Symmetry-adapted density functional theory

One-dimensional nanostructures such as nanotubes, nanowires, and nanocoils have received increased attention over the past three decades due to their fascinating mechanical, electronic, optical, and thermal properties. It is common for these systems to possess some form of nontranslational symmetry, with cyclic and helical perhaps the most frequent among the symmorphic and nonsymmorphic groups, respectively. Moreover, the application of torsional deformations on 1D nanostructures and bending deformations on 2D nanostructures results in systems with these symmetries. These systems are computationally intractable for standard density functional theory (DFT) implementations which are based on affine coordinate systems. In this work, we present a cyclic and helical symmetry-adapted formulation and its large-scale parallel implementation in the state-of-the-art real-space DFT code SPARC. Furthermore, we also develop a real-space formulation of density functional perturbation theory for phonons which is subsequently symmetry-adapted to enable the study of the linear response of low-dimensional systems with application to the stability analysis of carbon nanotubes.Ph.D