Skip to main content
SpringerLink
Log in
Book cover

Theoretical Molecular Biophysics pp 219–227Cite as

Crossing of Two Electronic States

  • Chapter
  • First Online:

  • 2190 Accesses

Part of the book series: Biological and Medical Physics, Biomedical Engineering ((BIOMEDICAL))

Abstract

We consider the avoided crossing of two electronic states along a nuclear coordinate Q. The two states are described by adiabatic wave functions

$$ \psi _{1,2}^{ad} (r,Q) $$
(21.1)

and the wave function

$$ \psi _1^{ad} (r,Q)\chi 1(Q) + \psi _2^{ad} (r,Q)\chi _2 (Q) $$
(21.2)

will be also written in matrix notation [57] as

$$ (\psi _1^{ad} (r,Q)\psi _2^{ad} (r,Q))\left( \begin{matrix} \chi _1 (Q) \cr \chi _2 (Q) \cr \end{matrix} \right). $$
(21.3)

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   64.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   84.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. T.L. Hill, An Introduction to Statistical Thermodynamics (Dover, New York, 1986)

    Google Scholar 

  2. S. Cocco, J.F. Marko, R. Monasson, arXiv:cond-mat/0206238v1

    Google Scholar 

  3. C. Storm, P.C. Nelson, Phys. Rev. E 67, 51906 (2003)

    MathSciNet  ADS  Google Scholar 

  4. K.K. Mueller-Niedebock, H.L. Frisch, Polymer 44, 3151 (2003)

    Google Scholar 

  5. C. Leubner, Eur. J. Phys. 6, 299 (1985)

    MATH  MathSciNet  Google Scholar 

  6. P.J. Flory, J. Chem. Phys. 10, 51 (1942)

    ADS  Google Scholar 

  7. M.L. Huggins, J. Phys. Chem. 46, 151 (1942)

    Google Scholar 

  8. M. Feig, C.L. Brooks III, Curr. Opin. Struct. Biol. 14, 217 (2004)

    Google Scholar 

  9. B. Roux, T. Simonson, Biophys. Chem. 78, 1 (1999)

    Google Scholar 

  10. A. Onufriev, Annu. Rep. Comput. Chem. 4, 125 (2008)

    Google Scholar 

  11. M. Born, Z. Phys. 1, 45 (1920)

    ADS  Google Scholar 

  12. D. Bashford, D. Case, Annu. Rev. Phys. Chem. 51, 29 (2000)

    Google Scholar 

  13. W.C. Still, A. Tempczyk, R.C. Hawley, T. Hendrickson, JACS 112, 6127 (1990)

    Google Scholar 

  14. G.D. Hawkins, C.J. Cramer, D.G. Truhlar, Chem. Phys. Lett. 246, 122 (1995)

    ADS  Google Scholar 

  15. M. Schaefer, M. Karplus, J. Phys. Chem. 100, 1578 (1996)

    Google Scholar 

  16. I.M. Wonpil, M.S. Lee, C.L. Brooks III, J. Comput. Chem. 24, 1691 (2003)

    Google Scholar 

  17. F. Fogolari, A. Brigo, H. Molinari, J. Mol. Recognit. 15, 377 (2002)

