Wannier Functions Dually Localized in Space and Energy

Abstract: The construction of Wannier functions from Bloch orbitals offers a unitary freedom that can be exploited to yield Wannier functions with advantageous properties. Minimizing the spatial variance is a well-known choice; another, previously proposed for Wannier functions constructed from the occupied Bloch manifold, minimizes a weighted sum of spatial and energy variance. Departing from all previous work, we extend dual localization to include both valence and conduction bands together. Near the Fermi energy, these dually localized Wannier functions yield frontier (bonding and antibonding) orbitals in bulk silicon and molecular ethylene, as well as $d$-orbital character in metallic copper. Because they are both localized and retain information about the orbital energy spectrum, dually localized Wannier functions are well suited to orbital-dependent methods that associate Wannier functions with specific energy ranges. They naturally induce fractional occupations, allowing for corrections to the DFA total energy.