Band gaps of crystalline solids from Wannier-localization-based optimal tuning of a screened range-separated hybrid functional.

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.

Predicting the Color Polymorphism of ROY from a Time-Dependent Optimally Tuned Screened Range-Separated Hybrid Functional.

Polymorphism is a well-known property of molecular crystals, which allows the same molecule to form solids with several crystalline structures that can differ significantly in physical properties. Polymorphs that possess different optical absorption properties in the visible range may exhibit different perceived colors, a phenomenon known as color polymorphism. One striking example of color polymorphism is given by 5-methyl-2-[(2-nitrophenyl)amino]-3-thiophenecarbonitrile, known as ROY for its red-orange-yellow colors. First-principles prediction of color polymorphism may help in polymorph assignment and design but has proven to be challenging. Here, we predict the absorption spectra and simulate the colors of 12 ROY polymorphs using the general, nonempirical method of time-dependent (TD) optimally tuned screened range-separated hybrid (OT-SRSH) functional. For 5 ROY polymorphs with known experimental absorption spectra, we show that the TD-OT-SRSH approach predicts absorption spectra in quantitative agreement with experiment. For all polymorphs, we show that an accurate simulation of the colors is obtained, paving the way to a fully predictive, low-cost calculation of color polymorphism.

Nonempirical Prediction of the Length-Dependent Ionization Potential in Molecular Chains.

The ionization potential of molecular chains is well-known to be a tunable nanoscale property that exhibits clear quantum confinement effects. State-of-the-art methods can accurately predict the ionization potential in the small molecule limit and in the solid-state limit, but for intermediate, nanosized systems prediction of the evolution of the electronic structure between the two limits is more difficult. Recently, optimal tuning of range-separated hybrid functionals has emerged as a highly accurate method for predicting ionization potentials. This was first achieved for molecules using the ionization potential theorem (IPT) and more recently extended to solid-state systems, based on an ansatz that generalizes the IPT to the removal of charge from a localized Wannier function. Here, we study one-dimensional molecular chains of increasing size, from the monomer limit to the infinite polymer limit using this approach. By comparing our results with other localization-based methods and where available with experiment, we demonstrate that Wannier-localization-based optimal tuning is highly accurate in predicting ionization potentials for any chain length, including the nanoscale regime.