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

Viktor Atalla, Igor Ying Zhang, Oliver T. Hofmann, Xinguo Ren, Patrick Rinke, Matthias Scheffler

Research output: Contribution to journalArticlepeer-review


We obtain the exchange parameter of hybrid functionals by imposing the fundamental condition of a piecewise linear total energy with respect to electron number. For the Perdew-Burke-Ernzerhof (PBE) hybrid family of exchange-correlation functionals (i.e., for an approximate generalized Kohn-Sham theory) this implies that (i) the highest occupied molecular orbital corresponds to the ionization potential (I), (ii) the energy of the lowest unoccupied molecular orbital corresponds to the electron affinity (A), and (iii) the energies of the frontier orbitals are constant as a function of their occupation. In agreement with a previous study [N. Sai, Phys. Rev. Lett. 106, 226403 (2011)10.1103/PhysRevLett.106.226403], we find that these conditions are met for high values of the exact exchange admixture α and illustrate their importance for the tetrathiafulvalene-tetracyanoquinodimethane complex for which standard density functional theory functionals predict artificial electron transfer. We further assess the performance for atomization energies and weak interaction energies. We find that atomization energies are significantly underestimated compared to PBE or PBE0, whereas the description of weak interaction energies improves significantly if a 1/R6 van der Waals correction scheme is employed.
Original languageEnglish
Pages (from-to)035140
Number of pages1
JournalPhysical Review B
Issue number3
Publication statusPublished - 2016

Fields of Expertise

  • Advanced Materials Science

Treatment code (Nähere Zuordnung)

  • Basic - Fundamental (Grundlagenforschung)

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