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

这是一个纳米尺度探索性研究奖，通过纳米尺度科学与工程招标提交的提案，由材料研究部和土木与机械系统部联合资助。这项研究具有跨学科的味道。它涉及应用数学方法，首先开发用于机器人技术，以创建一种新的计算方法，使紧密结合的电子结构方法计算易于处理纳米级材料问题，其中耦合电子和机械性能感兴趣。该奖项支持基于经典的塞罗-拉克曼矩定理和构象统计的最新发展，开发一种新的紧密结合原子方法的研究。计算工作量与系统中的原子数量成线性关系，并利用快速数值技术计算晶格上的卷积。这些数值技术基于群论和谐波分析的最新发展，在计算材料和物理学界并不广为人知。最近，这些构象统计方法已被用于描述高度铰接的机械臂和长链聚合物分子的构型。众所周知的基于矩的紧密结合技术是基于描述结构中单个原子周围的局部拓扑结构。构象统计方法极大地减少了“暴力”枚举每个原子周围随机行走类型路径的计算成本，这些路径被解释为局部态密度的矩。每个原子的操作次数可以从K - M阶（K是每个原子的近邻数（通常为3或4），M是矩数（50阶））降至Md - logMd阶（d是空间维数）。现有的数值方法可以使用这些计算的矩来近似局部状态密度，从中可以获得系统的总能量和任何感兴趣的电子或机械特性。该方法将应用于纯碳纳米管、掺杂碳纳米管、常规碳纳米管、应变碳纳米管和缺陷碳纳米管的研究。在这些情况下，手性和非手性几何都可以处理。半导体量子点的研究是另一个应用。几个原子尺度的问题，包括表面台阶，量子效应在润湿层，和材料混合，将攻击。该奖项还有助于培养研究生水平的学生和开发新的高级研究生水平课程。这是一项纳米级探索性研究奖，由材料研究部和土木与机械系统部联合资助，该提案提交给纳米级科学与工程招标。该奖项支持跨学科的研究。它涉及使用数学方法首先开发用于机器人技术，以开发近似电子结构计算的有效计算方法。该方法将应用于纳米材料问题，重点关注耦合电子和机械性能。具体的应用涉及碳纳米管：纯的、掺杂的、规则的、应变的、有缺陷的和半导体量子点。在后者中，重点将放在原子尺度的问题上，包括表面步骤、润湿层中的量子效应和材料混合。新的精确和高效的计算方法能够预测纳米级原子和分子结构的电子和结构性质，并在其他材料中有更广泛的应用。该奖项有助于培养研究生水平的学生和开发新的高级研究生水平课程。＊＊＊

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. ***