Skip to main content
Log in

Overview of theoretical models for reaction rates

  • Articles
  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

There is enormous recent interest in the development of models for rate processes because rates are an almost universal characterization in the physical and biological sciences. In this paper we provide an introduction to several of the problems to be discussed in greater depth by other speakers at a symposium held at the National Institutes of Health on May 6–8, 1985. This review will focus on (1) the Smoluchowski model for reaction rates together with its extension by Onsager, (2) first passage time formalism for discrete and continuous master equations and Fokker-Planck equations, (3) the Kramers model and its extensions, (4) diffusion in the presence of trapping centers.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. R. M. Noyes,Prog. React. Kin. 1:129 (1961).

    Google Scholar 

  2. D. F. Calef, J. M. Deutch,Ann. Rev. Chem. Phys. 34:493 (1983).

    Google Scholar 

  3. J. T. Hynes, inThe Theory of Chemical Reactions, M. Baer, ed. (to appear).

  4. N. G. van Kampen,Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1981).

    Google Scholar 

  5. C. W. Gardiner,Handbook of Stochastic Methods (Springer-Verlag, Berlin, 1983).

    Google Scholar 

  6. R. v. Smoluchowski,Z. Phys. Chem. 29:129 (1917).

    Google Scholar 

  7. F. C. Collins and G. E. Kimball,J. Coll. Sci. 4:425 (1949).

    Google Scholar 

  8. H. L. Frisch and F. C. Collins,J. Chem. Phys. 20:1797 (1952);J. Chem. Phys. 21:2158 (1953).

    Google Scholar 

  9. P. Debye,Trans. Electrochem. Soc. 82:265 (1942).

    Google Scholar 

  10. D. Shoup, A. Szabo,Biophys. J. 40:33 (1982).

    Google Scholar 

  11. L. Monchick,J. Chem. Phys. 78:1808 (1983);J. Chem. Phys. 81:2010 (1984).

    Google Scholar 

  12. N. Agmon,J. Chem. Phys. 81:2811 (1984).

    Google Scholar 

  13. F. C. Goodrich,J. Chem. Phys. 22:588 (1954).

    Google Scholar 

  14. J. M. Schurr,Biophys. J. 10:700 (1970).

    Google Scholar 

  15. S. H. Northrup and J. T. Hynes,J. Stat. Phys. 18:91 (1978).

    Google Scholar 

  16. D. L. Weaver,J. Chem. Phys. 72:3483 (1980).

    Google Scholar 

  17. D. L. Weaver,Biopolymers. 21:1275 (1982).

    Google Scholar 

  18. T. R. Waite,Phys. Rev. 107:463 (1957).

    Google Scholar 

  19. T. R. Waite,J. Chem. Phys. 28:103 (1958).

    Google Scholar 

  20. L. Monchick, J. L. Magee, and A. H. Samuel,J. Chem. Phys. 26:935 (1957).

    Google Scholar 

  21. A. Szabo, G. Lamm, and G. H. Weiss,J. Stat. Phys. 34:225 (1984).

    Google Scholar 

  22. L. Monchick,J. Chem. Phys. 24:381 (1956);J. Chem. Phys. 62:1907 (1975).

    Google Scholar 

  23. K. Razi Naqvi, S. Waldenström, and K. J. Mork,J. Phys. Chem. 86:4750 (1982).

    Google Scholar 

  24. D. C. Torney and H. M. McConnell,Proc. R. Sos. (London) Ser. A 387:147 (1983);J. Phys. Chem. 87:1441 (1983).

    Google Scholar 

  25. G. H. Weiss and R. J. Rubin,Adv. Chem. Phys. 52:363 (1983).

