Large scale ab-initio simulations of dislocations

We present a novel methodology to compute relaxed dislocations core configurations, and their energies in crystalline metallic materials using large-scale ab-intio simulations. The approach is based on MacroDFT, a coarse-grained density functional theory method that accurately computes the electronic structure with sub-linear scaling resulting in a tremendous reduction in cost. Due to its implementation in real-space, MacroDFT has the ability to harness petascale resources to study materials and alloys through accurate ab-initio calculations. Thus, the proposed methodology can be used to investigate dislocation cores and other defects where long range elastic effects play an important role, such as in dislocation cores, grain boundaries and near precipitates in crystalline materials. We demonstrate the method by computing the relaxed dislocation cores in prismatic dislocation loops and dislocation segments in magnesium (Mg). We also study the interaction energy with a line of Aluminum (Al) solutes. Our simulations elucidate the essential coupling between the quantum mechanical aspects of the dislocation core and the long range elastic fields that they generate. In particular, our quantum mechanical simulations are able to describe the logarithmic divergence of the energy in the far field as is known from classical elastic theory. In order to reach such scaling, the number of atoms in the simulation cell has to be exceedingly large, and cannot be achieved with the state-of-the-art density functional theory implementations

Gradient type optimization methods for electronic structure calculations

The density functional theory (DFT) in electronic structure calculations can be formulated as either a nonlinear eigenvalue or direct minimization problem. The most widely used approach for solving the former is the so-called self-consistent field (SCF) iteration. A common observation is that the convergence of SCF is not clear theoretically while approaches with convergence guarantee for solving the latter are often not competitive to SCF numerically. In this paper, we study gradient type methods for solving the direct minimization problem by constructing new iterations along the gradient on the Stiefel manifold. Global convergence (i.e., convergence to a stationary point from any initial solution) as well as local convergence rate follows from the standard theory for optimization on manifold directly. A major computational advantage is that the computation of linear eigenvalue problems is no longer needed. The main costs of our approaches arise from the assembling of the total energy functional and its gradient and the projection onto the manifold. These tasks are cheaper than eigenvalue computation and they are often more suitable for parallelization as long as the evaluation of the total energy functional and its gradient is efficient. Numerical results show that they can outperform SCF consistently on many practically large systems.Comment: 24 pages, 11 figures, 59 references, and 1 acknowledgement

Cyclic Density Functional Theory : A route to the first principles simulation of bending in nanostructures

We formulate and implement Cyclic Density Functional Theory (Cyclic DFT) -- a self-consistent first principles simulation method for nanostructures with cyclic symmetries. Using arguments based on Group Representation Theory, we rigorously demonstrate that the Kohn-Sham eigenvalue problem for such systems can be reduced to a fundamental domain (or cyclic unit cell) augmented with cyclic-Bloch boundary conditions. Analogously, the equations of electrostatics appearing in Kohn-Sham theory can be reduced to the fundamental domain augmented with cyclic boundary conditions. By making use of this symmetry cell reduction, we show that the electronic ground-state energy and the Hellmann-Feynman forces on the atoms can be calculated using quantities defined over the fundamental domain. We develop a symmetry-adapted finite-difference discretization scheme to obtain a fully functional numerical realization of the proposed approach. We verify that our formulation and implementation of Cyclic DFT is both accurate and efficient through selected examples. The connection of cyclic symmetries with uniform bending deformations provides an elegant route to the ab-initio study of bending in nanostructures using Cyclic DFT. As a demonstration of this capability, we simulate the uniform bending of a silicene nanoribbon and obtain its energy-curvature relationship from first principles. A self-consistent ab-initio simulation of this nature is unprecedented and well outside the scope of any other systematic first principles method in existence. Our simulations reveal that the bending stiffness of the silicene nanoribbon is intermediate between that of graphene and molybdenum disulphide. We describe several future avenues and applications of Cyclic DFT, including its extension to the study of non-uniform bending deformations and its possible use in the study of the nanoscale flexoelectric effect.Comment: Version 3 of the manuscript, Accepted for publication in Journal of the Mechanics and Physics of Solids, http://www.sciencedirect.com/science/article/pii/S002250961630368

A simple algorithm for the Kohn-Sham inversion problem applicable to general target densities

A simple algorithm for the Kohn-Sham inversion problem is presented. The method is found to converge toward a nearby v-representable Kohn-Sham density irrespective of the fact whether the initial target density has been v-representable or not. For the proposed procedure, the target density can be of general nature. The algorithm can handle Hartree-Fock and post-Hartree-Fock, spin-unpolarized and polarized states equally well. Additionally, experimental densities and even general gedanken densities can be treated. The algorithm is easy to implement and does not require an additional procedure to adjust eigenvalues

Tuning the graphene band gap by thermodynamic control of molecular self-assembly on graphene

Recent interest in functionalised graphene has been motivated by the prospect of creating a two-dimensional semiconductor with a tuneable band gap. Various approaches to band gap engineering have been made over the last decade, one of which is chemical functionalisation. However, the patterning of molecular adsorption onto graphene has proved to be difficult, as grown structures tend to be stochastic in nature. In the first part of this work, a predictive physical model of the self-assembly of halogenated carbene layers on graphene is suggested. Self-assembly of the adsorbed layer is found to be governed by a combination of the curvature of the graphene sheet, local distortions, as introduced by molecular adsorption, and short-range intermolecular repulsion. The thermodynamics of bidental covalent molecular adsorption and the resultant electronic structure are computed using Density Functional Theory. It is predicted that a direct band gap is opened that is tuneable by varying coverages and is dependent on the ripple ampli- tude. This provides a mechanism for the controlled engineering of graphene’s electronic structure and thus its use in semiconductor technologies. In the second part of this work, the formation of intrinsic ripples in graphene sheets under isotropic compression is examined. An isotropic compression of graphene is shown to induce a structural deformation on the basis of Density Functional Perturbation Theory. Static instabilities, indicated by imaginary fre- quency phonon modes, are induced in the high symmetry Γ – K (zigzag) and Γ – M (armchair) directions by an isotropic compressive strain of the graphene sheet. The wavelength of the unstable modes (ripples) is directly related to the magnitude of the strain and remarkably insensitive to the direction of propagation in the 2D lattice. These calculations further suggest that the formation energy of the ripple is isotropic for lower strains and becomes anisotropic for larger strains. This is a result of graphene’s elastic property, which is depen- dent on direction and strain. Within the quasi harmonic approximation this is combined with the observation that molecular adsorption energies depend strongly on curvature to suggest a strategy for generating ordered overlayers in order to tune the functional properties of graphene. Based on the results of this work, we can conclude that (pre-)rippled graphene sheets can be used to direct molecular adsorption in order to form specific patterns by tuning the thermodynamic equilibrium of the addition reaction of small (organic) molecules.Open Acces