  In this article, we propose an energy functional at the level of DFT+U+V that
allows us to compute self-consistently the values of the on-site interaction,
Hubbard U and Hund J, as well as the intersite interaction V. This functional
extends the previously proposed ACBN0 functional [Phys. Rev. X 5, 011006
(2015)] including both on-site and intersite interactions. We show that this ab
initio self-consistent functional yields improved electronic properties for a
wide range of materials, ranging from $sp$ materials to strongly-correlated
materials. This functional can also be seen as an alternative general and
systematic way to construct parameter-free hybrid functionals, based on the
extended Hubbard model and a selected set of Coulomb integrals, and might be
used to develop novel approximations. By extending the DFT+U method to
materials where strong local and nonlocal interactions are relevant, this work
opens the door to the ab initio study the electronic, ionic, and optical
properties of a larger class of strongly correlated materials in and out of
equilibrium.
