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This paper reviews the basic principles of the density-functional tight-binding (DFTB) method, which is based on density-functional theory as formulated by Hohenberg, Kohn and Sham (KS-DFT). DFTB consists of a series of models that are derived from a Taylor series expansion of the KS-DFT total energy. In the lowest order (DFTB1), densities and potentials are written as superpositions of atomic densities and potentials. The KohnSham orbitals are then expanded to a set of localized atom-centred functions, which are obtained for spherical symmetric spin-unpolarized neutral atoms self-consistently. The whole Hamilton and overlap matrices contain one- and two-centre contributions only. Therefore, they can be calculated and tabulated in advance as functions of the distance between atomic pairs. The second contributions to DFTB1, the DFT double counting terms, are summarized together with nuclear repulsion energy terms and can be rewritten as the sum of pairwise repulsive terms. The second-order (DFTB2) and third-order (DFTB3) terms in the energy expansion correspond to a self-consistent representation, where the deviation of the ground-state density from the reference density is represented by charge monopoles only. This leads to a computationally efficient representation in terms of atomic charges (Mulliken), chemical hardness (Hubbard) parameters and scaled Coulomb laws. Therefore, no additional adjustable parameters enter the DFTB2 and DFTB3 formalism. The handling of parameters, the efficiency, the performance and extensions of DFTB are briefly discussed.

Monolayers of transition-metal dichalcogenides feature exceptional optical properties that are dominated by tightly bound electron–hole pairs, called excitons. Creating van der Waals heterostructures by deterministically stacking individual monolayers can tune various properties via the choice of materials1 and the relative orientation of the layers2,3. In these structures, a new type of exciton emerges where the electron and hole are spatially separated into different layers. These interlayer excitons4–6 allow exploration of many-body quantum phenomena7,8 and are ideally suited for valleytronic applications9. A basic model of a fully spatially separated electron and hole stemming from the K valleys of the monolayer Brillouin zones is usually applied to describe such excitons. Here, we combine photoluminescence spectroscopy and first-principles calculations to expand the concept of interlayer excitons. We identify a partially charge-separated electron–hole pair in MoS2/WSe2 heterostructures where the hole resides at the Γ point and the electron is located in a K valley. We control the emission energy of this new type of momentum-space indirect, yet strongly bound exciton by variation of the relative orientation of the layers. These findings represent a crucial step towards the understanding and control of excitonic effects in van der Waals heterostructures and devices.

One of the key challenges in two-dimensional (2D) materials is to go beyond graphene, a prototype 2D polymer (2DP), and to synthesize its organic analogues with structural control at the atomic- or molecular-level. Here we show the successful preparation of porphyrin-containing monolayer and multilayer 2DPs through Schiff-base polycondensation reaction at an air–water and liquid–liquid interface, respectively. Both the monolayer and multilayer 2DPs have crystalline structures as indicated by selected area electron diffraction. The monolayer 2DP has a thickness of∼0.7 nm with a lateral size of 4-inch wafer, and it has a Young’s modulus of 267±30 GPa. Notably, the monolayer 2DP functions as an active semiconducting layer in a thin film transistor, while the multilayer 2DP from cobalt-porphyrin monomer efficiently catalyses hydrogen generation from water. This work presents an advance in the synthesis of novel 2D materials for electronics and energy-related applications. Forming 2D polymers in a controlled manner on the atomic and molecular level is difficult. Here, Feng and others have used Schiff-base polycondensation reactions at an air-water or liquid-liquid interface to form porphyrin containing monolayer and multilayer 2D polymers.

Many methods have been proposed for efficient storage of molecular hydrogen for fuel cell applications. However, despite intense research efforts, the twin U.S. Department of Energy goals of 6.5% mass ratio and 62 kg/ m3volume density has not been achieved either experimentally or via theoretical simulations on reversible model systems. Carbon-based materials, such as carbon nanotubes, have always been regarded as the most attractive physisorption substrates for the storage of hydrogen. Theoretical studies on various model graphitic systems, however, failed to reach the elusive goal. Here, we show that insufficiently accurate carbon- H2interaction potentials, together with the neglect and incomplete treatment of the quantum effects in previous theoretical investigations, led to misleading conclusions for the absorption capacity. A proper account of the contribution of quantum effects to the free energy and the equilibrium constant for hydrogen adsorption suggest that the U.S. Department of Energy specification can be approached in a graphite-based physisorption system. The theoretical prediction can be realized by optimizing the structures of nano-graphite platelets (graphene), which are light-weight, cheap, chemically inert, and environmentally benign.

Wear in self-mated tetrahedral amorphous carbon (ta-C) films is studied by molecular dynamics and near-edge X-ray absorption fine structure spectroscopy. Both theory and experiment demonstrate the formation of a soft amorphous carbon (a-C) layer with increased sp 2 content, which grows faster than an a-C tribolayer found on self-mated diamond sliding under similar conditions. The faster sp 3 → sp 2 transition in ta-C is explained by easy breaking of prestressed bonds in a finite, nanoscale ta-C region, whereas diamond amorphization occurs at an atomically sharp interface. A detailed analysis of the underlying rehybridization mechanism reveals that the sp 3 → sp 2 transition is triggered by plasticity in the adjacent a-C. Rehybridization therefore occurs in a region that has not yet experienced plastic yield. The resulting soft a-C tribolayer is interpreted as a precursor to the experimentally observed wear.