    Google Scholar 

  26. L. Onsager,Phys. Rev. 54:554 (1938).

    Google Scholar 

  27. J. B. Pedersen and J. E. Larsen,J. Chem. Phys. 77:1061 (1982).

    Google Scholar 

  28. P. Sibani and J. B. Pedersen,J. Chem. Phys. 74:6934 (1981).

    Google Scholar 

  29. P. Sibani and J. B. Pedersen,Phys. Rev. Lett. 51:148 (1983).

    Google Scholar 

  30. K. M. Hong and J. Noolandi,J. Chem. Phys. 68:5163, 5172 (1978);J. Chem. Phys. 69:5026 (1979).

    Google Scholar 

  31. J. Noolandi,J. Electrostat. 12:13 (1982).

    Google Scholar 

  32. U. Gösele and A. Seeger,Philos. Mag. 34:177 (1976).

    Google Scholar 

  33. M. Tachiya,J. Chem. Phys. 69:2375 (1978);J. Chem. Phys. 70:238, 2021, 4701 (1979).

    Google Scholar 

  34. H. Sano,J. Chem. Phys. 74:1394 (1981).

    Google Scholar 

  35. B. U. Felderhof and J. M. Deutch,J. Chem. Phys. 64:4551 (1976).

    Google Scholar 

  36. J. M. Deutch, B. U. Felderhof, and M. J. Saxton,J. Chem. Phys. 64:4559 (1976).

    Google Scholar 

  37. R. Samson and J. M. Deutch,J. Chem. Phys. 67:847 (1977).

    Google Scholar 

  38. S. A. Rice and J. K. Baird,J. Chem. Phys. 69:1989 (1978).

    Google Scholar 

  39. H. Sano and M. Tachiya,J. Chem. Phys. 71:1276 (1979).

    Google Scholar 

  40. H. Sano and M. Tachiya,J. Chem. Phys. 75:2870 (1981).

    Google Scholar 

  41. Y. A. Berlin, P. Cordier, and J. A. Delaire,J. Chem. Phys. 73:4619 (1980).

    Google Scholar 

  42. H. Scher and S. Rackovsky,J. Chem. Phys. 81:1994 (1984).

    Google Scholar 

  43. V. M. Agranovich and M. D. Galanin,Electronic Excitation Energy Transfer in Condensed Matter (North-Holland, Amsterdam, 1982).

    Google Scholar 

  44. C. M. Lawson, E. E. Freed, and R. C. Powell,J. Chem. Phys. 76:4171 (1982).

    Google Scholar 

  45. L. Pontryagin, A. Andronow, and A. Witt,Zh. Eksp. Teor. Fiz. 3:172 (1933).

    Google Scholar 

  46. A. Szabo, K. Schulten, and Z. Schulten,J. Chem. Phys. 72:4350 (1980).

    Google Scholar 

  47. J. M. Deutch,J. Chem. Phys. 73:4700 (1980).

    Google Scholar 

  48. K. Schulten, Z. Schulten, and A. Szabo,J. Chem. Phys. 74:4426 (1981).

    Google Scholar 

  49. A. Mozumder,J. Chem. Phys. 76:5107 (1982).

    Google Scholar 

  50. S. H. Northrup and J. T. Hynes,J. Chem. Phys. 69:5246 (1978).

    Google Scholar 

  51. G. F. Newell,J. Math. Mech. 11:481 (1962).

    Google Scholar 

  52. P. Mandl,Analytical Treatment of One-Dimensional Markov Processes (Springer-Verlag, New York, 1968).

    Google Scholar 

  53. J. Keilson,Markov Chain Models—Rarity and Exponentially (Springer-Verlag, New York, 1979).

    Google Scholar 

  54. K. Lindenberg, K. E. Shuler, J. Freeman, and T. J. Lie,J. Stat. Phys. 12:217 (1975).

    Google Scholar 

  55. R. Courant and D. Hilbert,Methods of Mathematical Physics, Vol. 1 (Interscience, New York, 1962).

    Google Scholar 

  56. S. H. Northrup and J. T. Hynes,J. Chem. Phys. 73:2700 (1980); R. F. Grote and J. T. Hynes,J. Chem. Phys. 73:2715 (1980).

