Koopmans compliance: a functional theory for spectral properties

Energy functionals which depend explicitly on each individual orbital density, rather than the total charge density, appear naturally when applying self-interaction corrections to density-functional theory. Rather than a limitation, we argue that this is a powerful feature, and show how it is possible to interpret the orbital-dependency of densities and potentials as an effective frequency dependency. Such a frame is naturally amenable to describe electronic spectroscopies, and is free from e.g. the constraint of having derivative discontinuities in the exact formulation. Excellent agreement is achieved for ionization potentials and affinities, fundamental gaps, and deeper orbital levels (photoemission) for both molecules and solids. We believe that a functional theory for the spectral density is therefore emerging, able to address at the same time total energies and spectral properties.