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Since the preliminary work of Anisimov and co-workers, the Hubbard corrected DFT+$U$ functional has been used for predicting properties of correlated materials by applying on-site effective Coulomb interactions to specific orbitals. However, the determination of the Hubbard $U$ parameter has remained under intense discussion despite the multitude of approaches proposed. Here, we define a selection criterion based on the use of polaronic defect states for the enforcement of the piecewise linearity of the total energy upon electron occupation. A good agreement with results from piecewise linear hybrid functionals is found for the electronic and structural properties of polarons, including the formation energies. The values of $U$ determined in this way are found to give a robust description of the polaron energetics upon variation of the considered state. In particular, we also address a polaron hopping pathway, finding that the determined value of $U$ leads to accurate energetics without requiring a configurational-dependent $U$. It is emphasized that the selection of $U$ should be based on physical properties directly associated with the orbitals to which $U$ is applied, rather than on more global properties such as band gaps and band widths. For comparison, we also determine $U$ through a well-established linear-response scheme finding noticeably different values of $U$ and consequently different formation energies. Possible origins of these discrepancies are discussed. As case studies, we consider the self-trapped electron in BiVO$_4$, the self-trapped hole in MgO, the Li-trapped hole in MgO, and the Al-trapped hole in $\alpha$-SiO$_2$., Comment: 9 pages, 6 figures

We develop a computationally efficient scheme to accurately determine finite-temperature band gaps. We here focus on materials belonging to the class ABX3 (A = Rb, Cs; B = Ge, Sn, Pb; and X = F, Cl, Br, I), which includes halide perovskites. First, an initial estimate of the band gap is provided for the ideal crystalline structure through the use of a range-separated hybrid functional, in which the parameters are determined nonempirically from the electron density and the high-frequency dielectric constant. Next, we consider two kinds of band-gap corrections to account for spin-orbit coupling and thermal vibrations including zero-point motions. In particular, the latter effect is accounted for through the special displacement method, which consists in using a single distorted configuration obtained from the vibrational frequencies and eigenmodes, thereby avoiding lengthy molecular dynamics. The sequential consideration of both corrections systematically improves the band gaps, reaching a mean absolute error of 0.17 eV with respect to experimental values. The computational efficiency of our scheme stems from the fact that only a single calculation at the hybrid-functional level is required and that it is sufficient to evaluate the corrections at the semilocal level of theory. Our scheme is particularly convenient for large-size systems and for the screening of large databases of materials., Comment: 40 pages, 9 figures

The potential of lead-halide perovskites for realistic applications is currently hindered by their limited long-term stability under functional activation. While the role of lattice flexibility in the thermal response of perovskites has become increasingly evident, the description of thermally-induced distortions is still unclear. In this work, we provide a unified picture of thermal activation in CsPbBr3 across length scales, showing that lattice symmetry does not increase at high temperatures. We combine temperature-dependent XRD, Br K-edge XANES, ab initio MD simulations, and calculations of the XANES spectra by first-principles, accounting for both thermal fluctuations and core hole final state effects. We find that the octahedral tilting of the Pb-Br inorganic framework statistically adopts multiple local configurations over time - in the short-range. In turn, the stochastic nature of the local thermal fluctuations uplifts the longer-range periodic octahedral tilting characterizing the low temperature structure, with the statistical mean of the local configurations resulting in a cubic-like time-averaged lattice. These observations can be rationalized in terms of displacive thermal phase transitions through the soft mode model, in which the phonon anharmonicity of the flexible inorganic framework causes the excess free energy surface to change as a function of temperature. Our work demonstrates that the effect of thermal dynamics on the XANES spectra can be effectively described for largely anharmonic systems, provided ab initio MD simulations are performed to determine the dynamically fluctuating structures, and core hole final state effects are included in order to retrieve an accurate XANES line shape. Moreover, it shows that the soft mode model, previously invoked to describe displacive thermal phase transitions in oxide perovskites, carries a more general validity.