    Google Scholar 

  18. A.I. Shestakov, J.L. Milovich, A. Noy, J. Colloid Interface Sci. 247, 62 (2002)

    Google Scholar 

  19. B. Lu, D. Zhang, J.A. McCammon, J. Chem. Phys. 122, 214102 (2005)

    ADS  Google Scholar 

  20. P. Koehl, Curr. Opin. Struct. Biol. 16, 142 (2006)

    Google Scholar 

  21. P. Debye, E. Hueckel, Phys. Z. 24, 305 (1923)

    Google Scholar 

  22. G. Goüy, Comt. Rend. 149, 654 (1909)

    Google Scholar 

  23. G. Goüy, J. Phys. 9, 457 (1910)

    Google Scholar 

  24. D.L. Chapman, Philos. Mag. 25, 475 (1913)

    Google Scholar 

  25. O. Stern, Z. Elektrochem. 30, 508 (1924)

    Google Scholar 

  26. A.-S. Yang, M. Gunner, R. Sampogna, K. Sharp, B. Honig, Proteins 15, 252 (1993)

    Google Scholar 

  27. P.W. Atkins, Physical Chemistry (Freeman, New York, 2006)

    Google Scholar 

  28. W.J. Moore, Basic Physical Chemistry (Prentice-Hall, New York, 1983)

    Google Scholar 

  29. M. Schaefer, M. Sommer, M. Karplus, J. Phys. Chem. B 101, 1663 (1997)

    Google Scholar 

  30. R.A. Raupp-Kossmann, C. Scharnagl, Chem. Phys. Lett. 336, 177 (2001)

    ADS  Google Scholar 

  31. H. Risken, The Fokker–Planck Equation (Springer, Berlin, 1989)

    MATH  Google Scholar 

  32. H.A. Kramers, Physica 7, 284 (1941)

    MathSciNet  ADS  Google Scholar 

  33. P.O.J. Scherer, Chem. Phys. Lett. 214, 149 (1993)

    ADS  Google Scholar 

  34. E.W. Montroll, H. Scher, J. Stat. Phys. 9, 101 (1973)

    ADS  Google Scholar 

  35. E.W. Montroll, G.H. Weiss, J. Math. Phys. 6, 167 (1965)

    MathSciNet  ADS  Google Scholar 

  36. A.A. Zharikov, P.O.J. Scherer, S.F. Fischer, J. Phys. Chem. 98, 3424 (1994)

    Google Scholar 

  37. A.A. Zharikov, S.F. Fischer, Chem. Phys. Lett. 249, 459 (1995)

    ADS  Google Scholar 

  38. S.R. de Groot, P. Mazur, Irreversible Thermodynamics (Dover, New York, 1984)

    Google Scholar 

  39. D.G. Miller, Faraday Discuss. Chem. Soc. 64, 295 (1977)

    Google Scholar 

  40. R. Paterson, Faraday Discuss. Chem. Soc. 64, 304 (1977)

    Google Scholar 

  41. D.E. Goldman, J. Gen. Physiol. 27, 37 (1943)

    Google Scholar 

  42. A.L. Hodgkin, A.F. Huxley, J. Physiol. 117, 500 (1952)

    Google Scholar 

  43. J. Kenyon, How to solve and program the Hodgkin–Huxley equations (http://134.197.54.225/department/Faculty/kenyon/Hodgkin&Huxley/pdfs/HH.Program.pdf)

