Optical spectra and exchange-correlation effects in molecular crystals

We report the first-principles $GW$-Bethe–Salpeter equation and quantum Monte Carlo calculations of the optical and electronic properties of molecular and crystalline rubrene $\left({\mathrm{C}}_{42}{\mathrm{H}}_{28}\right)$. Many-body effects dominate the optical spectrum and quasiparticle gap of molecular crystals. We interpret the observed yellow-green photoluminescence in rubrene microcrystals as a result of the formation of intermolecular, charge-transfer, spin-singlet excitons. In contrast, spin-triplet excitons are localized and intramolecular with a predicted phosphorescence at the red end of the optical spectrum. We find that the exchange energy plays a fundamental role in raising the energy of intramolecular spin-singlet excitons above the intermolecular ones. Exciton binding energies are predicted to be around $0.5\mathrm{eV}$ (spin singlet) to $1\mathrm{eV}$ (spin triplet). The calculated electronic gap is $2.8\mathrm{eV}$. The theoretical absorption spectrum agrees very well with recent ellipsometry data.

Figure 1

(Color online) (a) LUMO and (b) HOMO isosurfaces in a rubrene molecule. The tetracene backbone is on the plane of the figure. Green/light gray and blue/dark gray colors denote positive and negative values. (c) Schematic view of the rubrene crystal.

Figure 2

(Color online) Calculated oscillator strength of the first few optical transitions in gas-phase rubrene. The inset shows the excitation energies, group symmetry characters, and oscillator strengths of the three lowest excitations.

Figure 3

(Color online) (a) Real and (b) imaginary parts of the refractive index along the crystalline axes of the rubrene crystal. The vertical line in the inset marks the $GW$ quasiparticle gap.

Figure 4

(Color online) Electron-hole probability distributions of the first (a) spin-singlet and (b) spin-triplet excitons of rubrene crystal. Red/gray dot in the center of the unit cell (viewed along $c$ axis) marks the hole, while the isosurfaces indicate the distribution of the electron. The probabilities for finding the electron on each molecular site are indicated by the percentage.