1 Development of quasi - continuum reduction of orbital - free

This report summarizes the research objectives achieved in this project during the period 0301-2009 to 12-31-2011. Computational techniques have been developed that enable electronic structure calculations at macroscopic scales by seamless bridging of the quantum length-scale with continuum. The various components of the developed multi-scale scheme include (i) real-space formulation of density-functional theory (DFT); (ii) finite-element discretization; (iii) an adaptive coarse-graining through quasi-continuum reduction. The formulation has been developed for orbital-free DFT with non-local kinetic energy functionals. Studies on the energetics of defects in materials using the developed techniques have provided many new insights into the behavior of defects, and the complex nature of the interacting lengthscales that influence their behavior. An extension of this formulation to Kohn-Sham DFT was attempted, and as part of this effort an efficient real-space formulation of Kohn-Sham DFT was developed. Studies show that the developed formulation compares favorably with existing conventional DFT implementations, enables consideration of complex geometries and boundary conditions, and exhibits good scalability on parallel computing architectures. Summary of Research Objectives Achieved In this project we have conducted a program of research to develop computational techniques that seamlessly bridge the quantum length-scale with the continuum and enable an accurate electronic structure study of defective crystals. The techniques have been developed for orbital-free DFT (Wang & Teter, 1992; Wang et al., 1998, 1999), which is an approximation to the Kohn-Sham density functional theory where the kinetic energy functionals are modeled and is applicable to materials systems whose electronic structure is close to a free electron gas. Further, in order to extend these techniques to Kohn-Sham density functional theory, we have developed a real-space formulation of Kohn-Sham density functional theory (Suryanarayana et al., 2010; Motamarri et al., 2012), which is the basis for the coarse-graining techniques based on quasi-continuum reduction (Gavini et al., 2007; Radhakrishnan & Gavini, 2010). A comprehensive summary of the important research objectives achieved in this project is presented below with references to the published articles.