  44. J. Vreeken, A friendly introduction to reaction–diffusion systems, Internship Paper, AILab, Zurich, July 2002

    Google Scholar 

  45. E. Pollak, P. Talkner, Chaos 15, 026116 (2005)

    MathSciNet  ADS  Google Scholar 

  46. F.T. Gucker, R.L. Seifert, Physical Chemistry (W.W. Norton, New York, 1966)

    Google Scholar 

  47. S. Glasstone, K.J. Laidler, H. Eyring, The Theory of Rate Processes (McGraw-Hill, New York, 1941)

    Google Scholar 

  48. K.J. Laidler, Chemical Kinetics, 3rd edn. (Harper & Row, New York, 1987)

    Google Scholar 

  49. G.A. Natanson, J. Chem. Phys. 94, 7875 (1991)

    ADS  Google Scholar 

  50. R.A. Marcus, Annu. Rev. Phys. Chem. 15, 155 (1964)

    ADS  Google Scholar 

  51. R.A. Marcus, N. Sutin, Biochim. Biophys. Acta 811, 265 (1985)

    Google Scholar 

  52. R.A. Marcus, Angew. Chem. Int. Ed. Engl. 32, 1111 (1993)

    Google Scholar 

  53. A.M. Kuznetsov, J. Ulstrup, Electron Transfer in Chemistry and Biology (Wiley, Chichester, 1998), p. 49

    Google Scholar 

  54. P.W. Anderson, J. Phys. Soc. Jpn. 9, 316 (1954)

    ADS  Google Scholar 

  55. R. Kubo, J. Phys. Soc. Jpn. 6, 935 (1954)

    MathSciNet  ADS  Google Scholar 

  56. R. Kubo, in Fluctuations, Relaxations and Resonance in Magnetic Systems, ed. by D. ter Haar (Plenum, New York, 1962)

    Google Scholar 

  57. T.G. Heil, A. Dalgarno, J. Phys. B 12, 557 (1979)

    ADS  Google Scholar 

  58. L.D. Landau, Phys. Z. Sowjetun. 1, 88 (1932)

    MATH  Google Scholar 

  59. C. Zener, Proc. R. Soc. Lond. A 137, 696 (1932)

    MATH  ADS  Google Scholar 

  60. E.S. Kryachko, A.J.C. Varandas, Int. J. Quant. Chem. 89, 255 (2001)

    Google Scholar 

  61. E.N. Economou, Green’s Functions in Quantum Physics (Springer, Berlin, 1978)

    Google Scholar 

  62. H. Scheer, W.A. Svec, B.T. Cope, M.H. Studler, R.G. Scott, J.J. Katz, JACS 29, 3714 (1974)

    Google Scholar 

  63. A. Streitwieser, Molecular Orbital Theory for Organic Chemists (Wiley, New York, 1961)

    Google Scholar 

  64. J.E. Lennard-Jones, Proc. R. Soc. Lond. A 158, 280 (1937)

    ADS  Google Scholar 

  65. B.S. Hudson, B.E. Kohler, K. Schulten, in Excited States, ed. by E.C. Lin (Academic, New York, 1982), pp. 1–95

    Google Scholar 

  66. B.E. Kohler, C. Spangler, C. Westerfield, J. Chem. Phys. 89, 5422 (1988)

    ADS  Google Scholar 

  67. T. Polivka, J.L. Herek, D. Zigmantas, H.-E. Akerlund, V. Sundstrom, Proc. Natl. Acad. Sci. USA 96, 4914 (1999)

    ADS  Google Scholar 

  68. B. Hudson, B. Kohler, Synth. Met. 9, 241 (1984)

    Google Scholar 

  69. B.E. Kohler, J. Chem. Phys. 93, 5838 (1990)

    ADS  Google Scholar 

  70. W.T. Simpson, J. Chem. Phys. 17, 1218 (1949)

    ADS  Google Scholar 

  71. H. Kuhn, J. Chem. Phys. 17, 1198 (1949)

    ADS  Google Scholar 

  72. M. Gouterman, J. Mol. Spectrosc. 6, 138 (1961)

    ADS  Google Scholar 

  73. M. Gouterman, J. Chem. Phys. 30, 1139 (1959)

    ADS  Google Scholar 

  74. M. Gouterman, G.H. Wagniere, L.C. Snyder, J. Mol. Spectrosc. 11, 108 (1963)

    ADS  Google Scholar 

  75. C. Weiss, The Porphyrins, vol. III (Academic, New York, 1978), p. 211

    Google Scholar 

  76. D. Spangler, G.M. Maggiora, L.L. Shipman, R.E. Christofferson, J. Am. Chem. Soc. 99, 7470 (1977)

    Google Scholar 

  77. B.R. Green, D.G. Durnford, Annu. Rev. Plant Physiol. Plant Mol. Biol. 47, 685 (1996)

    Google Scholar 

  78. H.A. Frank et al., Pure Appl. Chem. 69, 2117 (1997)

    Google Scholar 

  79. R.J. Cogdell et al., Pure Appl. Chem. 66, 1041 (1994)

    Google Scholar 

  80. H. van Amerongen, R. van Grondelle, J. Phys. Chem. B 105, 604 (2001)

    Google Scholar 

  81. T. Frster, Ann. Phys. 2, 55 (1948)

    Google Scholar 

  82. T. Frster, Disc. Faraday Trans. 27, 7 (1965)

    Google Scholar 

  83. D.L. Dexter, J. Chem. Phys. 21, 836 (1953)

    ADS  Google Scholar 

  84. F.J. Kleima, M. Wendling, E. Hofmann, E.J.G. Peterman, R. van Grondelle, H. van Amerongen, Biochemistry 39, 5184 (2000)