Obtaining a precise theoretical description of the spectral properties of liquid water poses challenges for both molecular dynamics (MD) and electronic structure methods. The lower computational cost of the Koopmans-compliant functionals with respect to Green's function methods allows the simulations of many MD trajectories, with a description close to the state-of-art quasi-particle self-consistent GW plus vertex corrections method (QSGW+f$_{xc}$). Thus, we explore water spectral properties when different MD approaches are used, ranging from classical MD to first-principles MD, and including nuclear quantum effects. We have observed that the different MD approaches lead to up to 1 eV change in the average band gap, thus, we focused on the band gap dependence with the geometrical properties of the system to explain such spread. We have evaluated the changes in the band gap due to variations in the intramolecular O-H bond distance, and HOH angle, as well as the intermolecular hydrogen bond O$\cdot\cdot\cdot$O distance, and the OHO angles. We have observed that the dominant contribution comes from the O-H bond length; the O$\cdot\cdot\cdot$O distance plays a secondary role, and the other geometrical properties do not significantly influence the gap. Furthermore, we analyze the electronic density of states (DOS), where the KIPZ functional shows a good agreement with the DOS obtained with state-of-art approaches employing quasi-particle self-consistent GW plus vertex corrections. The O-H bond length also significantly influences the DOS. When nuclear quantum effects are considered, a broadening of the peaks driven by the broader distribution of the O-H bond lengths is observed, leading to a closer agreement with the experimental photoemission spectra.

We investigate optical absorption spectra obtained through time-dependent density functional theory (TD-DFT) based on nonempirical hybrid functionals that are designed to correctly reproduce the dielectric function. The comparison with state-of-the-art $GW$ calculations followed by the solution of the Bethe-Sapeter equation (BSE-$GW$) shows close agreement for both the transition energies and the main features of the spectra. We confront TD-DFT with BSE-$GW$ by focusing on the model dielectric function and the local exchange-correlation kernel. The present TD-DFT approach achieves the accuracy of BSE-$GW$ at a fraction of the computational cost.

The pathway of the oxygen evolution reaction at the Pt(111)/water interface is disclosed through constant Fermi level molecular dynamics. Upon the application of a positive bias potential H 2 O ads and OH ads adsorbates are found to arrange in a hexagonal lattice with an irregular alternation. Increasing further the electrode potential then induces the oxygen evolution reaction, which is found to proceed through a hydrogen peroxide intermediate. Calculation of the associated overpotential shows a reduction of 0.2 eV compared to the associative mechanism. This result highlights the forcefullness of the applied scheme in exploring catalytic reactions in an unbiased way.

In this work we study and contrast implicit solvation models against explicit atomistic, quantum mechanical models in the description of the band alignment of semiconductors in aqueous environment, using simulations based on density functional theory. We find consistent results for both methods for 9 different terminations across 6 different materials whenever the first solvation shell is treated explicitly, quantum mechanically. Interestingly this first layer of explicit water is more relevant when water is adsorbed but not dissociated, hinting at the importance of saturating the surface with quantum mechanical bonds. Furthermore, we provide absolute alignments by determining the position of the averaged electrostatic reference potential in the bulk region of explicit and implicit water with respect to vacuum. It is found that the absolute level alignments in explicit and implicit simulations agree within $\sim 0.1-0.2$ V if the implicit potential is assumed to lie 0.33 V below the vacuum reference level. By studying the interface between implicit and explicit water we are able to trace back the origin of this offset to the absence of a water surface dipole in the implicit model, as well as a small additional inherent polarization across the implicit-explicit interface.

