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. Objective structures are ubiquitously present in all of materials science, biology and nanotechnology and examples of these structures include nanotubes, buckyballs, tail sheaths and capsids of viruses, graphene sheets and molecular bilayers. Due to their association with large degrees of symmetry, objective structures are likely to be a fertile source of materials with remarkable material properties: particularly, collective material properties such as ferromagnetism and ferroelectricity. A systematic study of objective structures therefore, is likely to lead to the discovery of novel materials. At the same time, formulation of computational methods specifically designed for studying objective structures, is likely to lead to the development of novel nanomechanics simulations methodologies. Following this line of thought, this thesis deals with the development of Objective Density Functional Theory: a suite of rigorously formulated Density Functional methods and numerical algorithms for carrying out abinitio simulation studies of objective structures. Drawing analogies from the classical planewave density functional method of solid state physics, our focus has been on the development of novel spectral schemes for studying objective structures using Kohn Sham Density Functional Theory. In this work, we demon strate how the equations of Kohn Sham Density Functional Theory for objective structures admit interpretation in terms of symmetry adapted cell problems. We propose complete orthonormal basis sets for discretizing these cell problems. Next, we discuss the significant challenges associated with the efficient solution of the discretized cell problems and our progress in addressing these challenges through a variety of numerical and algorithmic strategies. Many of these strategies and methods have been implemented within the framework of a powerful first principles simulation package called ClusterES (Cluster Electronic Structure) that we designed and developed as part of this work. We end with some examples highlighting the efficiency and accuracy of our numerical methods as well as a brief discussion of ongoing applications of our spectral schemes to the study of some problems in nanomechanics.
University of Minnesota Ph.D. dissertation. December 2013. Major: Aerospace Engineering and Mechanics. Advisors: Richard D. James, Ryan S. Elliott. 1 computer file (PDF); ix, 156 pages, appendices A-C.
Banerjee, Amartya Sankar.
Density functional methods for objective structures: theory and simulation schemes.
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