Optical-absorption spectra ofA6C60andA6C70: Theoretical evaluation of effective Coulomb interactions in Frenkel excitons

We theoretically investigate optical-absorption spectra of ${\mathrm{C}}_{60}^{6\mathrm{-}}$ and ${\mathrm{C}}_{70}^{6\mathrm{-}}$, and discuss relations with the optical properties of alkali-metal-doped fullerides ${\mathit{A}}_6$ ${\mathrm{C}}_{60}$ and ${\mathit{A}}_6$ ${\mathrm{C}}_{70}$. This is a valid approach for systems where molecular-exciton (Frenkel-exciton) effects are dominant. We use a tight-binding model with long-ranged Coulomb interactions and bond disorder. Optical spectra are obtained by the Hartree-Fock approximation and the configuration interaction method. We find that the Coulomb interaction parameters, which are relevant to the optical spectra of ${\mathit{A}}_6$ ${\mathrm{C}}_{60}$ (${\mathit{A}}_6$ ${\mathrm{C}}_{70}$) in order to explain the excitation energies and relative oscillator strengths of absorption peaks, are almost half of those of the neutral ${\mathrm{C}}_{60}$ (${\mathrm{C}}_{70}$). The reduction of the effective Coulomb interactions is concluded for the heavily doped case of ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{70}$. This finding is closely related to the experimental fact that dielectric constants of fullerides, which are maximumly doped with alkali metals, become about twice as large as those of the neutral systems.