The minimum energy paths for the migration of interstitial Mg in wurtzite GaN are studied through density functional calculations. The study also comprises Li, Na, and Be dopants to examine the dependence on size and charge of the dopant species. In all cases considered, the impurities diffuse like ions without any tendency of localizing charge. Li, Mg, and to some extent Na, diffuse almost isotropically in GaN, with average diffusion barriers of 1.1, 2.1, and 2.5 eV, respectively. Instead Be shows a marked anisotropy with energy barriers of 0.76 and 1.88 eV for diffusion paths perpendicular and parallel to the c-axis. The diffusion barrier generally increases with ionic charge and ionic radius, but their interplay is not trivial. The calculated migration barrier for Mg is consistent with the values estimated in a recent beta- emission channeling experiment.

We study the formation energies of native point defects in GaN through density-functional theory. In our first-principles scheme, the band edges are positioned in accord with hybrid density functional calculations, thus yielding a band-gap in agreement with experiment. With respect to previous semilocal calculations, the calculated formation energies and charge transition levels are found to be significantly different in quantitative terms, while the overall qualitative trend remains similar. In Ga-rich conditions, the nitrogen vacancy corresponds to the most stable defect for all Fermi energies in the band gap, but its formation energy is too high to account for autodoping. Our calculations also indicate that the gallium vacancy does not play any compensating role in n-type GaN.

We determine and compare structural, dynamical, and electronic properties of liquid water at near ambient conditions through density-functional molecular dynamics simulations, when using either plane-wave or atomic-orbital basis sets. In both frameworks, the electronic structure and the atomic forces are self-consistently determined within the same theoretical scheme based on a nonlocal density functional accounting for van der Waals interactions. The overall properties of liquid water achieved within the two frameworks are in excellent agreement with each other. Thus, our study supports that implementations with plane-wave or atomic-orbital basis sets yield equivalent results and can be used indiscriminately in study of liquid water or aqueous solutions.

We investigate the structural properties of liquid water at near ambient conditions using first-principles molecular dynamics simulations based on a semilocal density functional augmented with nonlocal van der Waals interactions. The adopted scheme offers the advantage of simulating liquid water at essentially the same computational cost of standard semilocal functionals. Applied to the water dimer and to ice Ih, we find that the hydrogen-bond energy is only slightly enhanced compared to a standard semilocal functional. We simulate liquid water through molecular dynamics in the NpH statistical ensemble allowing for fluctuations of the system density. The structure of the liquid departs from that found with a semilocal functional leading to more compact structural arrangements. This indicates that the directionality of the hydrogen-bond interaction has a diminished role as compared to the overall attractions, as expected when dispersion interactions are accounted for. This is substantiated through a detailed analysis comprising the study of the partial radial distribution functions, various local order indices, the hydrogen-bond network, and the selfdiffusion coefficient. The explicit treatment of the van der Waals interactions leads to an overall improved description of liquid water.

Using hybrid density functional theory, we address point defects susceptible to cause charge compensation upon Mg doping of GaN. We determine the free energy of formation of the nitrogen vacancy and of several Mg-related defects. The entropic contribution as a function of temperature is determined within the quasiharmonic approximation. We find that the Mg interstitial shows a noticeably lower free energy of formation than the Mg substitutional to Ga in p-type conditions. Therefore, the Mg impurity is amphoteric behaving like an acceptor when substitutional to Ga and like a double donor when accommodated in an interstitial position. The hybrid-functional results are then linked to experimental observations by solving the charge neutrality equations for semiconductor dominated by impurities. We show that a thermodynamic equilibrium model is unable to account for the experimental hole concentration as a function of Mg doping density, due to nitrogen vacancies and Mg interstitials acting as compensating donors. To explain the experimental result, which includes a dropoff of the hole concentration at high Mg densities, we thus resort to nonequilibrium models. We show that either nitrogen vacancies or Mg interstitials could be at the origin of the self-compensation mechanism. However, only the model based on interstitial Mg donors provides a natural mechanism to account for the sudden appearance of self-compensation. Indeed, the amphoteric nature of the Mg impurity leads to Fermi-level pinning and accounts for the observed dropoff of the hole concentration of GaN samples at high Mg doping. Our work suggests that current limitations in p-type doping of GaN could be overcome by extrinsically controlling the Fermi energy during growth.

