Ab initio study of electron-phonon coupling in rubrene

The use of ab initio methods for accurate simulations of electronic, phononic, and electron-phonon properties of molecular materials such as organic crystals is a challenge that is often tackled stepwise based on molecular properties calculated in gas phase and perturbatively treated parameters relevant for solid phases. In contrast, in this work we report a full first-principles description of such properties for the prototypical rubrene crystals. More specifically, we determine a Holstein-Peierls–type Hamiltonian for rubrene, including local and nonlocal electron-phonon couplings. Thereby, a recipe for circumventing the issue of numerical inaccuracies with low-frequency phonons is presented. In addition, we study the phenyl group motion with a molecular dynamics approach.

Figure 1

Perspective view to the rubrene unit cell with four molecules. The molecules are labeled (A–D).

Figure 2

Supercell of rubrene with definition of transfer integrals. Rich colored (pale) molecules belong to the herringbone plane in the foreground (background). The four molecules A and C (foreground) and B and D (background) belong to a unit cell. ${\varepsilon }_{\text{AC}}, {\varepsilon }_{\text{AD}}, {\varepsilon }_{\text{AB}}, {\varepsilon }_{\text{AA}+\mathbf{b}}$ are the four nearest-neighbor transfer integrals and ${\varepsilon }_{\text{AA}+2\mathbf{b}}$ is a second neighbor transfer integral along lattice vector $\mathbf{b}$.

Figure 3

Valence band structure of rubrene. Main frame: Comparison of DFT results (red) and TB-band structure (blue) obtained from fitting with Eq. (8). Upper inset: Comparison of different fit functions (see text). Lower inset: Brillouin zone and definition of special points.

Figure 4

Main frame: Change of the total energy of the system (per unit cell) with the amplitude of the phonon. Inset: Relative frequency change and corresponding median value.

Figure 5

Illustration of the changes in the band structure of rubrene with distorted geometry, namely without phonon (red) and with phonon (black).

Figure 6

Spectrally resolved polaron binding energy (red bars), lattice distortion energy (blue bars) of crystal, and polaron binding energy in gas phase (green bars).

Figure 7

Definition of the two angles between phenyl groups perpendicular to the tetracene backbone plane in schematic and perspective views.

Figure 8

Phenyl group dynamics measured with angles ${\alpha }_1$ and ${\alpha }_2$ at $T=500$ K.