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We report on an extensive survey of (ZnO)N nanostructures ranging from bottom-up generated nanoclusters to top-down nanoparticles cuts from bulk polymorphs. The obtained results enable us to follow the energetic preferences of structure and polymorphism in (ZnO)N systems with N varying between 10-1026. This size range encompasses small nanoclusters with 10s of atoms and nanoparticles with 100s of atoms, which we also compare with appropriate bulk limits. In all cases the nanostructures and bulk systems are optimized using accurate all-electron, relativistic density functional theory based calculations with numeric atom centered orbital basis sets. Specifically, sets of five families of (ZnO)N species are considered: single-layered and multi-layered nanocages, and bulk cut nanoparticles from the sodalite (SOD), body centered tetragonal (BCT), and wurtzite (WZ) ZnO polymorphs. Using suitable fits to interpolate and extrapolate these data allows us to assess the size-dependent energetic stabilities of each family. With increasing size our results indicate a progressive change in energetic stability from single-layered to multi-layered cage-like nanoclusters. For nanoparticles of around 2.6 nm diameter we identify a transitional region where multi-layered cages, SOD, and BCT nanostructures are very similar in energetic stability. This transition size also marks the size regime at which bottom-up nanoclusters give way to top-down bulk-cut nanoparticles. Eventually, a final crossover is found where the most stable WZ-ZnO polymorph begins to energetically dominate at N â¼ 2200. This size corresponds to an approximate nanoparticle diameter of 4.7 nm, in line with experiments reporting the observation of wurtzite crystallinity in isolated ligand-free ZnO nanoparticles of 4-5 nm size or larger.
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The effect of the amount of Hartree-Fock mixing parameter (α) and of the screening parameter (w) defining the range separated HSE type hybrid functional is systematically studied for a series of seven metal oxides: TiO2 , ZrO2 , CuO2 , ZnO, MgO, SnO2 , and SrTiO3 . First, reliable band gap values were determined by comparing the optimal α reproducing the experiment with the inverse of the experimental dielectric constant. Then, the effect of the w in the HSE functional on the calculated band gap was explored in detail. Results evidence the existence of a virtually infinite number of combinations of the two parameters which are able to reproduce the experimental band gap, without a unique pair able to describe the full studied set of materials. Nevertheless, the results point out the possibility of describing the electronic structure of these materials through a functional including a screened HF exchange and an appropriate correlation contribution. © 2017 Wiley Periodicals, Inc.
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All electron relativistic density functional theory (DFT) based calculations using numerical atom-centered orbitals have been carried out to explore the relative stability, atomic, and electronic structure of a series of stoichiometric TiO2 anatase nanoparticles explicitly containing up to 1365 atoms as a function of size and morphology. The nanoparticles under scrutiny exhibit octahedral or truncated octahedral structures and span the 1-6 nm diameter size range. Initial structures were obtained using the Wulff construction, thus exhibiting the most stable (101) and (001) anatase surfaces. Final structures were obtained from geometry optimization with full relaxation of all structural parameters using both generalized gradient approximation (GGA) and hybrid density functionals. Results show that, for nanoparticles of a similar size, octahedral and truncated octahedral morphologies have comparable energetic stabilities. The electronic structure properties exhibit a clear trend converging to the bulk values as the size of the nanoparticles increases but with a marked influence of the density functional employed. Our results suggest that electronic structure properties, and hence reactivity, for the largest anatase nanoparticles considered in this study will be similar to those exhibited by even larger mesoscale particles or by bulk systems. Finally, we present compelling evidence that anatase nanoparticles become effectively bulklike when reaching a size of â¼20 nm diameter.
