Valence-bond analysis of extended Hubbard models: Charge-transfer excitations of molecular conductors

Abstract

The low-energy charge transfer (CT) excitation characteristic of both $\ensuremath{\pi}$-molecular conductors and complex-ion-radical salts is interpreted as a nearest-neighbor Coulomb interaction $V$ that is comparable to the bandwidth, $4|t|$. Partly filled segregated regular stacks in organic conductors are represented by extended Hubbard models, whose exact CT energies and intensities are obtained by diagrammatic valence-bond (VB) methods for four electrons on finite rings and chains, together with an approximate treatment of $V$ in partly filled infinite stacks for infinite on-site correlations $U$. Finite $V\ensuremath{\sim}4|t|$ yields an intense low-lying CT band, containing $V$ and $U\ensuremath{-}2V$ excitations, that depends weakly on the band filling. Finite $V$ also splits the usual CT absorption around $U$ for half filled bands into strong absorptions around $U\ensuremath{-}V$, weak ones around $U$, and much weaker bands around $U+V$ and $U+2V$. The CT spectra of mixed-valence tetrathiofulvalene (TTF) salts are modeled with $V\ensuremath{\sim}0.4$ eV, $U\ensuremath{\sim}1.4$ eV, and $|t|\ensuremath{\sim}0.10\ensuremath{-}0.13$ eV. Similar CT transitions in complex tetracyanoquinodimethane (TCNQ) salts are consistent with the insensitivity of the $V$ peak's position to the filling or the structure. Restricting the basis to one valence state per site produces several general consequences for dipole-allowed optical transitions.