DFTB+, a software package for efficient approximate density functional theory based atomistic simulations.

DFTB+ is a versatile community developed open source software package offering fast and efficient methods for carrying out atomistic quantum mechanical simulations. By implementing various methods approximating density functional theory (DFT), such as the density functional based tight binding (DFTB) and the extended tight binding method, it enables simulations of large systems and long timescales with reasonable accuracy while being considerably faster for typical simulations than the respective ab initio methods. Based on the DFTB framework, it additionally offers approximated versions of various DFT extensions including hybrid functionals, time dependent formalism for treating excited systems, electron transport using non-equilibrium Green's functions, and many more. DFTB+ can be used as a user-friendly standalone application in addition to being embedded into other software packages as a library or acting as a calculation-server accessed by socket communication. We give an overview of the recently developed capabilities of the DFTB+ code, demonstrating with a few use case examples, discuss the strengths and weaknesses of the various features, and also discuss on-going developments and possible future perspectives.

Quantum mechanical rippling of a MoS2 monolayer controlled by interlayer bilayer coupling.

Nanoscale corrugations are of great importance in determining the physical properties of two-dimensional crystals. However, the mechanical behavior of atomically thin films under strain is not fully understood. In this Letter, we show a layer-dependent mechanical response of molybdenum disulfide (MoS(2)) subject to atomistic-precision strain induced by 2H-bilayer island epitaxy. Dimensional crossover in the mechanical properties is evidenced by the formation of star-shaped nanoripple arrays in the first monolayer, while rippling instability is completely suppressed in the bilayer. Microscopic-level quantum mechanical simulations reveal that the nanoscale rippling is realized by the twisting of neighboring Mo-S bonds without modifying the chemical bond length, and thus invalidates the classical continuum mechanics. The formation of nanoripple arrays significantly changes the electronic and nanotribological properties of monolayer MoS(2). Our results suggest that quantum mechanical behavior is not unique for sp(2) bonding but general for atomic membranes under strain.

Ewald summation on a helix: A route to self-consistent charge density-functional based tight-binding objective molecular dynamics.

We explore the generalization to the helical case of the classical Ewald method, the harbinger of all modern self-consistent treatments of waves in crystals, including ab initio electronic structure methods. Ewald-like formulas that do not rely on a unit cell with translational symmetry prove to be numerically tractable and able to provide the crucial component needed for coupling objective molecular dynamics with the self-consistent charge density-functional based tight-binding treatment of the inter-atomic interactions. The robustness of the method in addressing complex hetero-nuclear nano- and bio-systems is demonstrated with illustrative simulations on a helical boron nitride nanotube, a screw dislocated zinc oxide nanowire, and an ideal DNA molecule.

Eshelby twist and magic helical zinc oxide nanowires and nanotubes.

Twisted zinc oxide nanowires and nanotubes were recently synthesized by screw-dislocation growth. We show theoretically that once their diameter increases above a critical size of the order of a few atomic spacings, the existence of these structures can be rationalized in terms of the energetics of surfaces and veritable Eshelby's twist linear elasticity mechanics supplemented by a nonlinear core term. For Burgers vector larger than the minimum allowed one, a twisted nanotube with well-defined thickness, rather than a nanowire, is the most stable nanostructure. Results are assistive for designing ultrathin nanostructures made out of nonlayered materials.

Chiral graphene nanoribbons: Objective molecular dynamics simulations and phase-transition modeling.

There is a growing need to understand the stability of quasi-one-dimensional one-layer-thick graphene nanoribbons. Objective molecular dynamics based on density-functional tight-binding models are used to investigate the stability against torsional deformations of nanoribbons with bare, F-, and OH-decorated armchair edges. The prevalence of chiral nanoribbons, including homochiral ones, prompted the construction of a simple phenomenological model inspired from the Landau phase transition theory. Our model is based on atomistic data and gives the structural parameters of the nanoribbon as a function of its edge chemistry and axial strain.

Bending ultrathin graphene at the margins of continuum mechanics.

Deviations from continuum mechanics are always expected in nanoscale structures. We investigate the validity of the plate idealization of ultrathin graphene by gaining insight into the response of chemical bonds to bending deformations. In the monolayer, a bond orbital model reveals the breakdown of the plate phenomenology. In the multilayer, objective molecular dynamics simulations identify the validity margin and the role of discreteness in the plate idealization. Our result has implications for a broad class of phenomena where the monolayer easily curves, and for the design of mass and force detection devices.

