Band structure calculations based on density functional theory (DFT) with local or gradient-corrected exchange-correlation potentials are known to severely underestimate the band gap of semiconducting and insulating materials. Alternative approaches have been proposed: from semiempirical setups, such as the so-called DFT+U, to hybrid density functionals using a fraction of nonlocal Fock exchange, to modifications of semilocal density functionals. However, the resulting methods appear to be material dependent and lack theoretical rigor. The rigorous many-body perturbation theory based on GW methods provides accurate results but at a very high computational cost. Hereby, we show that a linear correlation between the electronic band gaps obtained from standard DFT and GW approaches exists for most materials and argue that (1) this is a strong indication that the problem of predicting band gaps from standard DFT calculation arises from the assignment of a physical meaning to the Kohn–Sham energy levels rather than from intrinsic errors of the DFT methods and (2) it provides a practical way to obtain GW-like quality results from standard DFT calculations. The latter will be especially useful for systems where the unit cell involves a large number of atoms as in the case of doped or defect-containing materials for which GW calculations become unfeasible.

This work investigates crystal lattice, electronic structure, relative stability, and high pressure behavior of TiO₂ polymorphs (anatase, rutile, and columbite) using the density functional theory (DFT) improved by an on-site Coulomb self-interaction potential (DFT+U). For the latter the effect of the U parameter value (0 < U < 10 eV) is analyzed within the local density approximation (LDA+U) and the generalized gradient approximation (GGA+U). Results are compared to those of conventional DFT and Heyd-Scuseria-Ernzehorf screened hybrid functional (HSE06). For the investigation of the individual polymorphs (crystal and electronic structures), the GGA+U/LDA+U method and the HSE06 functional are in better agreement with experiments compared to the conventional GGA or LDA. Within the DFT+U the reproduction of the experimental band-gap of rutile/anatase is achieved with a U value of 10/8 eV, whereas a better description of the crystal and electronic structures is obtained for U < 5 eV. Conventional GGA/LDA and HSE06 fail to reproduce phase stability at ambient pressure, rendering the anatase form lower in energy than the rutile phase. The LDA+U excessively stabilizes the columbite form. The GGA+U method corrects these deficiencies; U values between 5 and 8 eV are required to get an energetic sequence consistent with experiments (E_rutile < E_anatase < E_columbite). The computed phase stability under pressure within the GGA+U is also consistent with experimental results. The best agreement between experimental and computed transition pressures is reached for U ≈ 5 eV.

Density functional simulations of CO₂adsorption an desorption rates as a function of CO₂pressure and temperature reveal that two-dimensional MXene materials of M₂C formula (M = Ti, Zr, Hf, V, Nb, Ta, Cr, Mo, W) are able to adsorb, store, and activate CO₂molecules, with promising applications in carbon capture and storage strategies.

Searching for two-dimensional (2D) materials with room-temperature magnetic order and high spin-polarization is essential for the development of next-generation nanospintronic devices. A new class of 2D magnetic materials with high Néel temperature, fully compensated antiferromagnetic order (zero magnetization) and completely spin-polarized semiconductivity is proposed for the first time. Based on the density functional theory calculations, we predict these properties for asymmetrically functionalized MXenes (Janus Cr₂C) – Cr₂CXX′ (X, X′ = H, F, Cl, Br, OH). The valence and conduction bands in these materials are made up of opposite spin channels and they can behave as bipolar magnetic semiconductors with zero magnetization. A Néel temperature as high as 400 K has been found for Cr₂CFCl, Cr₂CClBr, Cr₂CHCl, Cr₂CHF, and Cr₂CFOH materials. Remarkably, the spin carrier orientation and induced transition from bipolar magnetic semiconductors to half-metal antiferromagnets can be easily controlled by electron or hole doping. The band gap of Janus MXenes can be effectively tuned by the selection of a pair of chemical elements/functional groups terminating the upper and the lower surfaces. The spin-polarized semiconductivity with zero magnetism is preserved when MXenes are put on the SiC(0001) support. The results presented herein open a new road towards the construction of 2D high-temperature spin-polarized materials with antiferromagnetism potentially suitable for spintronic applications.

The future challenges in modeling nano-photocatalysts involve combining different methods in a hierarchical way, a path that will provide understanding on how to design catalysts for producing fuel needed for a sustainable life in the future.