    Google Scholar 

  57. H. A. Kramers,Physica 7:284 (1940).

    Google Scholar 

  58. O. Klein,Arkiv. Mat. Astr. Fys. 16:5 (1922).

    Google Scholar 

  59. M. v. Smoluchowski,Ann. Phys. (Leipzig) 21:756 (1906).

    Google Scholar 

  60. S. Chandrasekhar,Rev. Mod. Phys. 15:1 (1943).

    Google Scholar 

  61. H. Eyring,J. Chem. Phys. 3:1035 (1935).

    Google Scholar 

  62. B. J. Matkowsky, Z. Schuss, and C. Tier,J. Stat. Phys. 35:443 (1984).

    Google Scholar 

  63. E. Edholm and O. Leimar,Physica A98:313 (1979).

    Google Scholar 

  64. B. Carmeli and A. Nitzan,Phys. Rev. A 29:1481 (1984).

    Google Scholar 

  65. M. Büttiker, E. P. Harris, and R. Landauer,Phys. Rev. B 28:1268 (1983).

    Google Scholar 

  66. P. B. Visscher,Phys. Rev. B 13:3273 (1976);Phys. Rev. B 14:347 (1976).

    Google Scholar 

  67. M. Mangel,J. Chem. Phys. 72:6606 (1980).

    Google Scholar 

  68. H. C. Brinckman,Physica 22:29, 149 (1956).

    Google Scholar 

  69. R. Landauer and J. A. Swanson,Phys. Rev. 121:1668 (1961).

    Google Scholar 

  70. J. S. Langer,Ann. Phys. (N.Y.) 54:258 (1969).

    Google Scholar 

  71. N. G. van Kampen,J. Stat. Phys. 17:71 (1977).

    Google Scholar 

  72. R. S. Larson and M. D. Kostin,J. Chem. Phys. 69:4821 (1978).

    Google Scholar 

  73. R. S. Larson and M. D. Kostin,J. Chem. Phys. 72:1392 (1980).

    Google Scholar 

  74. R. S. Larson,J. Chem. Phys. 81:1731 (1984).

    Google Scholar 

  75. B. J. Matkowsky and Z. Schuss,Siam J. Appl. Math. 33:365 (1977).

    Google Scholar 

  76. D. Ludwig,SIAM Rev. 17:605 (1975).

    Google Scholar 

  77. B. J. Matkowsky, Z. Schuss, and E. Ben-Jacob,Siam J. Appl. Math. 42:835 (1982).

    Google Scholar 

  78. R. F. Grote and J. T. Hynes,J. Chem. Phys. 74:4465 (1981);J. Chem. Phys. 75:2191 (1981).

    Google Scholar 

  79. P. Hänggi,Phys. Rev. A 25:1130 (1981).

    Google Scholar 

  80. P. Hänggi and F. Mojtabai,Phys. Rev. A 26:1168 (1982).

    Google Scholar 

  81. R. F. Grote and J. T. Hynes,J. Chem. Phys. 77:3736 (1982).

    Google Scholar 

  82. B. Carmeli and A. Nitzan,Phys. Rev. Lett. 49:423 (1982);J. Chem. Phys. 79:393 (1983);Isr. J. Chem. 22:360 (1982);Chem. Phys. Lett. 102:517 (1983);Chem. Phys. Lett. 106:329 (1984);J. Chem. Phys. 80:3596 (1984);Phys. Rev. A 29:1481 (1984).

