Semiclassical theory for tunneling of electrons interacting with media

Journal of Physical Chemistry A

Volumn 105, Issue 12, 2001, Pages 2652-2659

  Burin, Alexander L ^a   Berlin, Yuri A ^a   Ratner, Mark A ^a  

^a NORTHWESTERN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRON DYNAMICS;

CHARGE TRANSFER; DEGREES OF FREEDOM (MECHANICS); ELECTRON TRANSPORT PROPERTIES; ELECTRONS;

ELECTRON TUNNELING;

EID: 0035967359     PISSN: 10895639     EISSN: None     Source Type: Journal    
DOI: 10.1021/jp0037697     Document Type: Article

References (62)

1. Barbara, P. F.; Meyer, T. J.; Ratner, M. A. J. Phys. Chem. 1996, 100, 13148.
2. Billing, G. D.; Mikkelsen, K. V. Advanced Molecular Dynamics and Chemical Kinetics; Wiley: New York, 1997.
3. Kuznetsov, A. M.; Ulstrup, J. Electron Transfer in Chemistry and Biology; Wiley: Chichester, U.K., 1999.
4. Bixon, M.; Jortner, J. Adv. Chem. Phys. 1999, 106, 35.
5. Ratner, M. A.; Jortner, J. Molecular Electronics; Blackwell: Oxford, U.K., 1997.
6. Aviram, A.; Ratner, M. A. Molecular Electronics: Science and Technology; New York Academy of Sciences: New York, 1998.
7. Bumm L. A.; Arnold J. J.; Dunbar T. D.; Allara D. L.; Weiss P. S. J. Phys. Chem B 1999, 103, 8122.
8. Makri, N.; Miller, W. H. J. Chem. Phys. 1989, 91, 4026.
9. Miller, W. H.; Manz, J.; Jost, R.; Troe, J.; Gaspard, P.; Marcus, R. A. Adv. Chem. Phys. 1997, 101, 853.
10. Miller, W. H. Faraday Discuss. 1995, 102, 53.
11. Skinner, D. E.; Miller, W. H. Chem. Phys. Lett. 1999, 300, 20.
12. Marcus, R. A. Rev. Mod. Phys. 1993, 65, 599.
13. Buttiker, M.; Landauer, R. Phys. Rev. Lett. 1982, 49, 1739.
14. Imry, Y.; Landauer, R. Rev. Mod. Phys. 1999, 71, S306.
15. Gasparian, V. Superlaltice Microst. 1998, 23, 809.
16. Steinberg, A. M. Superlaltice Microst. ibid. 1998, 23, 823.
17. For a generalization to the tight-binding model, see: Nitzan, A.; Jortner, J.; Wilkie, J.; Burin, A. L.; Ratner, M. A. J. Phys. Chem. B 2000, 104, 5661.
18. Leggett, A. J.; Chakravarty, S.; Dorsey, A. T.; Fisher, M. P. A.; Garg, A.; Zwerger, W. Rev. Mod. Phys. 1987, 59, 1.
19. Kagan, Yu.; Prokofev, N. V. Quantum Tunneling in Condensed Media, Kagan, Yu., Leggett, A. J., Eds.; Elsevier: Amsterdam, 1992.
20. (a) Pazy, E.; Laikhtman, B. Phys. Rev. B 1999, 59, 15854.
21. (b) Sumetskii, M. Yu. Sov. Phys. JETP1985, 62, 355;
22. Sumetskii, M. Yu. Phys. Rev. B 1992, 46, 4702.
23. Pollard, W. T.; Friesner, R. A. J. Chem. Phys. 1994, 100, 5054.
24. Skourtis, S. S.; Mukamel, S. Chem. Phys. 1995, 197, 367.
25. Davis, W. B.; Wasielewski, M. R.; Ratner, M. A.; Mujica, V.; Nitzan, A. J. Phys. Chem. A 1997, 101, 6158.
26. Bixon M.; Jortner J. J. Chem. Phys. 1997, 107, 5154.
27. Davis, W. B.; Svec, W. A.; Ratner, M. A.; Wasielewski, M. R. Nature 1998, 396, 60.
28. Ness, H.; Fisher, A. J: Phys. Rev. Lett. 1999, 83, 452.
29. Emberly, E. G.; Kirczenow, G. Phys. Rev. B 2000, 61, 5740.
30. Bonca, J.; Trugman, S. A. Phys. Rev. Lett. 1997, 79, 4874.
31. Thompson, K.; Makri, N. Phys. Rev. E 1999, 49, R4729.
32. Yu, Z. G.; Smith, D. L.; Saxena, A.; Bishop, A. R. Phys. Rev. B 1999, 59, 16001.
33. Segal, D.; Nitzan, A.; Davis, W. B.; Wasielewski, M. R.; Ratner, M. A. J. Phys. Chem. B 2000, 104, 3817.