We address the energetic stability of the graphene/SiC(0001) interface and the associated binding mechanism by studying a series of low-strain commensurate interface structures within a density functional scheme. Among the structures with negligible strain, the 6\surd3\times6\surd3 R30{\deg} SiC periodicity shows the lowest interface energy, providing a rationale for its frequent experimental observation. The interface stability is driven by the enhanced local reactivity of the substrate-bonded graphene atoms undergoing sp2-to-sp3 rehybridization (pyramidalization). By this mechanism, relaxed structures of higher stability exhibit more pronounced graphene corrugations at the atomic scale.

Calculations of formation energies and charge transition levels of defects routinely rely on density functional theory (DFT) for describing the electronic structure. Since bulk band gaps of semiconductors and insulators are not well described in semilocal approximations to DFT, band-gap correction schemes or advanced theoretical models which properly describe band gaps need to be employed. However, it has become apparent that different methods that reproduce the experimental band gap can yield substantially different results regarding charge transition levels of point defects. We investigate this problem in the case of the (+2/0) charge transition level of the O vacancy in ZnO, which has attracted considerable attention as a benchmark case. For this purpose, we first perform calculations based on non-screened hybrid density functionals, and then compare our results with those of other methods. While our results agree very well with those obtained with screened hybrid functionals, they are strikingly different compared to those obtained with other band-gap corrected schemes. Nevertheless, we show that all the different methods agree well with each other and with our calculations when a suitable alignment procedure is adopted. The proposed procedure consists in aligning the electron band structure through an external potential, such as the vacuum level. When the electron densities are well reproduced, this procedure is equivalent to an alignment through the average electrostatic potential in a calculation subject to periodic boundary conditions. We stress that, in order to give accurate defect levels, a theoretical scheme is required to yield not only band gaps in agreement with experiment, but also band edges correctly positioned with respect to such a reference potential.

Periodically corrugated epitaxial graphene and hexagonal boron nitride (h-BN) on metallic substrates are considered as perspective templates for the self-assembly of nanoparticles arrays. By using first-principles calculations, we determine binding energies and diffusion activation barriers of metal adatoms on graphene and h-BN. The observed chemical trends can be understood in terms of the interplay between charge transfer and covalent bonding involving the adatom d electrons. We further investigate the electronic effects of the metallic substrate and find that periodically corrugated templates based on graphene in combination with strong interactions at the metal/graphene interface are the most suitable for the self-assembly of highly regular nanoparticle arrays., Comment: 5 pages, 3 figures, 1 table

When described through a plane-wave basis set, the inclusion of exact nonlocal exchange in hybrid functionals gives rise to a singularity, which slows down the convergence with the density of sampled $k$ points in reciprocal space. In this work, we investigate to what extent the treatment of the singularity through the use of an auxiliary function is effective for $k$-point samplings of limited density, in comparison to analogous calculations performed with semilocal density functionals. Our analysis applies for instance to calculations in which the Brillouin zone is sampled at the sole $\Gamma$-point, as often occurs in the study of surfaces, interfaces, and defects or in molecular dynamics simulations.

We propose monolayer epitaxial graphene and hexagonal boron nitride (h-BN) as ultimate thickness covalent spacers for magnetoresistive junctions. Using a first-principles approach, we investigate the structural, magnetic and spin transport properties of such junctions based on structurally well defined interfaces with (111) fcc or (0001) hcp ferromagnetic transition metals. We find low resistance area products, strong exchange couplings across the interface, and magnetoresistance ratios exceeding 100% for certain chemical compositions. These properties can be fine tuned, making the proposed junctions attractive for nanoscale spintronics applications., Comment: 5 pages

