Skip to main content
SpringerLink
Log in

Extended π-networks with multiple spin-pairing phases: resonance-theory calculations on poly-polyphenanthrenes

  • Published:
Theoretica chimica acta Aims and scope Submit manuscript

Abstract

The poly-polyphenanthrene family of extended π-network strips with members ranging from polyacetylene to graphite is considered in terms of the locally correlated valence-bond or Heisenberg Hamiltonian. Resonance theory wavefunctions which provide a variational upper bound to the ground state energy are developed in a graph-theoretic formalism extendable to more general localized wavefunction cluster expansions. The graph-theoretic formalism facilitates the use of general transfer matrix techniques, which are especially powerful in application to quasi-one-dimensional systems such as are illustratively treated here. It is argued that these strips exhibit states of different long-range spin-pairing orderings. Novel properties associated with these different resulting phases are briefly indicated, including the possibilities of solitonic excitations and the reactivity at the ends of the strips. The qualitative arguments are supported by numerical calculations for strips up to width 8.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Pauling L (1940) The nature of the chemical bond. Cornell University Press, Ithaca, New York

    Google Scholar 

  2. Van Vleck JH (1932) The theory of electric and magnetic susceptibilities. University Press, Oxford

    Google Scholar 

  3. Numerically exact computations for the ground state of the VB model have been performed for systems having up to 24 sites: Alexander SA, Schmalz TG, J Am Chem Soc (submitted)

  4. Numerically exact computations for the ground state of the VB model have been performed for systems having up to 24 sites: see also, Ramasesha S, Soos ZG (1984) Int J Quantum Chem 25:1003

    Google Scholar 

  5. The special case of the ground state of a cyclic chain without bond-alternation turns out to be exactly soluble by a complex many-body technique which has not been extended to other structures: Hulthen L (1938) Ark Mat Astron Fys A26:1

    Google Scholar 

  6. See, for example, Mattis DC (1965) The theory of magnetism. Harper and Row, New York

    Google Scholar 

  7. Murakami M, Yoshimura S (1984) J Chem Soc Chem Commun p. 1649; (1985) Mol Cryst Liq Cryst 118:95

  8. Tanaka K, Ohzeki K, Yamabe T, Yata S (1984) Synth Met 9:41

    Google Scholar 

  9. Seitz WA, Klein DJ, Schmalz TG, Graciá-Bach MA (1985) Chem Phys Lett 115:139

    Google Scholar 

  10. Klein DJ, Schmalz TG, Hite GE, Metropoulos A, Seitz WA (1985) Chem Phys Lett 120:367

    Google Scholar 

  11. See, e.g., Thompson CJ (1972) Mathematical statistical mechanics. Macmillan Co, New York

    Google Scholar 

  12. Early references include: Montroll EW (1941) J Chem Phys 9:706

    Google Scholar 

  13. Early references include: Kramers HA, Wannier GH (1941) Phys Rev 60:252

    Google Scholar 

  14. Early references include: Lassertre EN, Howe JP (1941) J Chem Phys 9:747

    Google Scholar 

  15. Early references include: Kubo R (1943) Busserion Kenkyu 1

  16. For other graph-theoretic applications see, e.g., Klein DJ (1980) J Stat Phys 23:561

    Google Scholar 

  17. For other graph-theoretic applications see, e.g., Derrida B (1981) J Phys A14 L5

    Google Scholar 

  18. For other graph-theoretic applications see, e.g., Derrida B, DeSeze L (1982) J Phys 43;475

    Google Scholar 

  19. There is also the question of a “proper” derivation of such models. See, e.g., Van Vleck JH (1963) Phys Rev 49:232

    Google Scholar 

  20. There is also the question of a “proper” derivation of such models. See, e.g., Simpson WT (1956) J Chem Phys 25:1124

    Google Scholar 

  21. There is also the question of a “proper” derivation of such models. See, e.g., Herring C In: Rado GT, Stuhl H (ed) Magnetism 2B, Academic Press, NY, p. 1

  22. There is also the question of a “proper” derivation of such models. See, e.g., Buleavski LN (1966) Zh Eksp Teor Fiz 51:230

    Google Scholar 

  23. There is also the question of a “proper” derivation of such models. See, e.g., Klein DJ, Foyt DC (1973) Phys. Rev 8A:2280

    Google Scholar 

  24. There is also the question of a “proper” derivation of such models. See, e.g., White CT, Economou EN (1982) Phys Rev 18B:3959

    Google Scholar 

  25. There is also the question of a “proper” derivation of such models. See, e.g., Malrieu JP, Maynau D (1982) J Am Chem Soc 104:3021 and 3029

    Google Scholar 

  26. There is also the question of a “proper” derivation of such models. See, e.g., Poshusta RD, Klein DJ (1982) Phys Rev Lett 48:1555

