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

Abstract

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 et al., Phys. Rev. Lett. 106, 226403 (2011)], 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/R 6 van der Waals correction scheme is employed.

First-principles supercell calculations of small polarons with proper account for long-range polarization effects

“…This strong functional dependence makes even a qualitative assessment of the existence of a self-trapped polarons impossible. Several approaches have been suggested in the literature for determining the correct or at least optimal value of α [20][21][22][23][24][25][26]. Here we focus on restoring the IP theorem [22] as a consistent DFT-based solution of the problem.…”

“…with the self-interaction error Π causing a convex curvature of the total energy as a function of occupation, and the orbital relaxation Σ a concave curvature. The optimal α=α opt minimizing the XC error [21,29] is then determined from the condition Δ XC (α opt )=0.…”

Generalization of Dielectric-Dependent Hybrid Functionals to Finite Systems

“…(8) predicted Δ > 0, with ε TCNQ LUMO ¼ −4.32 and ε TTF HOMO ¼ −6.15 eV. The mixing fraction that minimizes the deviation from the straight-line error was shown to be 0.70 for TCNQ and 0.8 for TTF [77,78], not dissimilar from the values predicted by Eq. (8).…”

Communication: Coupled cluster and many-body perturbation theory for fractional charges and spins

“…5,12,29 Importantly, this is achieved in a very different way, however. For DFAs, the delocalization error is decreased by compensating it with the over-localization of HF.…”

“…The "tuned" rangeseparated DFA approach likely benefits from the same effect on a system-by-system basis, although they lack transferability. [12][13][14][15] (Range-separated) hybrid functionals thus offer a pragmatic way to deal with the delocalization error, provided that it is the dominant error source for the system of interest (e.g., for charge-transfer excitations). 11 However, their performance is not necessarily better for all (e.g., thermochemical) properties.…”