We study the charge state of the diffusing O$_2$ molecule during silicon oxidation through hybrid functional calculations. We calculate charge transition levels of O$_2$ in bulk SiO$_2$ and use theoretical band offsets to align these levels with respect to the Si band edges. To overcome the band-gap problem of semilocal density fuctionals, we employ hybrid functionals with both predefined and empirically adjusted mixing coefficients. We find that the charge transition level $\epsilon^{0/-}$ in bulk SiO$_2$ occurs at $\sim$1.1 eV above the silicon conduction band edge, implying that the O$_2$ molecule diffuses through the oxide in the neutral charge state. While interfacial effects concur to lower the charge transition level, our estimates suggest that the neutral charge state persists until silicon oxidation., Comment: 4 pages, 3 figures

Band offsets at semiconductor-oxide interfaces are determined through a scheme based on hybrid density functionals, which incorporate a fraction $\alpha$ of Hartree-Fock exchange. For each bulk component, the fraction $\alpha$ is tuned to reproduce the experimental band gap, and the conduction and valence band edges are then located with respect to a reference level. The lineup of the bulk reference levels is determined through an interface calculation, and shown to be almost independent of the fraction $\alpha$. Application of this scheme to the Si-SiO$_2$, SiC-SiO$_2$, and Si-HfO$_2$ interfaces yields excellent agreement with experiment., Comment: 4 pages, 4 figures

For materials of varying band gap, we compare energy levels of atomically localized defects calculated within a semilocal and a hybrid density-functional scheme. Since the latter scheme partially relieves the band gap problem, our study describes how calculated defect levels shift when the band gap approaches the experimental value. When suitably aligned, defect levels obtained from total-energy differences correspond closely, showing average shifts of at most 0.2 eV irrespective of band gap. Systematic deviations from ideal alignment increase with the extent of the defect wave function. A guideline for comparing calculated and experimental defect levels is provided., Comment: 4 pages, 3 figures

We use many-body perturbation theory, the state-of-the-art method for band gap calculations, to compute the band offsets at the Si/SiO$_2$ interface. We examine the adequacy of the usual approximations in this context. We show that (i) the separate treatment of band-structure and potential lineup contributions, the latter being evaluated within density-functional theory, is justified, (ii) most plasmon-pole models lead to inaccuracies in the absolute quasiparticle corrections, (iii) vertex corrections can be neglected, (iv) eigenenergy self-consistency is adequate. Our theoretical offsets agree with the experimental ones within 0.3 eV.

Using first principles calculations, we model the chemical vapor deposition (CVD) growth of carbon nanotubes (CNT) on nanoparticles of late transition (Ni, Pd, Pt) and coinage (Cu, Ag, Au) metals. The process is analyzed in terms of the binding of mono- and diatomic carbon species, their diffusion pathways, and the stability of the growing CNT. We find that the diffusion pathways can be controlled by the choice of the catalyst and the carbon precursor. Binding of the CNT through armchair edges is more favorable than through zigzag ones, but the relative stability varies significantly among the metals. Coinage metals, in particular Cu, are found to favor CVD growth of CNTs at low temperatures and with narrow chirality distributions., Comment: Phys. Rev. Lett., accepted

Using a first-principles approach, we investigate the origin of the fine structure in Si 2$p$ photoelectron spectra at the Si(100)2$\times$1 surface and at the Si(100)-SiO$_2$ interface. Calculated and measured shifts show very good agreement for both systems. By using maximally localized Wannier functions, we provide an interpretation in which the effects due to the electronegativity of second nearest neighbor atoms and due to the local strain field are distinguished. Hence, in combination with accurate modeling, photoelectron spectroscopy can provide a direct measure of the strain field at the atomic scale., Comment: to appear in the Proceedings of the 28th International Conference on the Physics of Semiconductors (Vienna, Austria, July 24-28, 2006). Original work: Phys. Rev. Lett. 96, 157601 (2006)