NER: Coupled Electronic and Mechanical Properties by Conformational Statistics Tight-Binding

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This is a Nanoscale Exploratory Research award on a proposal submitted through the Nanoscale Science and Engineering Solicitation and is jointly funded by the Division of Materials Research and the Division of Civil and Mechanical Systems. The research has an interdisciplinary flavor. It involves the application of mathematical methods first developed for use in robotics to create a new computational method to make a tight-binding electronic structure method computationally tractable for nanoscale materials problems in which coupled electronic and mechanical properties are of interest.This award supports research to develop a new tight-binding atomistic method, based on the classical Cyrot-Lackmann moments theorem and recent developments in conformational statistics. The computational effort scales linearly with the number of atoms in the system and takes advantage of fast numerical techniques for computing convolutions on lattices. These numerical techniques, which are based on recent developments in group theory and harmonic analysis, are not widely known to the computational materials and physics communities. Most recently, these conformational statistics methods have been used to delineate configurations of highly articulated robot-arms and, separately, long-chain polymer molecules. The well-known moments based tight-binding technique is based on delineating the local topology surrounding individual atoms in a structure. The conformational statistics method dramatically reduces the computational cost of "brute-force" enumeration of the random-walk type paths around each atom, which are interpreted as moments of the local density of states. The number of operations per atom can be reduced from order K M , where K is the number of near neighbors per atom (usually 3 or 4), and M is the number of moments (of order 50), to order Md logMd , where d is the number of spatial dimensions. Existing numerical methods enable the use of these computed moments to approximate the local density of states, from which the total energy of the system and any electronic or mechanical properties of interest can be obtained. The method will be applied to the study of pure, doped, regular, strained, and defective carbon nanotubes. In each of these cases chiral and nonchiral geometries can be handled. The study of semiconductor quantum dots is another application. Several atomic scale problems, including surface steps, quantum effects in the wetting layer, and material intermixing, will be attacked.This award also contributes to the training of graduate level students and the development of a new advanced graduate level course. %%%This is a Nanoscale Exploratory Research award on a proposal submitted to the Nanoscale Science and Engineering solicitation and is jointly funded by the Division of Materials Research and the Division of Civil and Mechanical Systems. This award supports research with an interdisciplinary flavor. It involves the use of mathematical methods first developed for use in robotics to develop an efficient computational method for approximate electronic structure calculations. The method will be applied to nanoscale materials problems with a focus on coupled electronic and mechanical properties. Specific applications involve carbon nanotubes: pure, doped, regular, strained, and defective and semiconductor quantum dots. In the latter, the focus will be on atomic scale problems, including surface steps, quantum effects in the wetting layer, and material intermixing. New accurate and efficient computational methods enable the prediction of electronic and structural properties of nanoscale atomic and molecular structures and have broader applications to other materials.This award contributes to the training of graduate level students and the development of a new advanced graduate level course. ***