Neutral-ionic interface in organic charge-transfer salts

Abstract

Charge transfer (CT) stabilization in linear stacks $\dots{}{D}^{\ensuremath{\gamma}+}{A}^{\ensuremath{\gamma}\ensuremath{-}}{D}^{\ensuremath{\gamma}+}{A}^{\ensuremath{\gamma}\ensuremath{-}}\dots{}$ of $\ensuremath{\pi}$-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 $N\ensuremath{\rightarrow}\ensuremath{\infty}$, by adapting valence-bond techniques to electron-hole excitations. The ground state CT $\ensuremath{\gamma}(z)$ and the magnetic gap $\frac{\ensuremath{\Delta}{E}_{m}(z)}{\ensuremath{\surd}2|t|}$ to the lowest triplet are computed for arbitrary $z=\frac{\ensuremath{\delta}}{\ensuremath{\surd}2|t|}$, where $\ensuremath{-}2\ensuremath{\delta}$ is the energy for $\mathrm{DA}\ensuremath{\rightarrow}{D}^{+}{A}^{\ensuremath{-}}$, $\ensuremath{-}|t|=〈{D}^{+}{A}^{\ensuremath{-}}|\mathcal{H}|DA〉$ is the Mulliken CT integral, and ${D}^{2+}$, ${A}^{2\ensuremath{-}}$ sites are excluded. The spin degeneracy of ${A}^{\ensuremath{-}}\ensuremath{\sigma}$ and ${D}^{+}\ensuremath{\sigma}$ ion radicals is treated exactly. Instead of the discontinuous change from $\ensuremath{\gamma}=0$ to $\ensuremath{\gamma}=1$ in the limit $|t|\ensuremath{\rightarrow}0$, finite overlap gives a continuous $\ensuremath{\gamma}(z)$ and $\ensuremath{\gamma}({z}_{c})=0.68\ifmmode\pm\else\textpm\fi{}0.01$ at the neutral-ionic interface ${z}_{c}=0.53\ifmmode\pm\else\textpm\fi{}0.01$. The magnetic gap $\ensuremath{\Delta}{E}_{m}$ is finite for $z<{z}_{c}$ and vanishes for $z>{z}_{c}$, where there is a diamagnetic to paramagnetic transition and the ground state switches from $k=0$ to $k=\ensuremath{\pi}$ 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 $\ensuremath{\gamma}(z)$, when the critical value $\frac{m}{\ensuremath{\surd}2|t|}=1.4\ifmmode\pm\else\textpm\fi{}0.1$ 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 $z<{z}_{c}$. Valence-bond analysis of CT excitations models the physical properties of organic complexes with overlapping sites and intermediate $\ensuremath{\gamma}$.