    Google Scholar 

  85. T. Pullerits, M. Chachisvilis, V. Sundstrm, J. Phys. Chem. 100, 10787 (1996)

    Google Scholar 

  86. R.C. Hilborn, Am. J. Phys. 50, 982 (1982), revised 2002

    Google Scholar 

  87. S.H. Lin, Proc. R. Soc. Lond. A 335, 51 (1973)

    ADS  Google Scholar 

  88. S.H. Lin, W.Z. Xiao, W. Dietz, Phys. Rev. E 47, 3698 (1993)

    ADS  Google Scholar 

  89. MOLEKEL 4.0, P. Fluekiger, H.P. Luethi, S. Portmann, J. Weber, Swiss National Supercomputing Centre CSCS, Manno Switzerland, 2000

    Google Scholar 

  90. J. Deisenhofer, H. Michel, Science 245, 1463 (1989)

    ADS  Google Scholar 

  91. J. Deisenhofer, O. Epp, K. Miki, R. Huber, H. Michel, Nature 318, 618 (1985)

    ADS  Google Scholar 

  92. J. Deisenhofer, O. Epp, K. Miki, R. Huber, H. Michel, J. Mol. Biol. 180, 385 (1984)

    Google Scholar 

  93. H. Michel, J. Mol. Biol. 158, 567 (1982)

    Google Scholar 

  94. E.W. Knapp, P.O.J. Scherer, S.F. Fischer, BBA 852, 295 (1986)

    Google Scholar 

  95. P.O.J. Scherer, S.F. Fischer, in Chlorophylls, ed. by H. Scheer (CRC, Boca Raton, 1991), pp. 1079–1093

    Google Scholar 

  96. R.J. Cogdell, A. Gall, J. Koehler, Q. Rev. Biophys. 39, 227 (2006)

    Google Scholar 

  97. M. Ketelaars et al., Biophys. J. 80, 1591 (2001)

    ADS  Google Scholar 

  98. M. Matsushita et al., Biophys. J. 80, 1604 (2001)

    ADS  Google Scholar 

  99. K. Sauer, R.J. Cogdell, S.M. Prince, A. Freer, N.W. Isaacs, H. Scheer, Photochem. Photobiol. 64, 564 (1996)

    Google Scholar 

  100. A. Freer, S. Prince, K. Sauer, M. Papitz, A. Hawthorntwaite-Lawless, G. McDermott, R. Cogdell, N.W. Isaacs, Structure 4, 449 (1996)

    Google Scholar 

  101. M.Z. Papiz, S.M. Prince, A. Hawthorntwaite-Lawless, G. McDermott, A. Freer, N.W. Isaacs, R.J. Cogdell, Trends Plant Sci. 1, 198 (1996)

    Google Scholar 

  102. G. McDermott, S.M. Prince, A. Freer, A. Hawthorntwaite-Lawless, M. Papitz, R. Cogdell, Nature 374, 517 (1995)

    ADS  Google Scholar 

  103. N.W. Isaacs, R.J. Cogdell, A. Freer, S.M. Prince, Curr. Opin. Struct. Biol. 5, 794 (1995)

    Google Scholar 

  104. E.E. Abola, F.C. Bernstein, S.H. Bryant, T.F. Koetzle, J. Weng, in Crystallographic Databases – Information Content, Software Systems, Scientific Applications, ed. by F.H. Allen, G. Bergerhoff, R. Sievers (Data Commission of the International Union of Crystallography, Cambridge, 1987), p. 107

    Google Scholar 

  105. F.C. Bernstein, T.F. Koetzle, G.J.B. Williams, E.F. Meyer Jr., M.D. Brice, J.R. Rodgers, O. Kennard, T. Shimanouchi, M. Tasumi, J. Mol. Biol. 112, 535 (1977)