Edge-mediated dislocation processes in multishell carbon nano-onions?

We report in situ electron microscopy observations of dislocation dissociation and annihilation processes in individual nanometer-sized carbon onions. Essential for these processes is the counterintuitive motion of the 1/2(0001) edge from the outer surface to the inner region, which cross-links or unlinks a large number of shells. The correlation with atomistic simulations and analysis of the energy which separates the strain and edge components indicates that this inward glide originates in the reduction of edge with each inwards glide step, an effect specific to the spherical topology.

Helical nanotube structures of MoS2 with intrinsic twisting: an objective molecular dynamics study.

Objective molecular dynamics combined with density-functional-based tight binding makes it possible to compute chiral nanotubes as axial-screw dislocations. This enables the surprising revelation of a large catalog of MoS2 nanotubes that lack the prescribed translational symmetry and exhibit chirality-dependent electronic band gaps and elastic constants. Helical symmetry is the natural property to rely on when studying quasi-one-dimensional nanomaterials formally derived or grown via screw dislocations.

Modulating the optical and electronic properties of highly symmetric Si quantum dots.

The optical and electronic properties of quantum dots are critically influenced by the electronic states around the last occupied first empty levels. Using density functional theory calculations we show three alternative ways to alter the optical response of highly stable, highly symmetric hydrogen-terminated fullerene and polycrystalline Si quantum dots: small shape changes, applied uniaxial strain and exohedral doping. The demonstrated effectiveness renders symmetry lowering, the common theme of these processes, as a promising concept for deliberately adjusting optical response.

Dislocation onset and nearly axial glide in carbon nanotubes under torsion.

The torsional plastic response of single-walled carbon nanotubes is studied with tight-binding objective molecular dynamics. In contrast with plasticity under elongation and bending, a torsionally deformed carbon nanotube can slip along a nearly axial helical path, which introduces a distinct (+1,-1) change in wrapping indexes. The low energy realization occurs without loss in mass via nucleation of a 5-7-7-5 dislocation dipole, followed by glide of 5-7 kinks. The possibility of nearly axial glide is supported by the obtained dependence of the plasticity onset on chirality and handedness and by the presented calculations showing the energetic advantage of the slip path and of the initial glide steps.

Formation of Helices in Graphene Nanoribbons under Torsion.

We use objective boundary conditions and self-consistent charge density-functional-based tight-binding to simulate at the atomistic scale the formation of helices in narrow graphene nanoribbons with armchair edges terminated with fluorine and hydrogen. We interpret the microscopic data using an inextensible, unshearable elastic rod model, which considers both bending and torsional strains. When fitted to the atomistic data, the simple rod model uses closed-form solutions for a cubic equation to predict the strain energy and morphology at a given twist angle and the crossover point between pure torsion and a helix. Our modeling and simulation bring key insights into the origin of the helical graphene morphologies stored inside of carbon nanotubes. They can be useful for designing chiral nanoribbons with tailored properties.

Stability of polycrystalline and wurtzite Si nanowires via symmetry-adapted tight-binding objective molecular dynamics.

The stability of the most promising ground state candidate Si nanowires with less than 10 nm in diameter is comparatively studied with objective molecular dynamics coupled with nonorthogonal tight-binding and classical potential models. The computationally expensive tight-binding treatment becomes tractable due to the substantial simplifications introduced by the presented symmetry-adapted scheme. It indicates that the achiral polycrystalline of fivefold symmetry and the wurtzite wires of threefold symmetry are the most favorable quasi-one-dimensional Si arrangements. Quantitative differences with the classical model description are noted over the whole diameter range. Using a Wulff energy decomposition approach it is revealed that these differences are caused by the inability of the classical potential to accurately describe the interaction of Si atoms on surfaces and strained morphologies.

Phase-transition plasticity response in uniaxially compressed silicon nanospheres.

We present a microscopic description for the response of crystalline Si nanospheres up to 10 nm in radius for various uniaxial compression levels. The behavior at low compressions closely resembles the Hertzian predictions. At higher compressions the creation of a new beta-tin phase in the particle core leads to (i) volumetric changes (ii) an increase in elastic moduli, and (iii) significant hardening. Further, (iv) a reversible character of the transformation is obtained with molecular dynamics simulations. The agreement of (i)-(iv) with recent experimental findings challenges the current exclusive view of a dislocation plasticity response in somewhat larger nanoparticles. The phase-transition path should dominate in ultrasmall structures, where dislocation activity is prohibited.