Lattice distortion and energy-level structures in doped ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{70}$ molecules studied with the extended Su-Schrieffer-Heeger model: Polaron excitations and optical absorption

We extend the Su-Schrieffer-Heeger model of polyacetylene to the cases of ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{70}$ molecules. The results of our numerical calculations of the undoped systems agree well with the known results. When the system (${\mathrm{C}}_{60}$ or ${\mathrm{C}}_{70}$) is doped with one or two electrons (or holes), additional charges accumulate nearly along an equatorial line of the molecule. The dimerization becomes weaker along the same line. Two energy levels intrude deeply into the gap; the intrusion is deeper in ${\mathrm{C}}_{70}$ than in ${\mathrm{C}}_{60}$. Therefore, ‘‘polarons’’ are predicted in doped fullerenes. We calculate the optical-absoprtion coefficient for the ${\mathrm{C}}_{60}$ fullerene in order to consider how the polarons will be observed. It is predicted that an additional absorption peak appears at an energy lower than the intergap transition peaks of the undoped ${\mathrm{C}}_{60}$. It is found that the ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{70}$ fullerenes are closely related in their electronic structures as well as lattice geometries.