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Introduction

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Spin Dynamics in Radical Pairs

Part of the book series: Springer Theses ((Springer Theses))

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Abstract

Radical pair reactions play an important role in a wide range of biological and technological processes. The overall rates and product yields of these reactions are strongly dependent on the spin dynamics of the radical pair, despite the fact that the magnetic interactions which produce these dynamics are far weaker than the thermal energy at room temperature. In this thesis we will outline the quantum mechanics which describes these radical pair reactions, before deriving semiclassical approximations which allow the computation of the ensemble averages of observables in realistic radical pairs. We will then apply these methods to three different problems in order to gain an insight into the physical processes which affect the rate and outcome of these radical pair reactions.

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References

  1. Dirac, P. A. M. (1928). The quantum theory of the electron. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 117, 610–624.

    Article  Google Scholar 

  2. Dirac, P. A. M. (1930). The Principles of Quantum Mechanics. Clarendon Press.

    Google Scholar 

  3. Slichter, C. P. (1963). Principles of Magnetic Resonance. Berlin: Springer.

    Google Scholar 

  4. Carrington, A. & McLachlan, A. D. (1967). Introduction to Magnetic Resonance with Applications to Chemistry and Chemical Physics. Harper & Row.

    Google Scholar 

  5. Atkins, P. W., & Friedman, R. S. (2011). Molecular Quantum Mechanics. Oxford: Oxford University Press.

    Google Scholar 

  6. Van Vleck, J. H. (1932). The Theory of Electric and Magnetic Susceptibilities. Clarendon Press.

    Google Scholar 

  7. Pauli, W. (1940). The connection between spin and statistics. Physical Review, 58, 716–722.

    Article  Google Scholar 

  8. Weller, A., Staerk, H., & Treichel, R. (1984). Magnetic-field effects on geminate radical-pair recombination. Faraday Discussions of the Chemical Society, 78, 271.

    Article  CAS  Google Scholar 

  9. Steiner, U. E., & Ulrich, T. (1989). Magnetic field effects in chemical kinetics and related phenomena. Chemical Reviews, 89, 51–147.

    Article  CAS  Google Scholar 

  10. Fuller, G. H. (1976). Nuclear spins and moments. Journal of Physical and Chemical Reference Data, 5, 835–1092.

    Article  CAS  Google Scholar 

  11. Rosman, K. J. R., & Taylor, P. D. P. (1998). Isotopic compositions of the elements 1997. Pure and Applied Chemistry, 70, 217–235.

    Article  CAS  Google Scholar 

  12. Brocklehurst, B. (1969). Formation of excited states by recombining organic ions. Nature, 221, 921–923.

    Article  CAS  Google Scholar 

  13. McLauchlan, K. A., & Steiner, U. E. (1991). The spin-correlated radical pair as a reaction intermediate. Molecular Physics, 73, 241–263.

    Article  CAS  Google Scholar 

  14. Hore, P. J., & Mouritsen, H. (2016). The radical-pair mechanism of magnetoreception. Annual Review of Biophysics, 45, 299.

    Article  CAS  Google Scholar 

  15. Rodgers, C. T., & Hore, P. J. (2009). Chemical magnetoreception in birds: the radical pair mechanism. Proceedings of the National Academy of Sciences of the United States of America, 106, 353–360.

    Article  Google Scholar 

  16. Closs, G. L. (1969). A mechanism explaining nuclear spin polarizations in radical combination reactions. Journal of the American Chemical Society, 91, 4552–4554.

    Article  CAS  Google Scholar 

  17. Kaptein, R., & Oosterhoff, J. (1969). Chemically induced dynamic nuclear polarization II. Chemical Physics Letters, 4, 195–197.

    Article  CAS  Google Scholar 

  18. Brocklehurst, B., & McLauchlan, K. A. (1996). Free radical mechanism for the effects of environmental electromagnetic fields on biological systems. International Journal of Radiation Biology, 69, 3–24.

    Article  CAS  Google Scholar 

  19. Till, U., & Hore, P. J. (1997). Radical pair kinetics in a magnetic field. Molecular Physics, 90, 289–296.

    Article  CAS  Google Scholar 

  20. Schulten, K., & Wolynes, P. G. (1978). Semi-classical description of electron-spin motion in radicals including effect of electron hopping. Journal of Chemical Physics, 68, 3292–3297.

