Koopmans-Compliant Functionals and Potentials and Their Application to the GW100 Test Set

Koopmans-compliant
(KC) functionals have been shown to provide
accurate spectral properties through a generalized condition of piecewise
linearity of the total energy as a function of the fractional addition/removal
of an electron to/from any orbital. We analyze the performance of
different KC functionals on a large and standardized set of 100 molecules,
the GW100 test set, comparing vertical ionization potentials (taken
as opposite of the orbital energies) to those obtained from accurate
quantum chemistry methods, and to experimental results. We find excellent
agreement, with a mean absolute error of 0.20 eV for the KIPZ functional
on the first ionization potential, which is state-of-the-art for both
density functional theory (DFT)-based calculations and many-body perturbation
theory. We highlight similarities and differences between KC functionals
and other electronic-structure approaches, such as dielectric-dependent
hybrid functionals and Green’s function methods, both from
a theoretical and from a practical point of view, arguing that KC
potentials can be considered as local and orbital-dependent approximations
to the electronic self-energy, already including approximate vertex
corrections.