Oligoacene exciton binding energies: Their dependence on molecular size

We show how the optical absorption properties of organic molecular crystals based on finite molecular units depend on the oligomer length. We calculate the dielectric tensor for the first four linear oligoacenes by solving the Bethe-Salpeter equation for the electron-hole Green’s function. The exciton binding energy significantly decreases with the molecular size. While strongly bound excitons are present in naphthalene, the carriers are only weakly bound in pentacene. This trend is understood in terms of the increasing dielectric screening and the spatial distribution of the exciton wave function.

Figure 1

$y$ and $z$ component of the $\mathrm{Im}{\epsilon }_{ii}\left(\omega \right)$ calculated for $n\mathrm{A}$ within the RPA (upper panels) and the BSE formalism (lower panels). A lifetime broadening of 0.1 eV has been included.

Figure 2

The 2D electron distribution $\mid {\psi }_{c\mathbf{k}}\left({\mathbf{r}}_e\right)\mid$ of $S_y$ with respect to the hole at a fixed position (dark cross) calculated for 2A and 4A. The unit cell is indicated by dashed rectangles. These xy (xz) maps represent slices at $z=0.3$ $(y=0.3)$ with the hole located at $z=0$ $\left(y=0\right)$ in units of $c$ $\left(b\right)$. The dark regions correspond to high density.

Figure 3

The ${\mathrm{SBE}}_y$ and the $S_z\text{−}{S}_y$ splitting as a function of $1∕n$ in comparison to experiment.