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Linear scaling methods, or O(N) methods, have computational and memory requirements which scale linearly with the number of atoms in the system, N, in contrast to standard approaches which scale with the cube of the number of atoms. These methods, which rely on the short-ranged nature of electronic structure, will allow accurate, ab initio simulations of systems of unprecedented size. The theory behind the locality of electronic structure is described and related to physical properties of systems to be modelled, along with a survey of recent developments in real-space methods which are important for efficient use of high performance computers. The linear scaling methods proposed to date can be divided into seven different areas, and the applicability, efficiency and advantages of the methods proposed in these areas is then discussed. The applications of linear scaling methods, as well as the implementations available as computer programs, are considered. Finally, the prospects for and the challenges facing linear scaling methods are discussed.
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The electronic structure of carbon shells of carbon encapsulated iron nanoparticles carbon encapsulated Fe@C has been studied by X-ray resonant emission and X-ray absorption spectroscopy. The recorded spectra have been compared to the density functional calculations of the electronic structure of graphene. It has been shown that an Fe@C carbon shell can be represented in the form of several graphene layers with Stone-Wales defects. The dispersion of energy bands of Fe@C has been examined using the measured C Ka resonant X-ray emission spectra.
We report the results of X-ray spectroscopy and Raman measurements of as-prepared graphene on a high quality copper surface and the same materials after 1.5 years under different conditions (ambient and low humidity). The obtained results were compared with density functional theory calculations of the formation energies and electronic structures of various structural defects in graphene/Cu interfaces. For evaluation of the stability of the carbon cover, we propose a two-step model. The first step is oxidation of the graphene, and the second is perforation of graphene with the removal of carbon atoms as part of the carbon dioxide molecule. Results of the modeling and experimental measurements provide evidence that graphene grown on high-quality copper substrate becomes robust and stable in time (1.5 years). However, the stability of this interface depends on the quality of the graphene and the number of native defects in the graphene and substrate. The effect of the presence of a metallic substrate with defects on the stability and electronic structure of graphene is also discussed.
The electronic band structure of complex nanostructured semiconductors has a considerable effect on the final electronic and optical properties of the material and, ultimately, on the functionality of the devices incorporating them. Valence electron energy-loss spectroscopy (VEELS) in the transmission electron microscope (TEM) provides the possibility of measuring this property of semiconductors with high spatial resolution. However, it still represents a challenge for narrow-bandgap semiconductors, since an electron beam with low energy spread is required. Here we demonstrate that by means of monochromated VEELS we can study the electronic band structure of narrow-gap materials GaSb and InAs in the form of heterostructured nanowires, with bandgap values down to 0.5 eV, especially important for newly developed structures with unknown bandgaps. Using complex heterostructured InAs-GaSb nanowires, we determine a bandgap value of 0.54 eV for wurtzite InAs. Moreover, we directly compare the bandgaps of wurtzite and zinc-blende polytypes of GaSb in a single nanostructure, measured here as 0.84 and 0.75 eV, respectively. This allows us to solve an existing controversy in the band alignment between these structures arising from theoretical predictions. The findings demonstrate the potential of monochromated VEELS to provide a better understanding of the band alignment at the heterointerfaces of narrow-bandgap complex nanostructured materials with high spatial resolution. This is especially important for semiconductor device applications where even the slightest variations of the electronic band structure at the nanoscale can play a crucial role in their functionality.
Electronic structure of V$_{15}$ magnetic molecules (K$_6$ [V$_{15}$ As$_6$ O$_{42}$ (H$_2$O)] cdot 8H$_2$O)$ has been studied using LSDA+U band structure calculations, and measurements of X-ray photoelectron (valence band, core levels) and X-ray fluorescence spectra (vanadium K$beta_5$ and L$_{2,3}$, and oxygen K$alpha$). Experiments confirm that vanadium ions are tetravalent in V$_{15}$, and their local atomic structure is close to that of CaV$_3$O$_7$. Comparison of experimental data with the results of electronic structure calculations show that the LSDA+U method provides a description of the electronic structure of V$_{15}$ which agrees well with experiments.
Density Functional Theory calculations are used to investigate the role of substrate-induced cooperative effects on the adsorption of water on a partially oxidized transition metal surface, O(2x2)/Ru(0001). Focussing particularly on the dimer configuration, we analyze the different contributions to its binding energy. A significant reinforcement of the intermolecular hydrogen-bond (H-bond), also supported by the observed frequency shifts of the vibration modes, is attributed to the polarization of the donor molecule when bonded to the Ru atoms in the substrate. This result is further confirmed by our calculations for a water dimer interacting with a small Ru cluster, which clearly show that the observed effect does not depend critically on fine structural details and/or the presence of co-adsorbates. Interestingly, the cooperative reinforcement of the H-bond is suppressed when the acceptor molecule, instead of the donor, is bonded to the surface. This simple observation can be used to rationalize the relative stability of different condensed structures of water on metallic substrates.
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