Lowest Optical Excitations in Molecular Crystals: Bound Excitons versus Free Electron-Hole Pairs in Anthracene

By solving the Bethe-Salpeter equation for the electron-hole Green function for crystalline anthracene we find the lowest absorption peak generated by strongly bound excitons or by a free electron-hole pair, depending on the polarization direction being parallel to the short or the long molecular axis, respectively. Both excitations are shifted to lower energies by pressure. The physical difference of these excitations is apparent from the electron-hole wave functions. Our findings are a major contribution to solve the long-standing puzzle about the nature of the lowest optical excitations in organic materials.

Figure 1

$b$ ($c$) component of the imaginary part of the DT on the left (right) calculated using the RPA (upper panels) compared to the solution of the BSE (lower panels) versus pressure. The spectra have been corrected by the self-energy ${\Delta }_c$ given in Table . A lifetime broadening of 0.1 eV has been included. The inset shows one anthracene molecule, where the short (long) molecular axis is denoted by $b$ ($c$).

Figure 2

The 2D electron distribution $|{\psi }_{c\mathbf{k}}({\mathbf{r}}_e)|$ with respect to the hole at a fixed position (dark cross) calculated at ambient pressure for S (left) and FE (right), respectively. The unit cell is indicated by dashed rectangles and the molecules therein by thin solid lines. These $ab$ ($ac$) maps represent slices at $z=0.3$ ($y=0.3$) with the hole located at $z=0$ ($y=0$) in units of $c$ ($b$). The dark regions correspond to high density.

Figure 3

Analogous to Fig. 2, but evaluated at 10.2 GPa.