Noticias

The <i>K</i>₄ structure was theoretically predicted for trivalent chemical species, such as sp² carbon. However, since attempts to synthesize the <i>K</i>₄ carbon have not succeeded, this allotrope has been regarded as a crystal form that might not exist in nature. In the present work, we carried out electrochemical crystallization of the radical anion salts of a triangular molecule, naphthalene diimide (NDI)-Δ, using various electrolytes. X-ray crystal analysis of the obtained crystals revealed the <i>K</i>₄ structure, which was formed by the unique intermolecular π overlap directed toward three directions from the triangular-shape NDI-Δ radical anions. Electron paramagnetic resonance and static magnetic measurements confirmed the radical anion state of NDI-Δ and indicated an antiferromagnetic intermolecular interaction with the Weiss constant of θ = −10 K. The band structure calculation suggested characteristic features of the present material, such as a metallic ground state, Dirac cones, and flat bands

Biogas Upgrading by Transition Metal Carbides

The separation of carbon dioxide (CO₂) from methane (CH₄) is critical in biogas upgrading, requiring materials with high selectivity toward one of the two gas components. Hereby we show, by means of density functional theory based calculations including dispersive forces description, the distinct interaction of CO₂ and CH₄ with the most stable (001) surfaces of seven transition metal carbides (TMC; TM = Ti, Zr, Hf, V, Nb, Ta, and Mo). Transition state theory derived ad-/desorption rates suggest a very high CO₂ uptake and selectivity over CH₄ even at ambient temperature and low partial gas pressures

Performance of the TPSS Functional on Predicting Core Level Binding Energies of Main Group Elements Containing Molecules: A Good Choice for Molecules Adsorbed on Metal Surfaces

Here we explored the performance of Hartree–Fock (HF), Perdew–Burke–Ernzerhof (PBE), and Tao–Perdew–Staroverov–Scuseria (TPSS) functionals in predicting core level 1s binding energies (BEs) and BE shifts (ΔBEs) for a large set of 68 molecules containing a wide variety of functional groups for main group elements B → F and considering up to 185 core levels. A statistical analysis comparing with X-ray photoelectron spectroscopy (XPS) experiments shows that BEs estimations are very accurate, TPSS exhibiting the best performance. Considering ΔBEs, the three methods yield very similar and excellent results, with mean absolute deviations of ∼0.25 eV. When considering relativistic effects, BEs deviations drop approaching experimental values. So, the largest mean percentage deviation is of 0.25% only. Linear trends among experimental and estimated values have been found, gaining offsets with respect to ideality. By adding relativistic effects to offsets, HF and TPSS methods underestimate experimental values by solely 0.11 and 0.05 eV, respectively, well within XPS chemical precision. TPSS is posed as an excellent choice for the characterization, by XPS, of molecules on metal solid substrates, given its suitability in describing metal substrates bonds <i>and</i> atomic and/or molecular orbitals

Molecular Mechanism and Microkinetic Analysis of the Reverse Water Gas Shift Reaction Heterogeneously Catalyzed by the Mo₂C MXene

The potential of the Mo2C MXene to catalyze the reverse water gas shift (RWGS) reaction has been investigated by a combination of density functional theory (DFT)-based calculations, atomistic thermodynamics, and microkinetic simulations. Different catalytic routes are explored including redox and associative (carboxyl and formate) mechanisms at a high temperature at which the RWGS reaction is exothermic. The present study predicts that, on the Mo2C MXene, the RWGS reaction proceeds preferentially through the redox and formate catalytic routes, the rate-limiting step being the formation of the OH intermediate followed by the H2O formation, whereas the carboxyl route to form the carboxyl intermediate is hindered by a large energy barrier. Microkinetic simulations confirm the formation of carbon monoxide (CO) under relatively mild conditions (i.e., ∼400 °C and 1 bar). The CO formation is not affected either by the total pressure or by the CO2/H2 ratio. However, water formation requires high temperatures of ∼700 °C and pressures above 5 bar. In addition, an excess of hydrogen in the CO2/H2 ratio favors water formation. Shortly, the present study confirms that the Mo2C MXene emerges as a heterogeneous catalyst candidate for generating a CO feedstock that can be used for subsequent transformation into methanol through the Fischer–Tropsch process