    Article  CAS  Google Scholar 

  21. Weller, A., Nolting, F., & Staerk, H. (1983). A quantitative interpretation of the magnetic field effect on hyperfine-coupling-induced triplet fromation from radical ion pairs. Chemical Physics Letters, 96, 24–27.

    Article  CAS  Google Scholar 

  22. Klein, J., & Voltz, R. (1976). Time-resolved optical detection of coherent spin motion for organic-radical-ion pairs in solution. Physical Review Letters, 36, 1214–1217.

    Article  CAS  Google Scholar 

  23. Werner, H. J., Staerk, H., & Weller, A. (1978). Solvent, isotope, and magnetic field effects in the geminate recombination of radical ion pairs. Journal of Chemical Physics, 68, 2419.

    Article  CAS  Google Scholar 

  24. Brocklehurst, B. (1976). Magnetic field effect on the pulse shape of scintillations due to geminate recombination of ion pairs. Chemical Physics Letters, 44, 245–248.

    Article  CAS  Google Scholar 

  25. Timmel, C. R., Till, U., Brocklehurst, B., Mclauchlan, K. A., & Hore, P. J. (1998). Effects of weak magnetic fields on free radical recombination reactions. Molecular Physics, 95, 71–89.

    Article  CAS  Google Scholar 

  26. Werner, H. J., Schulten, Z., & Schulten, K. (1977). Theory of the magnetic field modulated geminate recombination of radical ion pairs in polar solvents: application to the pyrene-N. N-dimethylaniline system. Journal of Chemical Physics, 67, 646.

    Google Scholar 

  27. Fischer, H. (1983). The effect of a magnetic field on the product yield of a geminate radical-pair reaction in homogeneous solution. Chemical Physics Letters, 100, 255–258.

    Article  CAS  Google Scholar 

  28. Hamilton, C. A., Hewitt, J. P., McLauchlan, K. A., & Steiner, U. E. (1988). High resolution studies of the effects of magnetic fields on chemical reactions. Molecular Physics, 65, 423–438.

    Article  CAS  Google Scholar 

  29. Batchelor, S. N., Kay, C. W. M., McLauchlan, K. A., & Shkrob, I. A. (1993). Time-resolved and modulation methods in the study of the effects of magnetic fields on the yields of free-radical reactions. Journal of Chemical Physics, 97, 13250–13258.

    Article  CAS  Google Scholar 

  30. Brocklehurst, B. (1976). Spin correlation in the geminate reconibination of radical ions in hydrocarbons. Journal of the Chemical Society, Faraday Transactions, 2(72), 1869.

    Article  Google Scholar 

  31. Till, U., Timmel, C. R., Brocklehurst, B., & Hore, P. J. (1998). The inuence of very small magnetic fields on radical recombination reactions in the limit of slow recombination. Chemical Physics Letters, 298, 7–14.

    Article  CAS  Google Scholar 

  32. Norris, J. R., Lin, C. P., & Budil, D. E. (1987). Magnetic resonance of ultrafast chemical reactions. Journal of the Chemical Society, Faraday Transactions, 1(83), 13–27.

    Article  Google Scholar 

  33. Hamilton, C., McLauchlan, K., & Peterson, K. (1989). J-resonances in MARY and RYDMR spectra from freely diffusing radical ion pairs. Chemical Physics Letters, 162, 145–151.

    Article  CAS  Google Scholar 

  34. Weiss, E. A., Ratner, M. A., & Wasielewski, M. R. (2003). Direct measurement of singlet - triplet splitting within rodlike photogenerated radical ion pairs using magnetic field effects: estimation of the electronic coupling for charge recombination. Journal of Physical Chemistry, 107, 3639–3647.

    Article  CAS  Google Scholar 

  35. Weiss, E. A., Tauber, M. J., Ratner, M. A., & Wasielewski, M. R. (2005). Electron spin dynamics as a probe of molecular dynamics: temperature-dependent magnetic field effects on charge recombination within a covalent radical ion pair. Journal of the American Chemical Society, 127, 6052–6061.

    Article  CAS  Google Scholar 

  36. Staerk, H., Treichel, R., & Weller, A. (1983). Life uncertainty broadening in photoinduced electron transfer. Chemical Physics Letters, 96, 28–30.

