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  1. Free, publicly-accessible full text available December 1, 2024
  2. We introduce a maximally localized Wannier function representation of Bloch excitons, two-particle correlated electron-hole excitations, in crystalline solids, where the excitons are maximally localized with respect to an average electron-hole coordinate in real space. As a proof-of-concept, we illustrate this representation in the case of low-energy spin-singlet and -triplet excitons in cubic lithium fluoride, computed using the ab initio Bethe-Salpeter equation approach. We visualize the resulting maximally localized exciton Wannier functions (MLXWFs) in real space, detail the convergence of the exciton Wannier spreads, and demonstrate how Wannier-Fourier interpolation can be leveraged to obtain exciton energies and states at arbitrary exciton crystal momenta in the Brillouin zone. We further introduce an approach to treat the long-range dipolar coupling between singlet MLXWFs and discuss it in depth. The MLXWF representation sheds light on the fundamental nature of excitons and paves the way toward Wannier-based post-processing of excitonic properties, enabling the construction of ab initio exciton tight-binding models, efficient interpolation of the exciton-phonon vertex, the computation of Berry curvature associated with exciton bands, and beyond. 
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  3. Free, publicly-accessible full text available December 1, 2024
  4. Free, publicly-accessible full text available December 1, 2024
  5. null (Ed.)
    Accurate prediction of fundamental band gaps of crystalline solid-state systems entirely within density functional theory is a long-standing challenge. Here, we present a simple and inexpensive method that achieves this by means of nonempirical optimal tuning of the parameters of a screened range-separated hybrid functional. The tuning involves the enforcement of an ansatz that generalizes the ionization potential theorem to the removal of an electron from an occupied state described by a localized Wannier function in a modestly sized supercell calculation. The method is benchmarked against experiment for a set of systems ranging from narrow band-gap semiconductors to large band-gap insulators, spanning a range of fundamental band gaps from 0.2 to 14.2 electronvolts (eV), and is found to yield quantitative accuracy across the board, with a mean absolute error of ∼0.1 eV and a maximal error of ∼0.2 eV. 
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