    Google Scholar 

  83. F. Marchesoni and P. Grigolini,J. Chem. Phys. 78:6287 (1983).

    Google Scholar 

  84. S. P. Velsko and G. R. Fleming,Chem. Phys. 65:59 (1982);J. Chem. Phys. 76:3553 (1982).

    Google Scholar 

  85. S. P. Velsko, D. H. Waldeck, and G. R. Fleming,J. Chem. Phys. 78:249 (1983).

    Google Scholar 

  86. K. M. Keery and G. R. Fleming,Chem. Phys. Lett. 93:322 (1983).

    Google Scholar 

  87. B. Bagchi and D. W. Oxtoby,J. Phys. Chem. 78:2735 (1983).

    Google Scholar 

  88. C. W. Gardiner,J. Stat. Phys. 30:157 (1983).

    Google Scholar 

  89. J. L. Skinner and P. G. Wolynes,J. Chem. Phys. 69:2143 (1978);J. Chem. Phys. 72:4913.

    Google Scholar 

  90. Z. Schuss and B. J. Matkowsky,SIAM J. Appl. Math. 35:604 (1979).

    Google Scholar 

  91. B. Caroli, C. Caroli, and B. Roulet,J. Stat. Phys. 28, 757 (1982).

    Google Scholar 

  92. H. Risken,Z. Phys. 251:231 (1972).

    Google Scholar 

  93. B. Caroli, C. Caroli, B. Roulet, and D. Saint-James,Physica 108A:233 (1981).

    Google Scholar 

  94. S. A. Adelman,J. Chem. Phys. 71:4479 (1979).

    Google Scholar 

  95. M. Berkowitz, C. L. Brooks III, and S. A. Adelman,J. Chem. Phys. 72:3889 (1980).

    Google Scholar 

  96. S. A. Adelman,J. Chem. Phys. 73:3145 (1980).

    Google Scholar 

  97. C. L. Brooks III, M. Berkowitz, S. A. Adelman,J. Chem. Phys. 73:4353, 4472 (1980).

    Google Scholar 

  98. S. A. Adelman,J. Chem. Phys. 74:4646 (1981);J. Chem. Phys. 75:5837 (1981).

    Google Scholar 

  99. C. L. Brooks III and S. A. Adelman,J. Chem. Phys. 76:1007 (1982);J. Chem. Phys. 77:484 (1982).

    Google Scholar 

  100. S. A. Adelman,Adv. Chem. Phys. 44:143 (1980);Adv. Chem. Phys. 53:61 (1983).

    Google Scholar 

  101. S. A. Adelman and C. L. Brooks III,J. Phys. Chem. 86:1511 (1982).

    Google Scholar 

  102. E. W. Montroll and K. E. Shuler,Adv. Chem. Phys. 1:361 (1958).

    Google Scholar 

  103. L. Landau and E. Teller,Phys. Z. Sowjetunion 10:34 (1936).

    Google Scholar 

  104. S. K. Kim,J. Chem. Phys. 28:1057 (1958).

    Google Scholar 

  105. G. H. Weiss,Adv. Chem. Phys. 13:1 (1967).

    Google Scholar 

  106. G. H. Weiss,J. Stat. Phys. 24:581 (1981).

    Google Scholar 

  107. I. Oppenheim, K. E. Shuler, and G. H. Weiss,Physica A88:191 (1977).

    Google Scholar 

  108. N. G. van Kampen,Prog. Theor. Phys. 64:389 (1978).

    Google Scholar 

  109. P. Hänggi, H. Grabert, P. Talkner, and H. Thomas,Phys. Rev. A 29:371 (1984).

    Google Scholar 

  110. V. Seshadri, B. J. West, and K. Lindenberg,J. Chem. Phys. 72:1145 (1980).

    Google Scholar 

  111. P. Hänggi and P. Talkner,Z. Phys. B45:79 (1981).

    Google Scholar 

  112. N. G. van Kampen,Can. J. Phys. 39:551 (1961);Adv. Chem. Phys. 34:245 (1976).

    Google Scholar 

  113. H. Grabert, P. Hänggi, and I. Oppenheim,Physica 117A:300 (1983).

    Google Scholar 

  114. B. J. Matkowsky, Z. Schuss, C. Knessl, C. Tier, M. Mangel,Phys. Rev. 29A:3350 (1984).

    Google Scholar 

  115. C. Knessl, M. Mangel, B. J. Matkowsky, Z. Schuss, and C. Tier,J. Chem. Phys. 81:1285 (1984).

    Google Scholar 

  116. A. Wald,Ann. Math. Stat. 15:283 (1944);Ann. Math. Stat. 17:493 (1946).

    Google Scholar 

  117. J. H. B. Kemperman,The First Passage Problem for a Stationary Markov Chains (University of Chicago Press, Chicago, 1961).

    Google Scholar 

  118. D. Siegmund,Adv. Appl. Prob. 11:701 (1979);Ann. Prob. 10:581 (1982).

    Google Scholar 

  119. R. J. Beeler and J. A. Delaney,Phys. Rev. 130:926 (1963).

    Google Scholar 

  120. R. J. Beeler,Phys. Rev. 134A:1396 (1964).

    Google Scholar 

  121. H. B. Rosenstock,SIAM J. Appl. Math. 9:169 (1961);Phys. Rev. 187A:1166 (1969); J.Math. Phys. 11:487 (1970).

    Google Scholar 

  122. A. Dvoretzky and P. Erdös,Proceedings of the Second Berkeley Symposium (University of California Press, Berkeley, 1951).

    Google Scholar 

  123. N. C. Jain and W. E. Pruitt,Z. Wahrscheinlich. Verw. Geb. 16:279 (1970);J. Analys. Math. 24:369 (1971);Ann. Math. Stat. 43:1692 (1972);J. Analys. Math. 27:94 (1974).