The mechanical properties of materials and particularly the strength are greatly affected by the presence of defects; therefore, the theoretical strength (≈10% of the Young's modulus) is not generally achievable for macroscopic objects. On the contrary, nanotubes, which are almost defect-free, should achieve the theoretical strength that would be reflected in superior mechanical properties. In this study, both tensile tests and buckling experiments of individual WS₂ nanotubes were carried out in a highresolution scanning electron microscope. Tensile tests of MoS₂ nanotubes were simulated by means of a density-functional tightbinding-based molecular dynamics scheme as well. The combination of these studies provides a microscopic picture of the nature of the fracture process, giving insight to the strength and flexibility of the WS₂ nanotubes (tensile strength of ≈16 GPa). Fracture analysis with recently proposed models indicates that the strength of such nanotubes is governed by a small number of defects. A fraction of the nanotubes attained the theoretical strength indicating absence of defects.

An accurate total energy calculation is essential in materials computation. To date, many tight-binding (TB) approaches based on parameterized hopping can produce electronic structures comparable to those obtained using first-principles calculations. However, TB approaches still have limited applicability for determining material properties derived from the total energy. That is, the predictive power of the TB total energy is impaired by an inaccurate evaluation of the repulsive energy. The complexity associated with the parametrization of TB repulsive potentials is the weak link in this evaluation. In this study, we propose a new method for obtaining the pairwise TB repulsive potential for crystalline materials by employing the Chen-Möbius inversion theorem. We show that the TB-based phonon dispersions, calculated using the resulting repulsive potential, compare well with those obtained by first-principles calculations for various systems, including covalent and ionic bulk materials and two-dimensional materials. The present approach only requires the first-principles total energy and TB electronic band energy as input and does not involve any parameters. This striking feature enables us to generate repulsive potentials programmatically.

The recent discovery of borophene, a two-dimensional allotrope of boron, raises many questions about its structure and its chemical and physical properties. Boron has a high chemical affinity to oxygen but little is known about the oxidation behaviour of borophene. Here we use first principles calculations to study the phase diagram of free-standing, two-dimensional B1−xOx for compositions ranging from x = 0 to x = 0.6, which correspond to borophene and B 2 O 3 sheets, respectively. Our results indicate that no stable compounds except borophene and B 2 O 3 sheets exist. Intermediate compositions are heterogeneous mixtures of borophene and B 2 O 3 . Other hypothetical crystals such as B 2 O are unfavorable and some of them underwent spontaneous disproportionation into borophene and B 2 O 3 . It is also shown that oxidizing borophene inside the flakes is thermodynamically unfavorable over forming B 2 O 3 at the edges. All findings can be rationalized by oxygen's preference of two-fold coordination which is incompatible with higher in-plane coordination numbers preferred by boron. These results agree well with recent experiments and pave the way to better understand the process of oxidation of borophene and other two-dimensional materials.

The characterization of nanostructures down to the atomic scale is essential to understand some physical properties. Such a characterization is possible today using direct imaging methods such as aberration-corrected high-resolution transmission electron microscopy (HRTEM), when iteratively backed by advanced modeling produced by theoretical structure calculations and image calculations. Aberration-corrected HRTEM is therefore extremely useful for investigating low-dimensional structures, such as inorganic fullerene-like particles and inorganic nanotubes. The atomic arrangement in these nanostructures can lead to new insights into the growth mechanism or physical properties, where imminent commercial applications are unfolding. This article will focus on two structures that are symmetric and reproducible. The first structure that will be dealt with is the smallest stable symmetric closed-cage structure in the inorganic system, a MoS₂ nanooctahedron. It is investigated by means of aberration-corrected microscopy which allowed validating the suggested DFTB-MD model. It will be shown that structures diverging from the energetically most stable structures are present in the laser ablated soot and that the alignment of the different shells is parallel, unlike the bulk material where the alignment is antiparallel. These findings correspond well with the high-energy synthetic route and they provide more insight into the growth mechanism. The second structure studied is WS₂ nanotubes, which have already been shown to have a unique structure with very desirable mechanical properties. The joint HRTEM study combined with modeling reveals new information regarding the chirality of the different shells and provides a better understanding of their growth mechanism.

The synthesis of inorganic nanotubes (INT) from layered compounds of a small size (<10 nm in diameter) and number of layers (<4) is not a trivial task. Calculations based on density functional tight-binding theory (DFTB) predict that under highly exergonic conditions, the reaction could be driven into a “window” of (meta-) stability, where 1–3-layer nanotubes will be formed. Indeed, in this study, single- to triple-wall WS2 nanotubes with a diameter of 3–7 nm and a length of 20–100 nm were produced by high-power plasma irradiation of multiwall WS2 nanotubes. As target materials, plane crystals (2H), quasi spherical nanoparticles (IF) and multiwall, 20–30 layers, WS2 nanotubes were assessed. Surprisingly, only INT-WS2 treated by plasma resulted in very small, and of a few layers, “daughter” nanotubules. The daughter nanotubes occur mostly attached to the outer surface of the predecessor, i.e., the multiwall “mother” nanotubes. They appear having either a common growth axis with the multiwall nanotube or tilted by approximately 30° or 60° with respect to its axis. This suggests that the daughter nanotubes are generated by exfoliation along specific crystallographic directions. A growth mechanism for the daughter nanotubes is proposed. High resolution transmission and scanning electron microscopy (HRTEM/HRSEM) analyses revealed the distinctive nanoscale structures and helped elucidating their growth mechanism.