Tight-bindinc model for DNA double chains: Metal-insulator transition due to the formation of a double strand of DNA

International Journal of Modern Physics B

Volumn 11, Issue 20, 1997, Pages 2405-2423

  Iguchi, Kazumoto ^a  

^a NONE   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0010033846     PISSN: 02179792     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0217979297001222     Document Type: Article

References (47)

1. A. Szent-Györgyi. Science 93, 609 (1941); Nature 148, 157 (1941).
2. A. Szent-Györgyi. Science 93, 609 (1941); Nature 148, 157 (1941).
3. M. G. Evans and J. Gergely, Biochim. Biophys. Acta 3, 188 (1949).
4. D. D. Eley, G. P. Parfitt, M. B. Perry and D. H. Taytum, Trans. Fraday Soc. 49, 79 (1953); D. D. Eley and D. I. Spivey, Trans. Fraday Soc. 64, 1432 (1960).
5. D. D. Eley, G. P. Parfitt, M. B. Perry and D. H. Taytum, Trans. Fraday Soc. 49, 79 (1953); D. D. Eley and D. I. Spivey, Trans. Fraday Soc. 64, 1432 (1960).
6. S. Yomosa, Biopolymers Simposia 1. 1 (1964); J. Phys. Soc. Jpn. 19, 1718 (1964).
7. S. Yomosa, Biopolymers Simposia 1. 1 (1964); J. Phys. Soc. Jpn. 19, 1718 (1964).
8. J. Ladik. "Quantum mechanical considerations on some properties of DNA", in The Structure and Properties of Biomolecules and Biological Systems, ed. J. Duchesne, Adv. Chem. Phys. VII, 84 (1964). References therein; T. A. Hoffmann and J. Ladik, Cancer Res. 21, 474 (1961); J. Ladik and G. Biczó, J. Chem. Phys. 42, 1658 (1965); J. Ladik, Int. J. Quantum Chem.: Quantum Biology Symp. 1, 5 (1974).
9. J. Ladik. "Quantum mechanical considerations on some properties of DNA", in The Structure and Properties of Biomolecules and Biological Systems, ed. J. Duchesne, Adv. Chem. Phys. VII, 84 (1964). References therein; T. A. Hoffmann and J. Ladik, Cancer Res. 21, 474 (1961); J. Ladik and G. Biczó, J. Chem. Phys. 42, 1658 (1965); J. Ladik, Int. J. Quantum Chem.: Quantum Biology Symp. 1, 5 (1974).
10. J. Ladik. "Quantum mechanical considerations on some properties of DNA", in The Structure and Properties of Biomolecules and Biological Systems, ed. J. Duchesne, Adv. Chem. Phys. VII, 84 (1964). References therein; T. A. Hoffmann and J. Ladik, Cancer Res. 21, 474 (1961); J. Ladik and G. Biczó, J. Chem. Phys. 42, 1658 (1965); J. Ladik, Int. J. Quantum Chem.: Quantum Biology Symp. 1, 5 (1974).
11. J. Ladik. "Quantum mechanical considerations on some properties of DNA", in The Structure and Properties of Biomolecules and Biological Systems, ed. J. Duchesne, Adv. Chem. Phys. VII, 84 (1964). References therein; T. A. Hoffmann and J. Ladik, Cancer Res. 21, 474 (1961); J. Ladik and G. Biczó, J. Chem. Phys. 42, 1658 (1965); J. Ladik, Int. J. Quantum Chem.: Quantum Biology Symp. 1, 5 (1974).
12. A. K. Bakhshi. Prog. Biophys. Molec. Biol. 61, 187 (1994). References therein. This article is a review for the work of Ladik's group, where the theory is based upon the belief that DNA and protein can be treated by the same type of theory for electrons in linear chain systems, which is different from the author's assertion of the present paper.
13. D. Paterson, Sci. Am. 272, No. 5, 22 (1995).
14. T. J. Meade and J. F. Kayyem. Angew. Chem. Int. Ed. Engl. 34, 352 (1995).
15. C. J. Murphy, M. R. Arkin. Y. Jenkins, N. D. Ghatlia, S. H. Bossmann, N. J. Turro and J. K. Barton. Science 262, 1025 (1993).
16. A. K. Felts, W. T. Pollard and R. A. Friesner. J. Phys. Chem. 99, 2929 (1995).