    Google Scholar 

  124. G. H. Weiss,Proc. Natl. Acad. Sci. 77:4391 (1980).

    Google Scholar 

  125. M. D. Donsker and S. R. S. Varadhan,Commun. Pure Appl. Math. 32:721 (1979).

    Google Scholar 

  126. P. Grassberger and I. Procaccia,Phys. Rev. 26A:3686 (1982);J. Chem. Phys. 77:6281 (1982).

    Google Scholar 

  127. R. F. Kayser and J. B. Hubbard,Phys. Rev. Lett. 51:79 (1983).

    Google Scholar 

  128. G. H. Weiss and S. Havlin,J. Stat. Phys. 37:17 (1984).

    Google Scholar 

  129. J. Klafter, G. Zumofen, and A. Blumen,J. Phys. Lett. (Paris) 45:L49 (1984).

    Google Scholar 

  130. S. Havlin, G. H. Weiss, J. E. Kiefer, and M. Dishon,J. Phys. A17:L347 (1984).

    Google Scholar 

  131. S. Havlin, M. Dishon, J. E. Kiefer, and G. H. Weiss,Phys. Rev. Lett. 53:407 (1984).

    Google Scholar 

  132. M. Fixman,J. Chem. Phys. 81:3666 (1984).

    Google Scholar 

  133. M. Lax,Phys. Rev. 85:621 (1952).

    Google Scholar 

  134. R. I. Cukier,J. Phys. Chem. 87:582 (1983);J. Stat. Phys. 30:383 (1983).

    Google Scholar 

  135. M. Muthukumar and R. I. Cukier,J. Stat. Phys. 26:453 (1981).

    Google Scholar 

  136. M. Tokuyuma and R. I. Cukier,J. Chem. Phys. 76:6206 (1982).

    Google Scholar 

  137. R. I. Cukier and K. F. Freed,J. Chem. Phys. 78:2583 (1983).

    Google Scholar 

  138. D. F. Calef and J. M. Deutch,J. Chem. Phys. 79:203 (1983).

    Google Scholar 

  139. M. Muthukumar,J. Chem. Phys. 76:2667 (1982).

    Google Scholar 

  140. M. Lax,Rev. Mod. Phys. 23:287 (1951).

    Google Scholar 

  141. M. Bixon and R. Zwanzig,J. Chem. Phys. 75:2354 (1981).

    Google Scholar 

  142. D. L. Huber,J. Stat. Phys. 30:345 (1983) and references therein.

    Google Scholar 

  143. J. R. Lebenhaft and R. Kapral,J. Stat. Phys. 20:25 (1979).

    Google Scholar 

  144. M. Bixon and R. Zwanzig,J. Chem. Phys. 75:2354 (1981).

    Google Scholar 

  145. T. R. Kirkpatrick,J. Chem. Phys. 76:4225 (1982).

    Google Scholar 

  146. W. Th. F. den Hollander,J. Stat. Phys. 37:331 (1984).

    Google Scholar 

  147. D. Toussaint and F. Wilszek,J. Chem. Phys. 78:2642 (1983).

    Google Scholar 

  148. K. Kang and S. Redner,Phys. Rev. Lett. 52:955 (1984).

    Google Scholar 

  149. P. Meakin and H. E. Stanley,J. Phys. A17:L173 (1984).

    Google Scholar 

  150. K. Kang, P. Meakin, J. H. Oh, and S. Redner,J. Phys. A17:L665 (1984).

    Google Scholar 

  151. R. Kopelman, P. W. Klymko, J. S. Newhouse, and L. W. Anacker,Phys. Rev. B 29:3747 (1984).

    Google Scholar 

  152. P. Argyrakis and R. Kopelman,J. Theoret. Biol. 73:205 (1978).

    Google Scholar 

  153. R. Kopelman, J. Hoshen, J. S. Newhouse, and P. Argyrakis,J. Stat. Phys. 30:335 (1983).

    Google Scholar 

  154. R. Kopelman,J. Stat. Phys. (to appear).

  155. H. Scher and C. H. Wu,Proc. Natl. Acad. Sci. 78:22 (1981).

    Google Scholar 

  156. E. W. Montroll and B. J. West,Fluctuation Phemonema, J. L. Lebowitz and E. W. Montroll, eds. (North-Holland, Amsterdam, 1979), p. 63.

