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

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.

[1]  R. L. Brown,et al.  Chemical theory of graphite-like molecules , 1985 .

[2]  D. Klein,et al.  Variational localized-site cluster expansions. X. Dimerization in linear Heisenberg chains , 1979 .

[3]  L. Pauling.  The calculation of matrix elements for Lewis electronic structures of molecules , 1933 .

[4]  M. Rice.  Charged Π-phase kinks in lightly doped polyacetylene , 1979 .

[5]  Elliott W. Montroll,et al.  Statistical Mechanics of Nearest Neighbor Systems , 1941 .

[6]  Linus Pauling,et al.  The Nature of the Chemical Bond. V. The Quantum‐Mechanical Calculation of the Resonance Energy of Benzene and Naphthalene and the Hydrocarbon Free Radicals , 1933 .

[7]  D. Foyt,et al.  Variational Multistate-Ket Derivation of the Heisenberg Spin Hamiltonian , 1973 .

[8]  Linus Pauling,et al.  The Nature of the Chemical Bond. VII. The Calculation of Resonance Energy in Conjugated Systems , 1933 .

[9]  W. Simpson.  Modification of the Vector Model to Include a First‐Order Nonorthogonality Correction , 1956 .

[10]  F. R. Gantmakher.  The Theory of Matrices , 1984 .

[11]  J. Malrieu,et al.  A VALENCE BOND EFFECTIVE HAMILTONIAN FOR NEUTRAL STATES OF Π SYSTEMS. 1. METHOD , 1982 .

[12]  E. N. Lassettre,et al.  Thermodynamic Properties of Binary Solid Solutions on the Basis of the Nearest Neighbor Approximation , 1941 .

[13]  E. Clar.  The aromatic sextet , 1972 .

[14]  Resonance topology of polynuclear aromatic hydrocarbons , 1971 .

[15]  W. Simpson.  Theories of Electrons in Molecules , 1963 .

[16]  R. D. Poshusta,et al.  Novel Ab Initio Correlated Calculations for an Infinite Chain of Hydrogen Atoms , 1982 .

[17]  M. L. Ellzey,et al.  Resonance theory. V. Resonance energies of benzenoid and nonbenzenoid .pi. systems , 1974 .

[18]  L. Pauling.  The Nature Of The Chemical Bond , 1939 .

[19]  Van Vleck.  Nonorthogonality and Ferromagnetism , 1936 .

[20]  W. R. Salaneck,et al.  Dependence of polymer electronic structure on molecular architecture , 1982 .

[21]  S. McGlynn.  Introduction to applied quantum chemistry , 1971 .

[22]  D. Klein,et al.  The poly-polyphenanthrene family of multi-phase π-network polymers in a valence-bond picture , 1985 .

[23]  Alan J. Heeger,et al.  Solitons in polyacetylene , 1979 .

[24]  S. Yoshimura,et al.  Synthesis of One-Dimensional Graphite Polymer, Poly-Peri-Naphthalene, By Vapor Phase Polymerization , 1985 .

[25]  J. Chien.  Creation and annihilation of solitons, radicals, and ions in polyacetylene as related to the mechanisms of isomerization, doping, and conduction , 1981 .

[26]  T. Yamabe,et al.  A study on the pristine and the doped polyacenic semiconductive materials , 1984 .

[27]  W. C. Herndon.  Resonance energies of aromatic hydrocarbons. Quantitative test of resonance theory , 1973 .

[28]  Colin J. Thompson,et al.  Mathematical Statistical Mechanics , 1972 .

[29]  H. Kramers,et al.  Statistics of the Two-Dimensional Ferromagnet. Part II , 1941 .

[30]  Z. Soos,et al.  Diagrammatic valence‐bond theory for finite model Hamiltonians , 1984 .

[31]  J. V. Vleck,et al.  The theory of electric and magnetic susceptibilities , 1934, The Mathematical Gazette.

[32]  D. Klein.  Asymptotic distributions for self-avoiding walks constrained to strips, cylinders, and tubes , 1980 .

[33]  D. Mattis,et al.  The Theory of Magnetism I , 1981 .

[34]  J. H. Van Vleck,et al.  The Quantum Theory of Valence , 1935 .

[35]  R. L. Elsenbaumer,et al.  Structural basis for semiconducting and metallic polymer dopant systems , 1982 .