Addressing the electronic structure and mobility of materials with Koopmans spectral functionals and automated Wannier functions.

The electronic structure of materials is often described using density-functional theory; nevertheless, this is not a theory of charged excitations and band structures. Many-body perturbation theory targets instead precisely these quantities, albeit at a much increased computational costs, and can also provide the first step towards the calculation of further quantities, such as electron-hole or electron-phonon interactions. Independently of the level of theory chosen, the solution of the Boltzmann transport equation (e.g., to calculate mobilities in the phonon-limited regime) requires very fine samplings of the states around the Fermi energy, and interpolation techniques based on Wannier functions can greatly help in reaching numerical convergence. I will first discuss our approach in describing charged excitations, where we take a functional, rather than diagrammatic, approach to the problem, and have developed "spectral" functionals able to predict accurately and inexpensivley band structures and electronic excitations. These functionals cannot be functionals of the density alone, but can be functionals of the orbital densities, as a quasiparticle approximation to potentials of the spectral density. Since the minimizing orbitals in these functionals are localized, the connection with Wannier functions emerges very naturally. Here, I will present the general framework, its application to the electronic structure of solids, and to the calculation of electron-phonon couplings and mobilities. I will also present some novel approaches for the automated and realiable calculation of maximally localized Wannier functions, showing how these can capture effortlessly and accurately any target electronic structure based on localized orbitals, and provide the starting point for Koopmans formulations.