    Google Scholar 

  106. R. Sayle, E.J. Milner-White, Trends Biochem. Sci. 20, 374 (1995)

    Google Scholar 

  107. Y. Zhao, M.-F. Ng, G.H. Chen, Phys. Rev. E 69, 032902 (2004)

    ADS  Google Scholar 

  108. A.M. van Oijen, M. Ketelaars, J. Khler, T.J. Aartsma, J. Schmidt, Science 285, 400 (1999)

    Google Scholar 

  109. C. Hofmann, T.J. Aartsma, J. Khler, Chem. Phys. Lett. 395, 373 (2004)

    ADS  Google Scholar 

  110. S.E. Dempster, S. Jang, R.J. Silbey, J. Chem. Phys. 114, 10015 (2001)

    ADS  Google Scholar 

  111. S. Jang, R.J. Silbey, J. Chem. Phys. 118, 9324 (2003)

    ADS  Google Scholar 

  112. K. Mukai, S. Abe, Chem. Phys. Lett. 336, 445 (2001)

    ADS  Google Scholar 

  113. R.G. Alden, E. Johnson, V. Nagarajan, W.W. Parson, C.J. Law, R.G. Cogdell, J. Phys. Chem. B 101, 4667 (1997)

    Google Scholar 

  114. V. Novoderezhkin, R. Monshouwer, R. van Grondelle, Biophys. J. 77, 666 (1999)

    Google Scholar 

  115. M.K. Sener, K. Schulten, Phys. Rev. E 65, 31916 (2002)

    ADS  Google Scholar 

  116. A. Warshel, S. Creighton, W.W. Parson, J. Phys. Chem. 92, 2696 (1988)

    Google Scholar 

  117. M. Plato, C.J. Winscom, in The Photosynthetic Bacterial Reaction Center, ed. by J. Breton, A. Vermeglio (Plenum, New York, 1988), p. 421

    Google Scholar 

  118. P.O.J. Scherer, S.F. Fischer, Chem. Phys. 131, 115 (1989)

    ADS  Google Scholar 

  119. L.Y. Zhang, R.A. Friesner, Proc. Natl. Acad. Sci. USA 95, 13603 (1998)

    ADS  Google Scholar 

  120. M. Gutman, Structure 12, 1123 (2004)

    Google Scholar 

  121. P. Mitchell, Biol. Rev. Camb. Philos. Soc. 41, 445 (1966)

    Google Scholar 

  122. H. Luecke, H.-T. Richter, J.K. Lanyi, Science 280, 1934 (1998)

    ADS  Google Scholar 

  123. R. Neutze et al., BBA 1565, 144 (2002)

    Google Scholar 

  124. D. Borgis, J.T. Hynes, J. Chem. Phys. 94, 3619 (1991)

    ADS  Google Scholar 

  125. F. Juelicher, in Transport and Structure: Their Competitive Roles in Biophysics and Chemistry, ed. by S.C. Mller, J. Parisi, W. Zimmermann. Lecture Notes in Physics (Springer, Berlin, 1999)

    Google Scholar 

  126. A. Parmeggiani, F. Juelicher, A. Ajdari, J. Prost, Phys. Rev. E 60, 2127 (1999)

    ADS  Google Scholar 

  127. F. Jlicher, A. Ajdari, J. Prost, Rev. Mod. Phys. 69, 1269 (1997)

    ADS  Google Scholar 

  128. F. Jlicher, J. Prost, Progr. Theor. Phys. Suppl. 130, 9 (1998)

    ADS  Google Scholar 

  129. H. Qian, J. Math. Chem. 27, 219 (2000)

    MATH  MathSciNet  Google Scholar 

  130. M.E. Fisher, A.B. Kolomeisky, arXiv:cond-mat/9903308v1

    Google Scholar 

  131. N.D. Mermin, J. Math. Phys. 7, 1038 (1966)

    MathSciNet  ADS  Google Scholar 

  132. M.W. Schmidt, K.K. Baldridge, J.A. Boatz, S.T. Elbert, M.S. Gordon, J.J. Jensen, S. Koseki, N. Matsunaga, K.A. Nguyen, S. Su, T.L. Windus, M. Dupuis, J.A. Montgomery J. Comput. Chem. 14, 1347 (1993)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Physics Department T38, Technical University München, 85748, München, Germany

    Professor Dr. Philipp Scherer & Professor Dr. Sighart F. Fischer

Authors
  1. Professor Dr. Philipp Scherer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Professor Dr. Sighart F. Fischer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Philipp Scherer .

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Scherer, P., Fischer, S.F. (2010). Crossing of Two Electronic States. In: Theoretical Molecular Biophysics. Biological and Medical Physics, Biomedical Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85610-8_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-85610-8_21

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85609-2

  • Online ISBN: 978-3-540-85610-8

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics

Search

Navigation