First-principles description of charge transfer in donor-acceptor compounds from self-consistent many-body perturbation theory

We investigate charge transfer in prototypical molecular donor-acceptor compounds using hybrid density functional theory (DFT) and the $GW$ approximation at the perturbative level ($G_0{W}_0$) and at full self-consistency (sc-$GW$). For the systems considered here, no charge transfer should be expected at large intermolecular separation according to photoemission experiments and accurate quantum-chemistry calculations. The capability of hybrid exchange-correlation functionals of reproducing this feature depends critically on the fraction of exact exchange $\alpha$, as for small values of $\alpha$ spurious fractional charge transfer is observed between the donor and the acceptor. $G_0{W}_0$ based on hybrid DFT yields the correct alignment of the frontier orbitals for all values of $\alpha$. However, $G_0{W}_0$ has no capacity to alter the ground-state properties of the system because of its perturbative nature. The electron density in donor-acceptor compounds thus remains incorrect for small $\alpha$ values. In sc-$GW$, where the Green's function is obtained from the iterative solution of the Dyson equation, the electron density is updated and reflects the correct description of the level alignment at the $GW$ level, demonstrating the importance of self-consistent many-body approaches for the description of ground- and excited-state properties in donor-acceptor systems.

Figure 1

Schematic representation of the level alignment in weakly interacting donor-acceptor compounds. For $E_{\mathrm{CT}}>0$ (left), charge transfer occurs as an excitation (e.g., upon absorption of a photon with energy $h\nu \ge E_{\mathrm{CT}}$). For negative values of the charge-transfer energy (right), the system is characterized by charge transfer in the ground state.

Figure 2

Left: The charge difference between TTF and TCNE is estimated from the ratio between the dipole moment and the distance between the centers of two molecules. Right: Dipole moment of the TTF-TCNE dimer as a function of the intermolecular distance.

Figure 3

Volume slices of the density difference between the TTF-TCNE dimer at 5 Å  distance and the monomers in PBE (upper panel) and sc-$GW$ (lower panel). Units are Å${}^{-3}$.

Figure 4

Density difference between the TTF-TCNQ dimer and the monomers for PBE (left) and sc-$GW$ (right). Red (blue) isosurfaces indicate charge accumulation (depletion) resulting from the TTF-TCNQ level alignment.

Figure 5

$G_0{W}_0$@PBEh($\alpha$) and sc-$GW$ values for $E_{\mathrm{CT}}$ as a function of $\alpha$. The PBEh($\alpha$) values are estimated from the difference between the lowest-unoccupied and highest-occupied KS levels. The difference between the experimental IP of TTF and EA of TCNE is included for comparison.

Figure 6

Left: PBE, $G_0{W}_0$@PBE, and sc-$GW$ HOMO and LUMO levels for the TTF-TCNE dimer as a function of the distance between the monomers. Right: $E_{\mathrm{CT}}$ as a function of distance.

Figure 7

Mean absolute error (MAE, left) and mean error (ME, right) relative to experiments [28, 29, 30, 31] of the $G_0{W}_0$@PBEh($\alpha$) quasiparticle energies of TTF, TCNE, TCNQ, and p-chloranil as a function of $\alpha$ for the HOMO level (squares) and the full excitation spectrum (circles). The dashed lines refer to the sc-$GW$ errors for the full excitation spectrum. The (average) optimally tuned parameters ${\alpha }^{*}$ and $\overline{\alpha }$—determined according to Refs. [22] and [23], respectively—are reported as vertical solid lines, whereas the shaded region indicates the range of $\alpha$ yielding spurious asymptotic charge transfer for TTF and TCNE.