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Bottom-up and top-down derived nanoparticle structures refined by accurate ab initio calculations are used to investigate the size dependent emergence of crystallinity in titania from the monomer upwards. Global optimisation and data mining are used to provide a series of (TiO2)N global minima candidates in the range N = 1-38, where our approach provides many new low energy structures for N > 10. A range of nanocrystal cuts from the anatase crystal structure are also considered up to a size of over 250 atoms. All nanocrystals considered are predicted to be metastable with respect to non-crystalline nanoclusters, which has implications with respect to the limitations of the cluster approach to modelling large titania nanosystems. Extrapolating both data sets using a generalised expansion of a top-down derived energy expression for nanoparticles, we obtain an estimate of the non-crystalline to crystalline crossover size for titania. Our results compare well with the available experimental results and imply that anatase-like crystallinity emerges in titania nanoparticles of approximately 2-3 nm diameter.
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We investigated the influence of size and structure on the electronic structure of TiO2 nanoparticles 0.5-3.2 nm in diameter, in both vacuum and water, using density functional theory (DFT) calculations. Specifically, we tracked the optical and electronic energy gap of a set of (TiO2)n nanoparticles ranging from small non-bulklike clusters with n = 4, 8, and 16, to larger nanoparticles derived from the anatase bulk crystal with n = 35 and 84. As the difference between these two energy gaps (the exciton binding energy) becomes negligible in the bulk, this magnitude provides an indicator of the bulklike character of the electronic structure of the nanoparticles under study. Extrapolating our results to larger sizes, we obtain a rough estimate of the nanoparticle size at which the electronic structure will begin to be effectively bulklike. Our results generally confirmed that the electronic structure of the nanoparticle ground state and excited state has a more pronounced structure dependency than size dependency within a size range of 0.5-1.5 nm. We also showed that the thermodynamic preference for the photocatalytic species is the first S1 exciton. This S1 exciton is stable under vacuum but may evolve to free charge carriers upon structural relaxation in an aqueous environment for particles 0.5-1.5 nm in size studied in the present article. An analysis of ionization potentials and electron affinities, relative to the standard reduction potential for the water splitting half-reactions, revealed the importance of considering the structural relaxation in the excited states and the presence of water for assessing the thermodynamic conditions for photocatalytic water splitting.
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Conventional density functionals with either the local density approximation (LDA) or the generalized gradient approximation (GGA) form of the exchange-correlation potential fail to describe the electronic structure of a large number of metal oxides. Both the LDA and the GGA grossly underestimate the band gaps of these materials which severely affect the description of oxygen vacancy point defect states in reduced samples. To find a pragmatic approach to simultaneously and accurately describe the atomic and electronic structures of the most common TiO2 polymorphs, we explore the effect of the percentage of exact, non-local, Fock exchange on the electronic structure of stoichiometric rutile and anatase. From these results, a modified hybrid functional is proposed to properly describe the atomic structures, formation enthalpies and electronic structures of rutile and anatase and, at the same time, the results of reduced samples are also in good agreement with the available experimental results. The present approach can be safely used to accurately describe numerous TiO2 based materials containing defects or realistic nanoparticles for which the required large unit cells or system sizes hinder the use of GW related techniques.
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The interaction of trifluoroacetic acid with anatase TiO2(101) and TiO2(001) surfaces has been studied by means of periodic density functional theory based calculations. On the former, the interaction is weak with the adsorbed molecules in a configuration almost indistinguishable from the gas phase structure. On the latter, the interaction is very strong; the molecule adsorbs as trifluoroacetate and releases a proton that binds an oxygen surface atom with a significant distortion of the substrate. The difference in adsorption the mode and strength can be understood from the different structural features of both surfaces and provides arguments to the role of trifluoroacetic as a morphological control agent in the solvothermal synthesis of TiO2 nanoparticles with predominant (001) facets. This, in turn, has a very significant impact on industrial production strategies of value-added TiO2 for photocatalytic applications. Analysis of calculated core level binding energies for F(1s) confirms the experimental assignment to F at the surface as F(-) at Ti surface sites and to F in -CF3 groups of the adsorbed molecule.