Charge transfer from first principles: self-consistent GW applied to donor-acceptor systems

Charge transfer in donor-acceptor systems (DAS) is determined by the relative alignment between the frontier orbitals of the donor and the acceptor. Semi-local approximations to density functional theory (DFT) may give a qualitatively wrong level alignment in DAS, leading to unphysical fractional electron transfer in weakly bound donor-acceptor pairs. $GW$ calculations based on first-order perturbation theory ($G_0W_0$) correct the level alignment, but leave unaffected the electron density. We demonstrate that self-consistent $GW$ (sc$GW$) provides an ideal framework for the description of charge transfer in DAS. Moreover, sc$GW$ seamlessly accounts for many-body correlations and van der Waals interactions. As in $G_0W_0$, the sc$GW$ level alignment is in agreement with experimental reference data. However in sc$GW$, also the electron density is treated at the $GW$ level and, therefore, it is consistent with the level alignment between donor and acceptor leading to a qualitatively correct description of charge-transfer properties.