Koopmans-compliant functionals as spectral theories: molecules, solids, and liquids

Koopmans-compliant functionals\footnote{I. Dabo, M. Cococcioni, and N. Marzari, arXiv:0901.2637 (2009); I. Dabo {\it et al.}~Phys.~Rev.~B 82 115121 (2010).} enforce a generalized criterion of piecewise linearity with respect to the fractional removal or addition of an electron (i.e. a charged excitation) from any orbital in local or semi-local total-energy DFT functionals. By doing so they lead to beyond-DFT orbital-density dependent functionals that are able to deliver spectroscopic properties. We'll present an overview of the current status when applied to ionization potentials, electron affinities, photoemission spectra, and band gaps of molecules, solids, and liquids, with results that are comparable or slightly superior to many-body perturbation theory, but with functionals that rely only on the physics of the PBE generalized-gradient approximation.