Hybrid density functional theory meets quasiparticle calculations: A consistent electronic structure approach

We propose a scheme to obtain a system-dependent fraction of exact exchange ($\alpha$) within the framework of hybrid density functional theory (DFT) that is consistent with the $G_0{W}_0$ approach, where $G_0$ is the noninteracting Green function of the system and $W_0$ the screened Coulomb interaction. We exploit the formally exact condition of exact DFT that the energy of the highest occupied molecular orbital corresponds to the ionization potential of a finite system. We identify the optimal $\alpha$ value for which this statement is obeyed as closely as possible and thereby remove the starting point dependence from the $G_0{W}_0$ method. This combined approach is essential for describing electron transfer (as exemplified by the TTF/TCNQ dimer) and yields the vertical ionization potentials of the G2 benchmark set with a mean absolute percentage error of only $\approx$3%.

Figure 1

QP (filled circles), KS (open circles), $\Delta$SCF [(red) crosses], and sc$GW$ [dashed (red) line] HOMO level as a function of $\alpha$ for the (a) TTF and (b) TCNQmolecules. The molecules are shown at the right: White denotes hydrogen; gray, carbon; blue, nitrogen; yellow, sulfur.

Figure 2

Absolute value of the dipole moment (a) and electron transfer (b) for the TTF/TCNQ complex as a function of the dimer distance. A positive sign indicates electron transfer from TTF to TCNQ.

Figure 3

Differences ($\Delta$) in the generalized KS LUMO (L) of TCNQ vs HOMO (H) of TTF as a function of $\alpha$ (open circles) and corresponding $G_0{W}_0$ values (filled circles). A negative $\Delta$ value indicates artificial electron transfer in the noninteracting limit. The dotted vertical line corresponds to the PBE0 result.