    Google Scholar 

  157. G. Wilemski and M. Fixman,J. Chem. Phys. 58:4009 (1973);J. Chem. Phys. 60:866, 878 (1974).

    Google Scholar 

  158. M. Doi,Chem. Phys. 11:107 (1975).

    Google Scholar 

  159. M. Battezati and A. Perico,J. Chem. Phys. 75:886 (1981).

    Google Scholar 

  160. G. H. Weiss,J. Chem. Phys. 80:2880 (1984).

    Google Scholar 

  161. N. Agmon and J. J. Hopfield,J. Chem. Phys. 78:6947 (1983);J. Chem. Phys. 80:592 (1984).

    Google Scholar 

  162. B. Bagchi, G. R. Fleming, and D. W. Oxtoby,J. Chem. Phys. 78:7375 (1983).

    Google Scholar 

  163. E. P. Ippen, C. V. Shank, and A. Bergman,Chem. Phys. Lett. 38:611 (1976).

    Google Scholar 

  164. D. A. Cremers and M. W. Windsor,Chem. Phys. Lett. 71:27 (1980).

    Google Scholar 

  165. J. L. Skinner and P. G. Wolynes,J. Chem. Phys. 69:2143 (1978);J. Chem. Phys. 72:4913 (1980).

    Google Scholar 

  166. N. G. van Kampen and I. Oppenheim,J. Math. Phys. 13:842 (1972).

    Google Scholar 

  167. G. H. Weiss and A. Szabo,Physica 119A:569 (1983).

    Google Scholar 

  168. S. H. Northmp, F. Zarrin, and J. A. McCammon,J. Phys. Chem. 86:2314 (1982).

    Google Scholar 

  169. A. Szabo, D. Shoup, S. H. Northrup, and J. A. McCammon,J. Chem. Phys. 77:4484 (1982).

    Google Scholar 

  170. D. Shoup, G. Lipari, and A. Szabo,Biophys. J. 36:697 (1981).

    Google Scholar 

  171. K. Solc and W. H. Stockmayer,J. Chem. Phys. 54:2981 (1971);Int. J. Chem. Kinet. 5:733 (1973).

    Google Scholar 

  172. K. S. Schmitz and J. M. Schurr,J. Phys. Chem. 76:534 (1972).

    Google Scholar 

  173. J. M. Schurr and K. S. Schmitz,J. Phys. Chem. 80:1934 (1972).

    Google Scholar 

  174. T. L. Hill,Proc. Natl. Acad. Sci. 72:4918 (1975).

    Google Scholar 

  175. H. C. Berg and E. M. Purcell,Biophys. J. 20:193 (1977).

    Google Scholar 

  176. D. Shoup and A. Szabo,J. Electroanal. Chem. 140:237 (1982).

    Google Scholar 

  177. O. Berg,Biophys. J. 47:1 (1985).

    Google Scholar 

  178. C. Delisi, F. W. Wiegel,Proc. Natl. Acad. Sci. 78:5569 (1981).

    Google Scholar 

  179. M. C. Wang and G. E. Uhlenbeck,Rev. Mod. Phys. 17:323 (1945).

    Google Scholar 

  180. C. D. Pagani,Boll. Un. Mat. Ital. 3:961 (1970).

    Google Scholar 

  181. S. Harris,J. Phys. A13:2149 (1980);J. Chem. Phys. 75:3037, 3103 (1981).

    Google Scholar 

  182. M. A. Burschka and U. M. Tilulaer,J. Stat. Phys. 25:569 (1981);J. Stat. Phys. 26:59 (1981);Physica A112:315 (1982).

    Google Scholar 

  183. Y. S. Mayya and D. C. Sahni,J. Chem. Phys. 79:2302 (1983).

    Google Scholar 

  184. R. Beals and U. Prolopopescu,J. Stat. Phys. 32:565 (1983).

    Google Scholar 

  185. J. V. Selinger and U. M. Tilulaer,J. Stat. Phys. 36:293 (1984).

    Google Scholar 

  186. U. M. Tilulaer,J. Stat. Phys. 37:589 (1984).

    Google Scholar 

  187. M. Suzuki,Adv. Chem. Phys. 46:195 (1981) and references Iherein.

    Google Scholar 

  188. F. Haake, J. W. Haus, and R. Glauber,Phys. Rev. A 23:3255 (1980).

    Google Scholar 

  189. F. de Pasquale, P. Tarlaglia, and P. Tombesi,Phys. Rev. A 25:466 (1982).

    Google Scholar 

  190. G. Adam, M. Delbrück,Structural Chemistry and Molecular Biology, A. Rich and N. Davidson, eds. (W. H. Freeman & Co., San Francisco, 1968), p. 198.