    Article  CAS  Google Scholar 

  37. Anderson, P. W. (1959). New approach to the theory of superexchange interactions. Physical Review, 115, 2–13.

    Article  CAS  Google Scholar 

  38. McConnell, H. M. (1961). Intramolecular charge transfer in aromatic free radicals. Journal of Chemical Physics, 35, 508–515.

    Article  CAS  Google Scholar 

  39. Wasielewski, M. R. (2006). Energy, charge, and spin transport in molecules and self-assembled nanostructures inspired by photosynthesis. Journal of Organic Chemistry, 71, 5051–5066.

    Article  CAS  Google Scholar 

  40. Fromme, P., et al. (2002). Functional implications on the mechanism of the function of photosystem II including water oxidation based on the structure of photosystem II. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, 357, 1337–44.

    Google Scholar 

  41. Parson, W. W. (2003). Electron donors and acceptors in the initial steps of photosynthesis in purple bacteria: a personal account. Photosynthesis Research, 76, 81–92.

    Article  CAS  Google Scholar 

  42. Weiss, E. A., et al. (2005). Conformationally gated switching between superexchange and hopping within oligo-p-phenylene-based molecular wires. Journal of the American Chemical Society, 127, 11842–11850.

    Article  CAS  Google Scholar 

  43. Goldsmith, R. H., et al. (2005). Wire-like charge transport at near constant bridge energy through uorene oligomers. Proceedings of the National Academy of Sciences of the United States of America, 102, 3540–5.

    Article  CAS  Google Scholar 

  44. Jortner, J., & Ratner, M. A. (1997). Molecular Electronics. Oxford: Blackwell Science.

    Google Scholar 

  45. Nitzan, A. (2001). Electron transmission through molecules and molecular interfaces. Annual Review of Physical Chemistry, 52, 681–750.

    Article  CAS  Google Scholar 

  46. Moser, C. C., Keske, J. M., Warncke, K., Farid, R. S., & Dutton, P. L. (1992). Nature of biological electron transfer. Nature, 355, 796–802.

    Article  CAS  Google Scholar 

  47. Farid, R. S., Moser, C. C., & Dutton, P. L. (1993). Electron transfer in proteins. Current Opinion in Structural Biology, 3, 225–233.

    Article  CAS  Google Scholar 

  48. Murphy, C. J., et al. (1994). Fast photoinduced electron transfer through DNA intercalation. Proceedings of the National Academy of Sciences of the United States of America, 91, 5315–9.

    Article  CAS  Google Scholar 

  49. Davis, W. B., Svec, W. A., Ratner, M. A., & Wasielewski, M. R. (1998). Molecular-wire behaviour in p-phenylenevinylene oligomers. Nature, 396, 60–63.

    Article  CAS  Google Scholar 

  50. Weiss, E. A. (2004). Making a molecular wire: charge and spin transport through. Journal of The American Chemical Society, 126, 5577–5584.

    Article  CAS  Google Scholar 

  51. Tauber, M. J., Kelley, R. F., Giaimo, J. M., Rybtchinski, B., & Wasielewski, M. R. (2006). Electron hopping in pi-stacked covalent and self-assembled perylene diimides observed by ENDOR spectroscopy. Journal of the American Chemical Society, 128, 1782–1783.

    Article  CAS  Google Scholar 

  52. Scott, A. M., & Wasielewski, M. R. (2011). Temperature dependence of spin-selective charge transfer pathways in donor-bridge-acceptor molecules with oligomeric uorenone and p -phenylethynylene bridges. Journal of the American Chemical Society, 133, 3005–3013.

    Article  CAS  Google Scholar 

  53. Von Middendorf, A. (1859). Die Isepiptesen Rufflands. Mem. Acad. Sci. St Petersbourg VI. Ser. Tome, 8, 1–143.

    Google Scholar 

  54. Viguier, C. Le. (1882). Sens de L’orientation et ses Organes chez les Animaux et chez L’homme. Revue Philosophique de la France et de l’ Etranger, 14, 1–36.

    Google Scholar 

  55. Wiltschko, W. (1968). Über den Einflu statischer Magnetfelder auf die Zugorientierung der Rotkehlchen (Erithacus rubecula). Zeitschrift für Tierpsychologie, 25, 537–558.