34. Landau, L. D.; Lifshitz, E. M. Quantum Mechanics: nonrelativstic theory; Pergamon Press: Oxford, U.K., 1977.
35. Mujica, V.; Roitberg, A. E.; Ratner, M. A. J. Chem Phys. 2000, 112, 6834.
36. Xue, Y. Q.; Datta, S. Phys. Rev. Lett. 1999, 83, 4844.
37. We have assumed that the transport occurs by electron tunneling. In the (more common) case of hole tunneling, see: Newton, M. D. Chem. Rev. 1991, 91, 767, the barrier height is still the same in a symmetric junction.
38. Haag, R.; Rampi, M. A.; Holmin, R. E.; Whitesides, G. M. J. Am. Chem. Soc. 1999, 121, 7895.
39. Holmin, R. E.; Haag, R.; Ismagilov, R. F.; Rampi, M. A.; Whitesides, G. M. To be published.
40. Dresselhaus, M. S.; Eklund, P. C. Adv. Phys. 2000, 49, 705.
41. Mujica, V.; Kemp, M.; Ratner, M. A. J. Chem. Phys. 1994, 101, 6849 and 6856.
42. Petrov, E. G.; Tolokh, I. S.; Demidenko, A. A.; Gorbach, V. V. Chem. Phys. 1995, 193, 237.
43. Magoga M.; Joachim, C. Phys. Rev B 1997, 56, 4722.
44. Datta, S.; Tian, W. Phys. Rev. B 1997, 55, R1914.
45. The relationship between tight-binding and tunneling-barrier Hamiltonians is discussed by: Galperin, M.; Segal, D.; Nitzan, A. J. Chem. Phys. 1999, 111, 1569.
46. For polyalkane bandwidth see, e.g.: Miao, M. S.; Van Camp, P. E.; Ladik, J. J.; Mintmire, J. W. Phys. Rev. B 1996, 54, 10430.
47. Ladik, J. J. Quantum Theory of Polymers as Solids; Plenum: New York, 1987 and references therein.
48. Berlin, Yu. A.; Burin, A. L.; Ratner, M. A. To be published.
49. Castiglioni, C.; Lopez-Navarette, J. T.; Zerbi, G.; Gussoni, M. Solid State Commun. 1988, 65, 625.
50. Tian, B.; Zerbi, G.; Müllen, K. J. Chem. Phys. 1991, 95, 3198.
51. Burin, A. L.; Ratner, M. A. J. Chem. Phys. 1998, 109, 6102.
52. The general coupling to vibrations appears in the polaron problem, one of the standard issue in narrow band conduction. The classic works are: Holstein, T. Ann. Phys. 1959, 8, 325 and 343.
53. The coupling strengths can be observed using resonant Raman spectroscopy, see, e.g.: Meyers, A. B. Chem. Rev. 1996, 96, 911.
54. Williams, R. D.; Hupp, J. T.; Ramm, M. T.; Nelsen, S. F. J. Phys Chem. A 1999, 103, 11172.
55. Newton, M. D.; Sutin, N. Annu. Rev. Phys. Chem. 1984, 35, 437.
56. Bolton, J. R.; Archer, M. D. Electron Transfer in Inorganic, Organic and Biological Systems; Advances in Chemistry Series 228; Bolton, J. R., Malaga, N., McLendon, G., Eds.; American Chemical Society: Washington, 1991; p 91 .
57. Schatz, G. C.; Ratner, M. A. Quantum Mechanics in Chemistry; Prentice Hall: Englewood Cliffs, NJ, 1993.
58. Phillips, P.; Silbey, R. J. Phys. Rev. A 1986, 34, 707.
59. Persson, B. N. J.; Baratoff, A. Phys. Rev. Lett. 1987, 59, 339.
60. Similar behavior involving vibronic coupling along the bridge modifying mechanism and increasing rate has been noted in donor/bridge/ acceptor electron transfer; cf. e.g.: Ogawa, M. Y.; Wishart, J. F.; Young, Z. Y.; Miller, J. R.; Isied, S. S. J. Phys. Chem. 1993, 97, 11456 and refs 13 and 19 therein.
61. Path integral studies of the electron-transfer problem enable one to obtain the exact answer for linearly-coupled harmonic models, see: Makri, N.; Sim, E. J. Phys. Chem. B 1997, 101, 5446.
62. Evans, D. G.; Nitzan, A.; Ratner, M. A. J. Chem. Phys. 1998, 108, 6387.