A Novel Spectral Scheme for Abinitio Simulations of Objective Structures
Amartya Banerjee (University of Minnesota), Ryan Elliott (University of Minnesota), Richard James (University of Minnesota)
From Atomistics to Reality: Spanning Scales in Simulations and Experiments Symposium A
Tue 4:20 - 5:40
CIT 165
Objective structures are atomic/molecular configurations which generalize the notion of crystals and are such that all the constituent atoms/molecules of the structure “see” the same environment up to orthogonal transformations and translations. These structures are ubiquitously present in all of materials science, biology and nanotechnology, and due to their association with large degrees of symmetry, they are likely to be a fertile source of materials with remarkable material properties. In this work, drawing analogies from the classical plane-wave density functional theory method of solid state physics, we present a novel spectral scheme for studying objective structures using Kohn-Sham Density Functional Theory. This opens up the possibility of carrying out efficient and accurate abinitio simulations of a large class of nano-materials and structures. First, we demonstrate how the equations of Kohn-Sham Density Functional Theory for objective structures admit interpretation in terms of symmetry adapted cell problems. Next, we propose a complete orthonormal basis set for discretizing these cell problems. We then discuss the significant algorithmic challenges associated with the the efficient solution of the discretized cell problems. We describe our progress in addressing these challenges through transform methods of evaluation of certain nonlinearities, the use of radial multipole expansions and the use of a matrix-free block-preconditioned iterative diagonalization procedure. We also mention how our implementation benefits from two-level parallelism present in our scheme and the ability of the scheme to seamlessly make use of arbitrary point group symmetries. Finally, we present applications of our spectral scheme to the study of some problems in nano-mechanics, including the study of properties of nano-clusters and simulations of the bending of nano-beams.