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

Abstract

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.

Version 3 of the manuscript, Accepted for publication in Journal of the Mechanics and Physics of Solids, http://www.sciencedirect.com/science/article/pii/S0022509616303684

References in corpus (15)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Nearsightedness of Electronic Matter
• Density-functional tight-binding for beginners
• Gap opening in graphene by shear strain
• Quantum Flexoelectricity in Low Dimensional Systems
• Parallel Self-Consistent-Field Calculations via Chebyshev-Filtered Subspace Acceleration
• SPARC: Accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory: Extended systems
• SPARC: Accurate and efficient finite-difference formulation and parallel implementation of Density Functional Theory: Isolated clusters
• Periodic Pulay method for robust and efficient convergence acceleration of self-consistent field iterations
• Augmented Lagrangian formulation of Orbital-Free Density Functional Theory
• Chebyshev polynomial filtered subspace iteration in the Discontinuous Galerkin method for large-scale electronic structure calculations
• Structural, chemical and dynamical trends in graphene grain boundaries
• Graphene nanoribbons subject to gentle bends
• Electronic and optical trends in carbon nanotubes under pure bending
• Symmetry-Adapted Phonon Analysis of Nanotubes

Cited by in corpus (22)

• Curved Magnetism in CrI${}_3$
• Flexoelectricity in soft elastomers and the molecular mechanisms underpinning the design and emergence of giant flexoelectricity
• Symmetry-adapted real-space density functional theory for cylindrical geometries: application to large X (X=C, Si, Ge, Sn) nanotubes
• Chebyshev polynomial filtered subspace iteration in the Discontinuous Galerkin method for large-scale electronic structure calculations
• Transversal flexoelectric coefficient for nanostructures at finite deformations from first principles
• Strain engineering of Janus transition metal dichalcogenide nanotubes: An ab intio study
• Density functional theory method for twisted geometries with application to torsional deformations in group-IV nanotubes
• Ab initio framework for systems with helical symmetry: theory, numerical implementation and applications to torsional deformations in nanostructures
• Torsional strain engineering of transition metal dichalcogenide nanotubes: An ab initio study
• Phase transformations and compatibility in helical structures
• On the bending of rectangular atomic monolayers along different directions: an ab initio study
• Elastic properties of Janus transition metal dichalcogenide nanotubes from first principles
• Torsional moduli of transition metal dichalcogenide nanotubes from first principles
• Ab initio study on the electromechanical response of Janus transition metal dihalide nanotubes
• SPARC: Simulation Package for Ab-initio Real-space Calculations
• M-SPARC: MATLAB-Simulation Package for Ab-initio Real-space Calculations
• Quantum nuclear motion in silicene: Assessing structural and vibrational properties through path-integral simulations
• Generalization of Stoney's equation for flexoelectric thin films on elastic substrates
• Machine learning based prediction of the electronic structure of quasi-one-dimensional materials under strain
• Two-level Chebyshev filter based complementary subspace method: pushing the envelope of large-scale electronic structure calculations
• Transversal flexoelectric coefficients for fifty select atomic monolayers from first principles
• Elastic Constants and Bending Rigidities from Long-Wavelength Perturbation Expansions