  We investigate charge transfer in prototypical molecular donor-acceptor
compounds using hybrid density functional theory (DFT) and the GW approximation
at the perturbative level (G0W0) 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 experiment 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. G0W0 based on
hybrid DFT yields the correct alignment of the frontier orbitals for all values
of $\alpha$. However, G0W0 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.
