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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. 

The performance of optimally tuned range‐separated hybrid (OT‐RSH) functional calculations in predicting accurate isotropic nuclear magnetic shielding (σ) and chemical shift values is examined. To that end, the results of OT‐RSH and other approximate density functional theory calculations are assessed against recently published benchmark CCSD(T) calculations for a test set consisting of several molecules and bond types. It is found that for atoms in single bonds with a large paramagnetic contribution to σ, OT‐RSH offers a significant improvement in prediction of shielding constants over popular semi‐local and hybrid density functionals, yielding non‐empirical results that are as accurate as those of semi‐empirical density functionals often used for prediction of shielding constants. This success is attributed to the improved fundamental gap prediction of the OT‐RSH approach. For atoms in multiple bonds, however, larger errors often persist. By comparing OT‐RSH and recently reported double‐hybrid functional results, the remaining difficulties are traced to significant non‐local correlation.

 

In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.