    Google Scholar 

  191. A. J. Frank, M. Gratzel, and J. J. Kozak,J. Am. Chem. Soc. 98:3317 (1976).

    Google Scholar 

  192. M. D. Hatlee, J. J. Kozak, G. Rothenberger, P. P. Infelta, and M. Gratzel,J. Chem. Phys. 84:1508 (1980); M. D. Hatlee and J. J. Kozak,Proc. Natl. Acad. Sci. 28:972 (1981).

    Google Scholar 

  193. M. Karplus and D. L. Weaver,Biopol. 18:1421 (1979).

    Google Scholar 

  194. D. L. Weaver,Biopol. 21:1275 (1982).

    Google Scholar 

  195. G. P. Zienlara, J. A. Nagy, and J. H. Freed,J. Chem. Phys. 73:5092 (1980);J. Phys. Chem. 86:824 (1982).

    Google Scholar 

  196. L. N. M. Duysens,Prog. Biophys. Mol. Biol. 14:1 (1964).

    Google Scholar 

  197. R. M. Pearlstein,Brookhaven Natl. Lab. 19:19 (1967).

    Google Scholar 

  198. E. W. Monlroll,J. Math. Phys. 10:753 (1969);J. Phys. Soc. Jpn. Suppl. 26:6 (1969).

    Google Scholar 

  199. W. Th. F. den Hollander, J. G. C. Bakker, and R. van Grondelle,Biochim. Biophys. Acta. 725:492 (1983).

    Google Scholar 

  200. J. G. C. Bakker, R. van Grondelle, and W. Th. F. den Hollander,Biochim. Biophys. Acta. 725, 508 (1983).

    Google Scholar 

  201. A. Blumen,J. Chem. Phys. 72:2632 (1980);Nuov. Cim. 63B:50 (1981).

    Google Scholar 

  202. A. Blumen and G. Zumofen,J. Chem. Phys. 75:892 (1981);J. Chem. Phys. 77:5127 (1982);J. Stat. Phys. 30:487 (1983).

    Google Scholar 

  203. G. Zumofen and A. Blumen,J. Chem. Phys. 76:3713 (1982);Chem. Phys. Lett. 83:372 (1981);Chem. Phys. Lett. 88:63 (1982);Chem. Phys. Lett. 98:393 (1983).

    Google Scholar 

  204. G. Zumofen, J. Klafter, and A. Blumen,J. Chem. Phys. 79:5131 (1983).

    Google Scholar 

  205. R. M. Pearlstein,J. Chem. Phys. 56:2431 (1972).

    Google Scholar 

  206. R. P. Hemenger, K. Lakatos-Lindenberg, and R. M. Pearlstein,J. Chem. Phys. 60:3271 (1974).

    Google Scholar 

  207. R. P. Hemenger and R. M. Pearlstein,Chem. Phys. 2:424 (1973).

    Google Scholar 

  208. W. P. Helman and K. Funabashi,J. Chem. Phys. 66:5790 (1977);J. Chem. Phys. 70:4813 (1979).

    Google Scholar 

  209. V. M. Kenkre,Chem. Phys. 36:377 (1979).

    Google Scholar 

  210. K. Funabashi,J. Chem. Phys. 72:3123 (1980).

    Google Scholar 

  211. W. P. Helman and K. Funabashi,J. Chem. Phys. 66:5790 (1977);J. Chem. Phys. 71:2458 (1979).

    Google Scholar 

  212. M. F. Shlesinger,J. Chem. Phys. 70:4813 (1979).

    Google Scholar 

  213. K. Lindenberg and V. Seshardri,J. Chem. Phys. 71:4075 (1979).

    Google Scholar 

  214. V. Seshadri and K. Lindenberg,J. Stat. Phys. 22:69 (1980).

    Google Scholar 

  215. H. E. Daniels,Proc. Cambridge Philos. Soc. 37:244 (1941).

    Google Scholar 

  216. G. H. Weiss and R. J. Rubin,J. Stat. Phys. 14:333 (1976);J. Stat. Phys. 22:97 (1980).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Weiss, G.H. Overview of theoretical models for reaction rates. J Stat Phys 42, 3–36 (1986). https://doi.org/10.1007/BF01010838

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01010838

Key words

Navigation