The structural and electronic properties of both inorganic and hybrid organic-inorganic perovskites based on tin halides are investigated from the first principles. In particular, we contrast the inorganic ${\text{CsSnCl}}_3$ and ${\text{CsSnI}}_3$ to their hybrid counterparts $\left({\text{CH}}_3{\text{NH}}_3\right){\text{SnCl}}_3$, $\left({\text{CH}}_3{\text{NH}}_3\right){\text{SnI}}_3$, and $\left({\text{NH}}_2\text{CH}={\text{NH}}_2\right){\text{SnI}}_3$, which were obtained by substituting the inorganic Cs cation with the methylammonium ${\text{CH}}_3{\text{NH}}_3$ and the formamidinium ${\text{NH}}_2\text{CH}={\text{NH}}_2$ cations. The comparison between the hybrid perovskites and the inorganic counterparts sheds light on the effects of the filling molecule on the structural and electronic properties of the compound. We show that the stability against the distortion of the perovskitic cage strongly depends on the embedded cation. The electronic properties (in particular, the band gap) can be tuned by a suitable choice of the organic molecule, and, in particular, of its size.

We combine state-of-the-art large-scale first-principles calculations with a low-energy continuum model to describe the nearly flat bands of twisted bilayer graphene at the first magic angle $\theta =1.{08}^{\circ }$. We show that the energy width of the flat-band manifold, as well as the energy gap separating it from the valence and conduction bands, can be obtained only if the out-of-plane relaxations are fully taken into account. The results agree both qualitatively and quantitatively with recent experimental outcomes.

We report on an ab initio study of the structural and electronic properties of B- and P-doped Si nanoclusters. The neutral impurities formation energies are calculated. We show that they are higher in smaller nanoclusters and that this is not related to the structural relaxation around the impurity. Their dependence on the impurity position within the nanocluster is also discussed. Finally, we have calculated the B and P activation energies showing the existence of a nearly linear scaling with the nanocluster inverse radius. Interestingly, no significant variation of the activation energy on the impurity species is found and the cluster relaxation gives a minor contribution to it.

Oxygen vacancies at the ${\text{SnO}}_2$ (110) and (101) surface and subsurface sites have been studied in the framework of density functional theory by using both all-electron Gaussian and pseudopotential plane-wave methods. The all-electron calculations have been performed using the B3LYP exchange-correlation functional with accurate estimations of energy gaps and density of states. We show that bulk oxygen vacancies are responsible for the appearance of a fully occupied flat energy level lying at about 1 eV above the top valence band and an empty level resonant with the conduction band. Surface oxygen vacancies strongly modify the surface band structures with the appearance of intragap states covering most of the forbidden energy window, or only a small part of it, depending on the vacancy depth from the surface. Oxygen vacancies can account for electron affinity variations with respect to the stoichiometric surfaces as well. A significant support to the present results is found by comparing them to the available experimental data.

Well-oriented thin films of methyl-ammonium trihalogenostannates $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{Sn}{X}_3$ compounds $(X=\mathrm{Cl},\mathrm{Br})$ are grown by the single source thermal ablation technique. Optical absorption and structural analysis of $\mathrm{C}{\mathrm{H}}_3\mathrm{N}{\mathrm{H}}_3\mathrm{Sn}{X}_3$ thin films are combined with ab initio calculations in order to clarify their electronic properties and the role of the organic cation. The structural calculations reproduce well the measured lattice parameters, and optical measurements reveal a direct gap absorption onset for both compounds, in agreement with the calculated band structures. It turns out from projected density of states analysis that the valence and conduction bands take negligible contribution from the methylammonium. It is inferred that the band gap mainly depends on the ionicity and size of the inorganic cage $\mathrm{Sn}{X}_3$.

The structural and electronic properties of twisted bilayer graphene are investigated from first-principles and tight-binding approach as a function of the twist angle (ranging from the first “magic” angle $\theta =1.{08}^{\circ }$ to $\theta =13.{17}^{\circ }$, with the former corresponding to the largest unit cell, comprising 11,164 carbon atoms). By properly taking into account the long-range van der Waals (vdW) interaction, we provide the patterns for the atomic displacements (with respect to the ideal twisted bilayer). The out-of-plane relaxation shows an oscillating (“buckling”) behavior, very evident for the smallest angles, with the atoms around the AA stacking regions interested by the largest displacements. The out-of-plane displacements are accompanied by a significant in-plane relaxation, showing a vortexlike pattern, where the vorticity (intended as curl of the displacement field) is reverted when moving from the top to the bottom plane and vice versa. Overall, the atomic relaxation results in the shrinking of the AA stacking regions in favor of the more energetically favorable AB/BA stacking domains. The measured flat bands emerging at the first magic angle can be accurately described only if the atomic relaxations are taken into account. Quite importantly, the experimental gaps separating the flat-band manifold from the higher and lower energy bands are intimately related to out-of-plane relaxations. The stability of the relaxed bilayer at the first magic angle is estimated to be of the order of 0.5–0.9 meV per atom (or 7–10 K). Our calculations shed light on the importance of an accurate description of the vdW interaction and of the resulting atomic relaxation to envisage the electronic structure of this really peculiar kind of vdW bilayers.