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

The low-energy charge transfer (CT) excitation characteristic of both $\pi$-molecular conductors and complex-ion-radical salts is interpreted as a nearest-neighbor Coulomb interaction $V$ that is comparable to the bandwidth, $4\left|t\right|\mathrm{}$. 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 $V\sim 4\left|t\right|\mathrm{}$ yields an intense low-lying CT band, containing $V$ and $U-2V$ 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 $U-V$, 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 $V\sim 0.4$ eV, $U\sim 1.4$ eV, and $\mathrm{}\left|t\right|\mathrm{}\sim 0.10-0.13$ 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.