annu. Rev. Phys. Chem., 42, 83, 1991.ADSCrossRefGoogle Scholar
  102. [102]
    A. Laubereau and W. Kaiser, Rev. Mod. Phys., 50, 607, 1978.ADSCrossRefGoogle Scholar
  103. [103]
    P. Hamm, M. Lim, and R.M. Hochstrasser, J. Chem. Phys., 107, 1523, 1997.CrossRefGoogle Scholar
  104. [104]
    Q. Shi and E. Geva, J. Chem. Phys., 118, 7562, 2003.ADSCrossRefGoogle Scholar
  105. [105]
    B.J. Berne, J. Jortner, and R. Gordon, J. Chem. Phys., 47, 1600, 1967.ADSCrossRefGoogle Scholar
  106. [106]
    J.S. Bader and B.J. Berne, J. Chem. Phys., 100, 8359, 1994.ADSCrossRefGoogle Scholar
  107. [107]
    S.A. Egorov, K.F. Everitt, and J.L. Skinner, J. Phys. Chem. A, 103, 9494, 1999.CrossRefGoogle Scholar
  108. [108]
    S.A. Egorov and J.L. Skinner, J. Chem. Phys., 112, 275, 2000.ADSCrossRefGoogle Scholar
  109. [109]
    J.L. Skinner and K. Park, J. Phys. Chem. B, 105, 6716, 2001.CrossRefGoogle Scholar
  110. [110]
    D. Rostkier-Edelstein, P. Graf, and A. Nitzan, J. Chem. Phys., 107, 10470, 1997.ADSCrossRefGoogle Scholar
  111. [111]
    D. Rostkier-Edelstein, P. Graf, and A. Nitzan, J. Chem. Phys., 108, 9598, 1998.ADSCrossRefGoogle Scholar
  112. [112]
    K.F. Everitt, J.L. Skinner, and B.M. Ladanyi, J. Chem. Phys., 116, 179, 2002.ADSCrossRefGoogle Scholar
  113. [113]
    P.H. Berens, S.R. White, and K.R. Wilson, J. Chem. Phys., 75, 515, 1981.ADSCrossRefGoogle Scholar
  114. [114]
    L. Frommhold, Collision-induced absorption in gases, vol. 2 of Cambridge Monographs on Atomic, Molecular, and Chemical Physics, (Cambridge University Press, England, 1993), 1st ed.Google Scholar
  115. [115]
    J.L. Skinner, J. Chem. Phys., 107, 8717, 1997.ADSCrossRefGoogle Scholar
  116. [116]
    S.C. An, C.J. Montrose, and T.A. Litovitz, J. Chem. Phys., 64, 3717, 1976.ADSCrossRefGoogle Scholar
  117. [117]
    S.A. Egorov and J.L. Skinner, Chem. Phys. Lett., 293, 439, 1998.CrossRefGoogle Scholar
  118. [118]
    P. Schofield, Phys. Rev. Lett., 4, 239, 1960.ADSCrossRefGoogle Scholar
  119. [119]
    P.A. Egelstaff, Adv. Phys., 11, 203, 1962.ADSCrossRefGoogle Scholar
  120. [120]
    G.R. Kneller, Mol. Phys., 83, 63, 1994.MathSciNetADSCrossRefGoogle Scholar
  121. [121]
    Q. Shi and E. Geva, J. Phys. Chem. A, 107, 9059, 2003.CrossRefGoogle Scholar
  122. [122]
    P.-N. Roy and G.A. Voth, J. Chem. Phys., 110, 3647, 1999.ADSCrossRefGoogle Scholar
  123. [123]
    P.-N. Roy, S. Jang, and G.A. Voth, J. Chem. Phys., 111, 5303, 1999.ADSCrossRefGoogle Scholar
  124. [124]
    N.V. Blinov, P.-N. Roy, and G.A. Voth, J. Chem. Phys., 115, 4484, 2001.ADSCrossRefGoogle Scholar
  125. [125]
    N.V. Blinov and P.-N. Roy, J. Chem. Phys., 115, 7822, 2001.ADSCrossRefGoogle Scholar
  126. [126]
    N.V. Blinov and P.-N. Roy, J. Chem. Phys., 116, 4808, 2002.ADSCrossRefGoogle Scholar
  127. [127]
    P.-N. Roy and N.V. Blinov, Isr. J. Chem., 42, 183, 2002.CrossRefGoogle Scholar
  128. [128]
    P. Moffatt, N. Blinov, and P.-N. Roy, J. Chem. Phys., in press, 2004.Google Scholar
  129. [129]
    J.L. Liao and G.A. Voth, J. Phys. Chem. B, 106, 8449, 2002.CrossRefGoogle Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  • Eitan Geva
    • 1
  • Seogjoo Jang
    • 2
  • Gregory A. Voth
    • 3
  1. 1.Department of ChemistryUniversity of MichiganAnn ArborUSA
  2. 2.Chemistry DepartmentBrookhaven National LaboratoryUptonUSA
  3. 3.Department of Chemistry and Henry Eyring Center for Theoretical ChemistryUniversity of UtahSalt Lake CityUSA

Personalised recommendations