Enforcing the linear behavior of the total energy with hybrid functionals: Implications for charge transfer, interaction energies, and the random-phase approximation

We investigate John Perdew's straight line condition for fractional electron numbers with hybrid density functionals. Enforcing the straight line behavior defines the optimal exact-exchange admixture. We then analyse the behavior of this hybrid functional for charge transfer in organic electronics and as a starting point for correlation in the random-phase approximation (RPA) or renormalized perturbation theory at second order (rPT2). More details can be found in our publication Phys. Rev. B 94, 035140 (2016) (http://journals.aps.org/prb/abstract/10.1103/PhysRevB.94.035140).

The density-difference distribution illustrates the erroneous charge transfer from the TTF to the TCNQ molecule. In the optimized hybrid functional (PBEh(α*)) and in self-consistent GW, no such erroneous charge transfer occurs.