Screening in Orbital-Density-Dependent Functionals

Electronic-structure
functionals that include screening effects,
such as Hubbard or Koopmans’ functionals, are required to describe
the response of a system to the fractional addition or removal of
an electron from an orbital or a manifold. Here, we present a general
method to incorporate screening based on linear-response theory, and
we apply it to the case of orbital-by-orbital screening of Koopmans’
functionals. We illustrate the importance of such generalization when
dealing with challenging systems containing orbitals with very different
chemical character, also highlighting the simple dependence of the
screening on the localization of the orbitals. We choose a set of
46 transition-metal complexes for which experimental data and accurate
many-body perturbation theory calculations are available. When compared
to experiment, results for ionization potentials show a very good
performance, with a mean absolute error of 0.2 eV, comparable to the
most accurate many-body perturbation theory approaches. These results
reiterate the role of Koopmans-compliant functionals as simple and
accurate quasiparticle approximations to the exact spectral functional,
bypassing diagrammatic expansions and relying only on the physics
of the local density or generalized-gradient approximation.