Kohn-Sham (KS) density functional theory (DFT) is a very efficient method for calculating various properties of solids as, for instance, the total energy, the electron density, or the electronic band structure. The KS-DFT method leads to rather fast calculations; however, the accuracy depends crucially on the chosen approximation for the exchange and correlation (xc) functional $E_{\mathrm{xc}}$ and/or potential $v_{\mathrm{xc}}$ . Here, an overview of xc methods to calculate the electronic band structure is given, with the focus on the so-called semilocal methods that are the fastest in KS-DFT and allow to treat systems containing up to thousands of atoms. Among them, there is the modified Becke-Johnson potential that is widely used to calculate the fundamental bandgap of semiconductors and insulators. The accuracy for other properties like magnetic moment or electron density, that are also determined directly by $v_{\mathrm{xc}}$ , is also discussed.

The density-functional theory (DFT) approximations that are the most accurate for the calculation of bandgap of bulk materials are hybrid functionals, such as HSE06, the modified Becke–Johnson (MBJ) potential, and the GLLB-SC potential. More recently, generalized gradient approximations (GGAs), such as HLE16, or meta-GGAs, such as (m)TASK, have also proven to be quite accurate for the bandgap. Here, the focus is on two-dimensional (2D) materials and the goal is to provide a broad overview of the performance of DFT functionals by considering a large test set of 298 2D systems. The present work is an extension of our recent studies [T. Rauch, M. A. L. Marques, and S. Botti, Phys. Rev. B 101, 245163 (2020); Patra et al., J. Phys. Chem. C 125, 11206 (2021)]. Due to the lack of experimental results for the bandgap of 2D systems, G₀W₀ results were taken as reference. It is shown that the GLLB-SC potential and mTASK functional provide the bandgaps that are the closest to G₀W₀. Following closely, the local MBJ potential has a pretty good accuracy that is similar to the accuracy of the more expensive hybrid functional HSE06.

Lung cancer ranks among the most prevalent forms of cancer and remains a significant factor in cancer-related mortality across the world. It poses significant challenges to healthcare systems and society as a whole due to its high incidence, mortality rates, and late-stage diagnosis. Resveratrol (RV), a natural compound found in various plants, has shown potential as a nanomedicine for lung cancer treatment. RV has varied effects on cancer cells, including promoting apoptosis by increasing pro-apoptotic proteins (Bax and Bak) and decreasing anti-apoptotic proteins (Bcl-2). It also hinders cell proliferation by influencing important signaling pathways (MAPK, mTOR, PI3K/Akt, and Wnt/β-catenin) that govern cancer progression. In addition, RV acts as a potent antioxidant, diminishing oxidative stress and safeguarding cells against DNA damage. However, using RV alone in cancer treatment has drawbacks, such as low bioavailability, lack of targeting ability, and susceptibility to degradation. In contrast, nanoparticle-based delivery systems address these limitations and hold promise for improving treatment outcomes in lung cancer; nanoparticle formulations of RV offer advantages such as improved drug delivery, increased stability, controlled release, and targeted delivery to lung cancer cells. This article will provide an overview of lung cancer, explore the potential of RV as a therapeutic agent, discuss the benefits and challenges of nanoparticle-based drug delivery, and highlight the promise of RV nanoparticles for cancer treatment, including lung cancer. By optimizing these systems for clinical application, future studies aim to enhance overall treatment outcomes and improve the prognosis for lung cancer patients.

The experimental and theoretical realization of two-dimensional (2D) materials is of utmost importance in semiconducting applications. Computational modeling of these systems with satisfactory accuracy and computational efficiency is only feasible with semilocal density functional theory methods. In the search for the most useful method in predicting the band gap of 2D materials, we assess the accuracy of recently developed semilocal exchange–correlation (XC) energy functionals and potentials. Though the explicit forms of exchange–correlation (XC) potentials are very effective against XC energy functionals for the band gap of bulk solids, their performance needs to be investigated for 2D materials. In particular, the LMBJ [ J. Chem. Theory Comput. 2020, 16, 2654] and GLLB-SC [ Phys. Rev. B 82, 2010, 115106] potentials are considered for their dominance in bulk band gap calculation. The performance of recently developed meta generalized gradient approximations, like TASK [ Phys. Rev. Res. 1, 2019, 033082] and MGGAC [ Phys. Rev. B. 100, 2019, 155140], is also assessed. We find that the LMBJ potential constructed for 2D materials is not as successful as its parent functional, i.e., MBJ [ Phys. Rev. Lett. 102, 2009, 226401] in bulk solids. Due to a contribution from the derivative discontinuity, the band gaps obtained with GLLB-SC are in a certain number of cases, albeit not systematically, larger than those obtained with other methods, which leads to better agreement with the quasi-particle band gap obtained from the GW method. The band gaps obtained with TASK and MGGAC can also be quite accurate.

Experimental studies have shown the possible production of hydrogen through photocatalytic water splitting using metal oxide (MO${}_y$) nanoparticles attached to an anatase TiO${}_2$ surface. In this work, we performed density functional theory (DFT) calculations to provide a detailed description of the stability and geometry of M${}_x$O${}_y$ clusters M = Cu, Ni, Co, Fe and Mn, x = 1–5, and y = 0–5 on the anatase TiO${}_2$(101) surface. It is found that unsaturated 2-fold-coordinated O-sites may serve as nucleation centers for the growth of metal clusters. The formation energy of Ni-containing clusters on the anatase surface is larger than for other M clusters. In addition, the Ni${}_n$ adsorption energy increases with cluster size n, which makes the formation of bigger Ni clusters plausible as confirmed by transition electron microscopy images. Another particularity for Ni-containing clusters is that the adsorption energy per atom gets larger when the O-content is reduced, while for other M atoms it remains almost constant or, as for Mn, even decreases. This trend is in line with experimental results. Also provided is a discussion of the oxidation states of M${}_5$O${}_y$ clusters based on their magnetic moments and Bader charges and their possible reduction with oxygen depletion.