    Article  CAS  Google Scholar 

  56. Walker, M. M., et al. (1997). Structure and function of the vertebrate magnetic sense. Nature, 390, 371–376.

    Article  CAS  Google Scholar 

  57. Lohmann, K. J., Lohmann, C. M. F., & Putman, N. F. (2007). Magnetic maps in animals: nature’s GPS. Journal of Experimental Biology, 210, 3697–3705.

    Article  Google Scholar 

  58. Mouritsen, H. (2013). Neurosciences - From Molecule to Behavior: A University Textbook (pp. 427–443). Berlin: Springer.

    Book  Google Scholar 

  59. Schulten, K., & Windemuth, A. (1986). Biophysical Effects of Steady Magnetic Fields (pp. 99–106). Berlin: Springer.

    Book  Google Scholar 

  60. Ritz, T., Adem, S., & Schulten, K. (2000). A model for photoreceptor-based magnetoreception in birds. Biophysical Journal, 78, 707–718.

    Article  CAS  Google Scholar 

  61. Wiltschko, W., & Wiltschko, R. (1972). Magnetic compass of European robins. Science, 176, 62–64.

    Article  CAS  Google Scholar 

  62. Wiltschko, W., & Wiltschko, R. (1996). Magnetic orientation in birds. Journal of Experimental Biology, 199, 29–38.

    Article  CAS  Google Scholar 

  63. Akesson, S., Morin, J., Muheim, R., & Ottosson, U. (2001). Avian orientation at steep angles of inclination: experiments with migratory white-crowned sparrows at the magnetic North Pole. Proceedings of the Royal Society B: Biological Sciences, 268, 1907–1913.

    Article  CAS  Google Scholar 

  64. Wiltschko, R., Ritz, T., Stapput, K., Thalau, P., & Wiltschko, W. (2005). Two different types of light-dependent responses to magnetic fields in birds. Current Biology, 15, 1518–1523.

    Article  CAS  Google Scholar 

  65. Wiltschko, R., et al. (2015). Magnetoreception in birds: the effect of radio-frequency fields. Journal of the Royal Society Interface, 12, 20141103.

    Article  Google Scholar 

  66. Maeda, K., et al. (2008). Chemical compass model of avian magnetoreception. Nature, 453, 387–390.

    Article  CAS  Google Scholar 

  67. Maeda, K., et al. (2012). Magnetically sensitive light-induced reactions in cryptochrome are consistent with its proposed role as a magnetoreceptor. Proceedings of the National Academy of Sciences of the United States of America, 109, 4774–4779.

    Article  Google Scholar 

  68. Dodson, C. A., Hore, P. J., & Wallace, M. I. (2013). A radical sense of direction: signaling and mechanism in cryptochrome magnetoreception. Trends in Biochemical Sciences, 38, 435–446.

    Article  CAS  Google Scholar 

  69. Lin, C., & Todo, T. (2005). The cryptochromes. Genome Biology, 6, 220.

    Article  CAS  Google Scholar 

  70. Nießner, C. (2011). Avian ultraviolet/violet cones identified as probable magnetoreceptors. PLOS ONE, 6, e20091.

    Article  CAS  Google Scholar 

  71. Solov’yov, I. A., Chandler, D. E., & Schulten, K. (2007). Magnetic field effects in arabidopsis thaliana cryptochrome-1. Biophysical Journal, 92, 2711–2726.

    Article  CAS  Google Scholar 

  72. Lee, A. A., et al. (2014). Alternative radical pairs for cryptochrome-based magnetoreception. Journal of the Royal Society Interface, 11, 20131063.

    Article  CAS  Google Scholar 

  73. Worster, S., Kattnig, D. R., & Hore, P. J. (2016). Spin relaxation of radicals in cryptochrome and its role in avian magnetoreception. Journal of Chemical Physics, 145, 035104.

    Article  CAS  Google Scholar 

  74. Kattnig, D. R., Solov’yov, I. A., & Hore, P. J. (2016). Electron spin relaxation in cryptochrome-based magnetoreception. Physical Chemistry Chemical Physics, 18, 12443–12456.