17. J. D. Watson and F. H. C. Crick, Nature 171, 737, 964 (1953); B. Lewin, Genes V, (Oxford University Press, Oxford. 1994).
18. J. D. Watson and F. H. C. Crick, Nature 171, 737, 964 (1953); B. Lewin, Genes V, (Oxford University Press, Oxford. 1994).
19. W. P. Su. J. R. Schrieffer and A. J. Heeger, Phys. Rev. Lett. 42, 1698 (1979); Phys. Rev. B22, 2099 (1980); W. P. Su and J. R. Schrieffer, Phys. Rev. Lett. 46, 738 (1981).
20. W. P. Su. J. R. Schrieffer and A. J. Heeger, Phys. Rev. Lett. 42, 1698 (1979); Phys. Rev. B22, 2099 (1980); W. P. Su and J. R. Schrieffer, Phys. Rev. Lett. 46, 738 (1981).
21. W. P. Su. J. R. Schrieffer and A. J. Heeger, Phys. Rev. Lett. 42, 1698 (1979); Phys. Rev. B22, 2099 (1980); W. P. Su and J. R. Schrieffer, Phys. Rev. Lett. 46, 738 (1981).
22. I did not pay any attention to many-body effects such as the electron-hole and electron-electron interactions, although it. is possible to include these effects. This is an interesting problem but out of the scope of my purpose here. So. I ignore such many-body effects in this paper. See W. Kohn, "Metals and Insulators", in Many-Body Physics, Edited by C. DeWitt and R. Balian, (Gordon and Breach. New York, 1968), p. 353. References therein.
23. M. Peyrard and A. R. Bishop, Phys. Rev. Lett. 62, 2755 (1989). References therein.
24. S. W. Englander, N. R. Kallenbach, A. J. Heeger, J. A. Krumhansl and S. Litwin, Proc. Natl. Acad. Sci. (USA) 77, 7222 (1980). S. Yomosa, Phys. Rev. A27, 2120 (1983); ibid. A30, 474 (1984). S. Takeno and S. Homma, Prog. Theor. Phys. 77, 548 (1987).
25. S. W. Englander, N. R. Kallenbach, A. J. Heeger, J. A. Krumhansl and S. Litwin, Proc. Natl. Acad. Sci. (USA) 77, 7222 (1980). S. Yomosa, Phys. Rev. A27, 2120 (1983); ibid. A30, 474 (1984). S. Takeno and S. Homma, Prog. Theor. Phys. 77, 548 (1987).
26. S. W. Englander, N. R. Kallenbach, A. J. Heeger, J. A. Krumhansl and S. Litwin, Proc. Natl. Acad. Sci. (USA) 77, 7222 (1980). S. Yomosa, Phys. Rev. A27, 2120 (1983); ibid. A30, 474 (1984). S. Takeno and S. Homma, Prog. Theor. Phys. 77, 548 (1987).
27. S. W. Englander, N. R. Kallenbach, A. J. Heeger, J. A. Krumhansl and S. Litwin, Proc. Natl. Acad. Sci. (USA) 77, 7222 (1980). S. Yomosa, Phys. Rev. A27, 2120 (1983); ibid. A30, 474 (1984). S. Takeno and S. Homma, Prog. Theor. Phys. 77, 548 (1987).
28. Y. Avishai and J. -M. Luck, Phys. Rev. B45, 1074 (1992); ibid. B49, 8679 (1994); Y. Avishai and J. Bar-Touv, ibid. B51, 8069 (1995). References therein.
29. Y. Avishai and J. -M. Luck, Phys. Rev. B45, 1074 (1992); ibid. B49, 8679 (1994); Y. Avishai and J. Bar-Touv, ibid. B51, 8069 (1995). References therein.
30. Y. Avishai and J. -M. Luck, Phys. Rev. B45, 1074 (1992); ibid. B49, 8679 (1994); Y. Avishai and J. Bar-Touv, ibid. B51, 8069 (1995). References therein.
31. N. W. Aschcroft and N. D. Mermin, Solid State Physics, (Holt-Saunders. New York, 1976).
32. E. Hückel, Z. Phys. 70, 204 (1931).
33. K. Fukui, T. Yonezawa and H. Shingu. J. Chem. Phys. 20, 722 (1952); K. Fukui, "A Simple Quantum-Theoretical Interpretation of the Chemical Reactivity of Organic Compounds" in Molecular Orbitals in Chemistry, Physics and Biology, Edited by P. -O. Löwdin and B Pullman (Academic Press, New York. 1964), p. 513; Chemical Reactions and Electronic Orbitals, in Japanese, (Maruzen, Tokyo. 1976). R. Hoffmann, "Introduction to the Electronic Structure of Extended Systems", in Modern Perspectives in Inorganic Crystal Chemistry. Edited by E. Parthé, (Kluwer, Amsterdam. 1992), p. 97.
