Neutral-ionic interface in organic charge-transfer salts

Abstract

Charge transfer (CT) stabilization in linear stacks $\dots D^{\gamma +}{A}^{\gamma -}{D}^{\gamma +}{A}^{\gamma -}\dots$ of $\pi$-electron donors ($D$) and acceptors ($A$) involve spin-dependent configuration interactions that are treated exactly in rings of $N=4, 6, 8, 10$ sites, and extrapolated to $N\to \infty$, by adapting valence-bond techniques to electron-hole excitations. The ground state CT $\gamma \mathrm{}\left(z\right)\mathrm{}$ and the magnetic gap $\frac{\Delta E_m\mathrm{}\left(z\right)\mathrm{}}{\surd 2\left|t\right|\mathrm{}}$ to the lowest triplet are computed for arbitrary $z=\frac{\delta }{\surd 2\left|t\right|\mathrm{}}$, where $-2\mathrm{}\delta$ is the energy for $\mathrm{DA}\to D^{+}{A}^{-}$, $-\left|t\right|=〈D^{+}{A}^{-}\left|\mathcal{H}\right|DA〉$ is the Mulliken CT integral, and $D^{2+}$, $A^{2-}$ sites are excluded. The spin degeneracy of $A^{-}\sigma$ and $D^{+}\sigma$ ion radicals is treated exactly. Instead of the discontinuous change from $\gamma =0\mathrm{}$ to $\gamma =1\mathrm{}$ in the limit $\mathrm{}\left|t\right|\mathrm{}\to 0$, finite overlap gives a continuous $\gamma \mathrm{}\left(z\right)\mathrm{}$ and $\gamma \left(z_c\right)=0.68\mathrm{}\pm 0.01$ at the neutral-ionic interface $z_c=0.53\mathrm{}\pm 0.01$. The magnetic gap $\Delta E_m$ is finite for $z<\mathrm{}{z}_c$ and vanishes for $z>\mathrm{}{z}_c$, where there is a diamagnetic to paramagnetic transition and the ground state switches from $k=0\mathrm{}$ to $k=\pi$ symmetry. Collective effects due to long-range three-dimensional Coulomb interactions are included in a Hartree approximation and produce a first-order transition, with discontinuous $\gamma \mathrm{}\left(z\right)\mathrm{}$, when the critical value $\frac{m}{\surd 2\left|t\right|\mathrm{}}=1.4\mathrm{}\pm 0.1$ of the Madelung stabilization $m$ of a dimer is exceeded. The puzzling magnetic gaps in paramagnetic organic CT salts with mixed regular stacks arise naturally for partial CT and $z<\mathrm{}{z}_c$. Valence-bond analysis of CT excitations models the physical properties of organic complexes with overlapping sites and intermediate $\gamma$.