    Article  CAS  Google Scholar 

  75. Kattnig, D. R., Sowa, J. K., Solov’yov, I. A., & Hore, P. J. (2016). Electron spin relaxation can enhance the performance of a cryptochrome-based magnetic compass sensor. New Journal of Physics, 18, 063007.

    Article  CAS  Google Scholar 

  76. Tang, C. W., & Vanslyke, S. A. (1987). Organic electroluminescent diodes. Applied Physics Letters, 51, 913–915.

    Article  CAS  Google Scholar 

  77. Kido, J. (1999). Organic displays. Physics World, 12, 27–30.

    Article  CAS  Google Scholar 

  78. OLED displays and organic photovoltaics. (2009). Nature Photonics, 3, 457.

    Article  CAS  Google Scholar 

  79. Forrest, S. R. (2004). The path to ubiquitous and low-cost organic electronic appliances on plastic. Nature, 428, 911–918.

    Article  CAS  Google Scholar 

  80. Lupton, J. M., McCamey, D. R., & Boehme, C. (2010). Coherent spin manipulation in molecular semiconductors: getting a handle on organic spintronics. ChemPhysChem, 11, 3040–3058.

    Article  CAS  Google Scholar 

  81. Reineke, S. (2015). Complementary LED technologies. Nature Materials, 14, 459–462.

    Article  CAS  Google Scholar 

  82. Frankevich, E. L., et al. (1992). Polaron-pair generation in poly(phenylene vinylenes). Physical Review B, 46, 9320–9324.

    Article  CAS  Google Scholar 

  83. Hu, B., & Wu, Y. (2007). Tuning magnetoresistance between positive and negative values in organic semiconductors. Nature Materials, 6, 985–91.

    Article  CAS  Google Scholar 

  84. Bobbert, P. A., Nguyen, T. D., Van Oost, F. W. A., Koopmans, B., & Wohlgenannt, M. (2007). Bipolaron mechanism for organic magnetoresistance. Physical Review Letters, 99, 216801.

    Article  CAS  Google Scholar 

  85. Lupton, J. M., & Boehme, C. (2008). Magnetoresistance in organic semiconductors. Nature Materials, 7, 598.

    Article  CAS  Google Scholar 

  86. Nguyen, T. D., Gautam, B. R., Ehrenfreund, E., & Vardeny, Z. V. (2010). Magnetoconductance response in unipolar and bipolar organic diodes at ultrasmall fields. Physical Review Letters, 105, 166804.

    Article  CAS  Google Scholar 

  87. Ehrenfreund, E., & Vardeny, Z. V. (2012). Effects of magnetic field on conductance and electroluminescence in organic devices. Israel Journal of Chemistry, 52, 552–562.

    Article  CAS  Google Scholar 

  88. Cox, M., et al. (2014). Spectroscopic evidence for trap-dominated magnetic field effects in organic semiconductors. Physical Review B, 90, 155205.

    Article  CAS  Google Scholar 

  89. Kersten, S. P., Schellekens, A. J., Koopmans, B., & Bobbert, P. A. (2011). Magnetic-field dependence of the electroluminescence of organic light-emitting diodes: a competition between exciton formation and spin mixing. Physical Review Letters, 106, 197402.

    Article  CAS  Google Scholar 

  90. Nguyen, T. D., et al. (2010). Isotope effect in spin response of pi-conjugated polymer films and devices. Nature Materials, 9, 345–352.

    Article  CAS  Google Scholar 

  91. McCamey, D. R., Lee, S. Y., Paik, S. Y., Lupton, J. M., & Boehme, C. (2010). Spin-dependent dynamics of polaron pairs in organic semiconductors. Physical Review B, 82, 125206.

    Article  CAS  Google Scholar 

  92. Wang, F., Yang, C. G., Ehrenfreund, E., & Vardeny, Z. V. (2010). Spin dependent reactions of polaron pairs in PPV-based organic diodes. Synthetic Metals, 160, 297–302.

    Article  CAS  Google Scholar 

  93. Hiscock, H. G., et al. (2016). The quantum needle of the avian magnetic compass. Proceedings of the National Academy of Sciences of the United States of America, 113, 201600341.

    Article  CAS  Google Scholar 

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Lewis, A. (2018). Introduction. In: Spin Dynamics in Radical Pairs. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-00686-0_1

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