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The properties of excitons, or correlated electron–hole pairs, are of paramount importance to optoelectronic applications of materials. A central component of exciton physics is the electron–hole interaction, which is commonly treated as screened solely by electrons within a material. However, nuclear motion can screen this Coulomb interaction as well, with several recent studies developing model approaches for approximating the phonon screening of excitonic properties. While these model approaches tend to improve agreement with experiment, they rely on several approximations that restrict their applicability to a wide range of materials, and thus far they have neglected the effect of finite temperatures. Here, we develop a fully first-principles, parameter-free approach to compute the temperature-dependent effects of phonon screening within the ab initio $\mathit{GW}$-Bethe–Salpeter equation framework. We recover previously proposed models of phonon screening as well-defined limits of our general framework, and discuss their validity by comparing them against our first-principles results. We develop an efficient computational workflow and apply it to a diverse set of semiconductors, specifically AlN, CdS, GaN, MgO, and ${\text{SrTiO}}_3$. We demonstrate under different physical scenarios how excitons may be screened by multiple polar optical or acoustic phonons, how their binding energies can exhibit strong temperature dependence, and the ultrafast timescales on which they dissociate into free electron–hole pairs. 

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. 

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. 

All evidence to date indicates that at T = 100 K all protein crystals exhibit comparable sensitivity to X-ray damage when quantified using global metrics such as change in scaling B factor or integrated intensity versus dose. This is consistent with observations in cryo-electron microscopy, and results because nearly all diffusive motions of protein and solvent, including motions induced by radiation damage, are frozen out. But how do the sensitivities of different proteins compare at room temperature, where radiation-induced radicals are free to diffuse and protein and lattice structures are free to relax in response to local damage? It might be expected that a large complex with extensive conformational degrees of freedom would be more radiation sensitive than a small, compact globular protein. As a test case, the radiation sensitivity of 70S ribosome crystals has been examined. At T = 100 and 300 K, the half doses are 64 MGy (at 3 Å resolution) and 150 kGy (at 5 Å resolution), respectively. The maximum tolerable dose in a crystallography experiment depends upon the initial or desired resolution. When differences in initial data-set resolution are accounted for, the former half dose is roughly consistent with that for model proteins, and the 100/300 K half-dose ratio is roughly a factor of ten larger. 70S ribosome crystals exhibit substantially increased resolution at 100 K relative to 300 K owing to cooling-induced ordering and not to reduced radiation sensitivity and slower radiation damage.