Valence bond theory of narrow-band conductors

A diagrammatic valence bond (VB) theory is introduced for solids with one valence state per site, Coulomb intersite interactions, and nearest-neighbor electron transfers leading to a bandwidth 4 |t|. The VB method is applied to partly-filled regular segregated stacks of acceptors (A) and donors (D), which occur in all π-molecular organic conductors. The dimensions of the site representation for N_e = γN electrons or holes on N > N_e sites are found, each VB assignment is represented by a diagram, and the interconnection of these many-electron site functions due to electron transfers is also obtained diagrammatically. The resulting configuration interaction (CI) between all orbital assignments is solved exactly in subspaces of total spin, S. The complete thermodynamics of N_e = 4 electrons on chains of N = 4, 5, 6, and 7 sites are found for the Hubbard choice of on-site repulsion, U. The VB method extends the computation of the susceptibility χ(T) of partly-filled Hubbard models to the previously inaccessible regime U ∼ 4|t| which, however, is suggested by experiment. Comparison with absolute χ(T) data for TTF-TCNQ is slightly improved for U ∼ 4|t| = 0.56 eV. Extensions of the VB method to more realistic potentials, to other data, and to N → ∞ extrapolations are discussed.