    Google Scholar 

  27. See, e.g., Van Vleck JH, Sherman A (1935) Rev Mod Phys 7:167

    Google Scholar 

  28. See, e.g., Simpson WT (1962) Theories of electrons in molecules. Prentice-Hall, Englewood Cliffs, New Jersey

    Google Scholar 

  29. See, e.g., Eyring H, Walter J, Kimball GE (1944) Quantum Chemistry, Chap. 13, John Wiley and Sons, New York

    Google Scholar 

  30. See, e.g., Simpson WT (1962) Theories of electrons in molecules. Prentice-Hall, Englewood Cliffs, New Jersey

    Google Scholar 

  31. Pauling L (1933) J Chem Phys 1:280

    Google Scholar 

  32. Pauling L, Wheland GW (1933) J Chem Phys 1:362

    Google Scholar 

  33. Pauling L, Sherman J (1933) J Chem Phys 1:679

    Google Scholar 

  34. McGlynn SP, VanQuickenborne LG, Kinoshita M, Carroll DG (1972) Introduction to applied quantum chemistry, Section 6.2. Holt, Rinehart, and Winston, Inc, New York

    Google Scholar 

  35. Herndon WC (1973) J Am Chem Soc 95:2404

    Google Scholar 

  36. Herndon WC, Ellzey ML Jr (1974) J Am Chem Soc 96:6631

    Google Scholar 

  37. Such superposition graphs constructed only from Kekulé structures often arise in graph theory and are also termed Sachs graphs, as in Trinajstic N (1983) Chemical graph theory, vol II. CRC Press, Boca Raton, Florida

    Google Scholar 

  38. Klein DJ (1979) Int J Quantum Chem 138:293

    Google Scholar 

  39. Clar E (1972) The aromatic sextet. John Wiley and Sons, New York

    Google Scholar 

  40. Su WP, Schrieffer JR, Heeger AJ (1979) Phys Rev Lett 42:1698

    Google Scholar 

  41. Rice MJ (1979) Phys Lett 71A:152

    Google Scholar 

  42. Su WP, Schrieffer JR, Heeger AJ (1980) Phys Rev B22:2099

    Google Scholar 

  43. The effects described here are in fact evident in earlier enumerations restricted to global Kekulé structures on a rather wide class of polyphene structures. See, e.g. Yen TF (1971) Theor Chim Acta 20:399

    Google Scholar 

  44. The effects described here are in fact evident in earlier enumerations restricted to global Kekulé structures on a rather wide class of polyphene structures. See, e.g. Stein SE, Brown RL (1985) Carbon 23:105

    Google Scholar 

  45. See, e.g., the reviews: Heeger AJ (1981) Comments Solid State Phys 10:53

    Google Scholar 

  46. See, e.g., the reviews: Chien JCW (1981) J Pol Sci Lett 19:249

    Google Scholar 

  47. See, e.g., the reviews: Baughman RH, Bredas JL, Chance RR, Elsenbaumer RL, Shacklette LW (1982) Chem Rev 82:209

    Google Scholar 

  48. See, e.g., the reviews: Duke CB, Paton A, Salaneck WR (1982) Mol Cryst Liq Cryst 83:177

    Google Scholar 

  49. Carter FL (1984) Physica 10D:175

    Google Scholar 

  50. Klein DJ, Garcia-Bach MA (1979) Phys Rev 19B:877

    Google Scholar 

  51. Klein DJ (1982) J Phys 15A:661

    Google Scholar 

  52. Rumer G (1932) Nachr Ges Wiss Göttingen 1932:337

    Google Scholar 

  53. See, e.g., Gantmacher FR (1959) The theory of matrices, vol II, chap. 13. Chelsea, New York

    Google Scholar 

Download references

Author information

Author notes

  1. A. Metropoulos

    Present address: Theoretical Chemistry Institute, The National Hellenic Research Foundation, 48 Vassileos Konstantinou Avenue, Athens 501/1, Greece

Authors and Affiliations

  1. Theoretical Chemical Physics Group Department of Marine Sciences, Texas A and M University at Galveston, 77553, Galveston, Texas, USA

    G. E. Hite, A. Metropoulos, D. J. Klein, T. G. Schmalz & W. A. Seitz

Authors
  1. G. E. Hite
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Metropoulos
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. D. J. Klein
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. T. G. Schmalz
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. W. A. Seitz
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research supported by The Robert A. Welch Foundation of Houston, Texas

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hite, G.E., Metropoulos, A., Klein, D.J. et al. Extended π-networks with multiple spin-pairing phases: resonance-theory calculations on poly-polyphenanthrenes. Theoret. Chim. Acta 69, 369–391 (1986). https://doi.org/10.1007/BF00526698

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00526698

Key words

Search

Navigation