Impact of exact exchange in the description of the electronic structure of organic charge-transfer molecular crystals

We evaluate the impact that the amount of nonlocal Hartree-Fock (%HF) exchange included in a hybrid density functional has on the microscopic parameters (transfer integrals, band gaps, bandwidths, and effective masses) describing charge transport in high-mobility organic crystals. We consider both crystals based on a single molecule, such as pentacene, and crystals based on mixed-stack charge-transfer systems, such as dibenzo-TTF–TCNQ. In the pentacene crystal, the band gap decreases and the effective masses increase linearly with an increase in the amount of %HF exchange. In contrast, in the charge-transfer crystals, while the band gap increases linearly, the effective masses vary only slightly with an increase in %HF exchange. We show that the superexchange nature of the electronic couplings in charge-transfer systems is responsible for this peculiar evolution of the effective masses. We compare the density functional theory results with results obtained within the $G_0{W}_0$ approximation as a way of benchmarking the optimal amount of %HF exchange needed in a given functional.

Figure 1

Chemical and crystal structures of the investigated systems: Pentacene [11] (left) and DBTTF-TCNQ [12] (right). Red arrows indicate the directions of the largest transfer integrals as well as the smallest effective masses for both holes and electrons.

Figure 2

Dependence of the fundamental gap, valence and, conduction bandwidths on the %HF exchange (left); dependence of the largest hole electronic coupling and smallest hole effective mass on %HF exchange (right) in the crystalline pentacene.

Figure 3

Left: Valence and conduction bands of pentacene obtained using the αPBE functional with different %HF. Right: Comparison of αPBE (solid lines) and $G_0{W}_0$ (crosses) results. The points of high symmetry in the first Brillouin zone are labeled as follows: Γ = (0,0,0), $X=(0.5,0,0)$, $Y=(0,0.5,0)$, $B=(0,0,0.5)$, $C=(0.5,0.5,0)$, $A=(0.5,0,0.5)$, $E=(0.5,0.5,0.5)$, and $D=(0,0.5,0.5)$, all in crystallographic coordinates. The zero of energy corresponds to the top of the valence band, at the $C$ point.

Figure 4

Left: Valence and conduction bands of DBTTF-TCNQ obtained using the αPBE functional with different amount of %HF and different basis sets: atomic orbitals (solid lines) and PAWs (colored crosses). Right: Comparison of αPBE and $G_0{W}_0$ (black crosses). The points of high symmetry in the first Brillouin zone are labeled as follows: Γ = (0,0,0), $X=(0.5,0,0)$, $Y=(0,0.5,0)$, $B=(0,0,0.5)$, $C=(0.5,0.5,0)$, $A=(0.5,0,0.5)$, $E=(0.5,0.5,0.5)$, and $D=(0,0.5,0.5)$, all in crystallographic coordinates. The zero of energy corresponds to the top of the valence band, at the $D$ point.

Figure 5

(a) Dependence of the donor-acceptor electronic coupling and molecular fundamental gap on the %HF exchange; (b) dependence of the largest effective hole electronic coupling based on the energy splitting approach (dashed line) and using Eq. (2) (solid red line) and the smallest hole effective mass (solid blue line), on the %HF exchange in the DBTTF-TCNQ crystal.