Jacob’s Ladder as Sketched by Escher: Assessing the Performance of Broadly Used Density Functionals on Transition Metal Surface Properties

The present work surveys the performance of various widely used density functional theory exchange–correlation (xc) functionals in describing observable surface properties of a total of 27 transition metals with face-centered cubic (fcc), body-centered cubic (bcc), or hexagonal close-packed (hcp) crystallographic structures. A total of 81 low Miller index surfaces were considered employing slab models. Exemplary xc functionals within the three first rungs of Jacob’s ladder were considered, including the Vosko–Wilk–Nusair xc functional within the local density approximation, the Perdew–Burke–Ernzerhof (PBE) functional within the generalized gradient approximation (GGA), and the Tao–Perdew–Staroverov–Scuseria functional as a meta-GGA functional. Hybrids were excluded in the survey because they are known to fail in properly describing metallic systems. In addition, two variants of PBE were considered, PBE adapted for solids (PBEsol) and revised PBE (RPBE), aimed at improving adsorption energies. Interlayer atomic distances, surface energies, and surface work functions were chosen as the scrutinized properties. A comparison with available experimental data, including single-crystal and polycrystalline values, shows that no xc functional is best at describing all of the surface properties. However, in statistical mean terms the PBEsol xc functional is advised, while PBE is recommended when considering both bulk and surface properties. On the basis of the present results, a discussion of adapting GGA functionals to the treatment of metallic surfaces in an alternative way to meta-GGA or hybrids is provided

Structure and Properties of Zirconia Nanoparticles from Density Functional Theory Calculations

The structure, stability, and electronic properties of a series of zirconia nanoparticles between 1.5 and 2 nm in size, (ZrO_2±<i>x</i>)_<i>n</i> within the <i>n</i> = 13 to <i>n</i> = 85 range, have been investigated through density functional theory (DFT) based calculations. On the methodological side we compare results obtained with standard DFT functionals with the DFT+<i>U</i> approach and with hybrid functionals. As representative models, octahedral and truncated octahedral morphologies have been considered for the zirconia nanoparticles. Partly truncated octahedral nanoparticles with ZrO₂ stoichiometry display the highest stability. On the contrary, nanoparticles with octahedral and cuboctahedral (totally truncated octahedral) shapes are less stable due to oxygen deficiency or excess, respectively. We show that the calculated formation energies scale linearly with the average coordination number of the Zr ions and converge to the bulk value as the particle size increases. The formation energy of a neutral oxygen vacancy in the nanoparticles has also been investigated. In comparison to the ZrO₂(101) surface of tetragonal zirconia, we found that three- and four-coordinated O atoms have similar formation energies. However, the two-coordinated O ions on the surface of the nanoparticles have considerably smaller formation energies. In this respect the effect of nanostructuring can be substantial for the reactivity of the material and its reducibility. The low-coordinated sites create defective states in the electronic structure and reduce the effective band gap, which can result in enhanced interaction with deposited species and modified photocatalytic activity

An Empirical, yet Practical Way To Predict the Band Gap in Solids by Using Density Functional Band Structure Calculations

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+<i>U</i>, 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 <i>GW</i> 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 <i>GW</i> 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 <i>GW</i>-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 <i>GW</i> calculations become unfeasible

Performance of the <i>G</i>₀<i>W</i>₀ Method in Predicting the Electronic Gap of TiO₂ Nanoparticles

