Theoretical study of molecular electronic excitations and optical transitions of ${\text{C}}_{60}$

We report results of ab initio calculations of excited states of the fullerene molecule using the configuration-interaction approach with singly excited determinants (SCI). We have used both experimental geometry and the geometry optimized by the density functional method and worked with basis sets at the correlation-consistent polarization valence triple-$\zeta$ (cc-pVTZ) and augmented cc-pVTZ levels. In contrast to the early SCI semiempirical calculations, we find that the two lowest ${{}^{1}T}_{1u}\leftarrow {{}^{1}A}_g$ electron optical lines are situated at relatively high energies of $\sim 5.8\text{eV}$ (214 nm) and $\sim 6.3\text{eV}$ (197 nm). These two lines originate from two ${{}^{1}T}_{1u}\leftarrow {{}^{1}A}_g$ transitions: from the highest occupied molecular orbital (HOMO) to one above the lowest unoccupied molecular orbital $\left(\text{LUMO}+1\right)$ $\left(6h_u\to 3t_{1g}\right)$ and from $\left(\text{HOMO}-1\right)$ to LUMO $\left(10h_g\to 7t_{1u}\right)$. The lowest molecular excitation, which is the $1{{}^{3}T}_{2g}$ level, is found at $\sim 2.5\text{eV}$. Inclusion of doubly excited determinants leads only to minor corrections to this picture. We discuss possible assignment of absorption bands at energies smaller than 5.8 eV (or $\lambda$ larger than 214 nm).

Figure 1

Upper panel: Experimental optical density, Ref. [12], and the calculated spin singlet lines of ${\text{C}}_{60}$. The dashed line is the electronic contribution from two $T_{1u}$ transitions broadened with linewidth of 0.5 eV. Lower panel: Density of singlet lines (broadened with linewidth of 0.5 eV).