34. K. Fukui, T. Yonezawa and H. Shingu. J. Chem. Phys. 20, 722 (1952); K. Fukui, "A Simple Quantum-Theoretical Interpretation of the Chemical Reactivity of Organic Compounds" in Molecular Orbitals in Chemistry, Physics and Biology, Edited by P. -O. Löwdin and B Pullman (Academic Press, New York. 1964), p. 513; Chemical Reactions and Electronic Orbitals, in Japanese, (Maruzen, Tokyo. 1976). R. Hoffmann, "Introduction to the Electronic Structure of Extended Systems", in Modern Perspectives in Inorganic Crystal Chemistry. Edited by E. Parthé, (Kluwer, Amsterdam. 1992), p. 97.
35. K. Fukui, T. Yonezawa and H. Shingu. J. Chem. Phys. 20, 722 (1952); K. Fukui, "A Simple Quantum-Theoretical Interpretation of the Chemical Reactivity of Organic Compounds" in Molecular Orbitals in Chemistry, Physics and Biology, Edited by P. -O. Löwdin and B Pullman (Academic Press, New York. 1964), p. 513; Chemical Reactions and Electronic Orbitals, in Japanese, (Maruzen, Tokyo. 1976). R. Hoffmann, "Introduction to the Electronic Structure of Extended Systems", in Modern Perspectives in Inorganic Crystal Chemistry. Edited by E. Parthé, (Kluwer, Amsterdam. 1992), p. 97.
36. K. Fukui, T. Yonezawa and H. Shingu. J. Chem. Phys. 20, 722 (1952); K. Fukui, "A Simple Quantum-Theoretical Interpretation of the Chemical Reactivity of Organic Compounds" in Molecular Orbitals in Chemistry, Physics and Biology, Edited by P. -O. Löwdin and B Pullman (Academic Press, New York. 1964), p. 513; Chemical Reactions and Electronic Orbitals, in Japanese, (Maruzen, Tokyo. 1976). R. Hoffmann, "Introduction to the Electronic Structure of Extended Systems", in Modern Perspectives in Inorganic Crystal Chemistry. Edited by E. Parthé, (Kluwer, Amsterdam. 1992), p. 97.
37. R. E. Peierls, Quantum. Theory of Solids. (Clarendon Press, Oxford, 1995).
38. P. W. Anderson. Phys. Rev. 109, 1492 (1958).
39. N. F. Mott, Proc. Phys. Soc. A62, 416 (1949); Metal-Insulator Transitions, (Taylor & Francis, London, 1974).
40. N. F. Mott, Proc. Phys. Soc. A62, 416 (1949); Metal-Insulator Transitions, (Taylor & Francis, London, 1974).
41. B. Sutherland, Phys. Rev. B34, 5208 (1986).
42. K. Iguchi, Int. J. Mod. Phys. B10, 3827 (1996).
43. W. R. Bauer, F. H. C. Crick and J. H. White, Scientific American 243, 100 (1980): J. C. Wang, Scientific American 247, 94 (1982). De Witt Sumners, Math. Intelligencer 12, 71 (1990).
44. W. R. Bauer, F. H. C. Crick and J. H. White, Scientific American 243, 100 (1980): J. C. Wang, Scientific American 247, 94 (1982). De Witt Sumners, Math. Intelligencer 12, 71 (1990).
45. W. R. Bauer, F. H. C. Crick and J. H. White, Scientific American 243, 100 (1980): J. C. Wang, Scientific American 247, 94 (1982). De Witt Sumners, Math. Intelligencer 12, 71 (1990).
46. n+1,n is satisfied. In the ladder and decorated ladder I assume that it is always satisfied. Hence. M is simplectic in our models.
47. J. K. Burdett, Prog. Solid. St. Chem. 15, 173 (1984). The method of Burdett is applicable to only the double chain structures with monatomic unit cells. However, the method that I am proposing in the present paper is applicable to the double chain structures with polyatomic unit cells as well as with an aperiodic arrangement of potentials in the system.