The electronic structure of $\zeta$-BEDT-TTF$\cdot$PF$_6$; a comparison of self-consistent field and Hubbard model analyses*

The electronic structure of the organic charge-transfer salt $\zeta$-BEDT-TTF$\cdot$PF$_6$ was studied using both density functional and Hartree-Fock theories. The results were in qualitative disagreement with experimental conductivity and optical measurements for the material\footnote{H.-L. Liu and co-workers,{\em{Chem. Mater.}} {\bf{9}}, 1865 (1997) } which suggested a Mott insulator behavior. We examine the Hubbard model for this system to understand both the Mott insulating behavior and the failure of the self-consistent field methods to model it. Using a Hubbard dimer model, we find that an important component of the analysis is the inclusion of more valence-bond than ionic character in the ground state wavefunction. The Hartree-Fock treatment includes too much ionic character which destabilizes the result. A spin density wave treatment reduces the ionic character, but also contaminates the wavefunction with terms having the incorrect total spin. We have also shown that the one-electron density and therefore the density functional approach in its usual form is nearly blind to the valence-bond content of the wavefunction.