Using a relativistic all-electron description and numerical atomic-centered orbital basis set, the performance of the <i>G</i>₀<i>W</i>₀ method on the electronic band gap of (TiO₂)<i>_n</i> nanoparticles (<i>n</i> = 1–20) is investigated. Results are presented for <i>G</i>₀<i>W</i>₀ on top of hybrid (PBE0 and a modified version with 12.5% of Fock exchange) functionals. The underestimation of the electronic band gap from Kohn–Sham orbital energies is corrected by the quasiparticle energies from the <i>G</i>₀<i>W</i>₀ method, which are consistent with the variational ΔSCF approach. A clear correlation between both methods exists regardless of the hybrid functional employed. In addition, the vertical ionization potential and electron affinity from quasiparticle energies show a systematic correlation with the ΔSCF calculated values. On the other hand, the shape of the nanoparticles promotes some deviations on the electronic band gap. In conclusion, this study shows the following: (i) A systematic correlation exists between band gaps, ionization potentials, and electron affinities of TiO₂ nanoparticles as predicted from variational ΔSCF and <i>G</i>₀<i>W</i>₀ methods. (ii) The <i>G</i>₀<i>W</i>₀ approach can be successfully used to study the electronic band gap of realistic size nanoparticles at an affordable computational cost with a ΔSCF accuracy giving results that are directly related with those from photoemission spectroscopy. (iii) The quasiparticle energies are explicitly required to shed light on the photocatalytic properties of TiO₂. (iv) The <i>G</i>₀<i>W</i>₀ approach emerges as an accurate method to investigate the photocatalytic properties of both nanoparticles and extended semiconductors

Theoretical Modeling of Electronic Excitations of Gas-Phase and Solvated TiO₂ Nanoclusters and Nanoparticles of Interest in Photocatalysis

The optical absorption spectra of (TiO₂)_<i>n</i>, nanoclusters (<i>n</i> = 1–20) and nanoparticles (<i>n</i> = 35, 84) have been calculated from the frequency-dependent dielectric function in the independent particle approximation under the framework of density functional theory. The PBE generalized gradient approach based functional, the so-called PBE+<i>U</i> method and the PBE0 and PBEx hybrid functionalscontaining 25% and 12.5% of nonlocal Fock exchange, respectivelyhave been used. The simulated spectra have been obtained in the gas phase and in water on previously PBE0 optimized atomic structures. The effect of the solvent has been accounted for by using an implicit water solvation model. For the smallest nanoclusters, the spectra show discrete peaks, whereas for the largest nanoclusters and for the nanoparticles they resemble a continuum absorption band. In the gas phase and for a given density functional, the onset of the absorption (optical gap, <i>O</i>_gap) remains relatively constant for all nanoparticle sizes although it increases with the percentage of nonlocal Fock exchange, as expected. For all tested functionals, the tendency of <i>O</i>_gap in water is very similar to that observed in the gas phase with an almost constant upshift. For comparison, the optical gap has also been calculated at the TD-DFT level with the PBEx functional in the gas phase and in water. Both approaches agree reasonably well although the TD-DFT gap values are lower than those derived from the dielectric-function. Overall, the position of the spectral maxima and the width of the spectra are relatively constant and independent of particle size which may have implications in the understanding of photocatalysis by TiO₂

Effect of Nanostructuring on the Reactivity of Zirconia: A DFT+<i>U</i> Study of Au Atom Adsorption

The reactivity of zirconia nanoparticles has been investigated by means of DFT+<i>U</i> calculations as a function of the morphology and stoichiometry. For comparative purposes, a single Au atom has been deposited on the stoichiometric and O-deficient regular (101) surface, on the stepped (156) surface, and on nanoparticles in the range of 0.9–1.9 nm in size. We show that, under stoichiometric conditions, nanostructuring leads to enhanced binding energies and redox processes with the supported metal that are not found on the extended surfaces. These new features are due to the structural flexibility and peculiar electronic structure displayed by the nanoparticles. In this respect, nanostructuring of oxide supports can modify and possibly improve the catalytic activity of the deposited metals. In contrast, we show that under reducing conditions nanostructuring stabilizes the O vacancies making zirconia nanoparticles less reactive toward Au adsorption than O-deficient extended surfaces