CAREER: Visualization, Interpretation, and Modeling of Exchange-Correlation Hole for Density Functional Theory

职业：密度泛函理论的交换相关空洞的可视化、解释和建模

• 批准号: 2042618
• 负责人: Jianwei Sun
• 金额: $ 50万
• 依托单位: Tulane University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-07-01 至 2026-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2042618&HistoricalAwards=false
• 关键词: CAREER; Visualization; Interpretation; Modeling; Exchange

Non-Technical AbstractFrom the metallurgy of the bronze age to the silicon semi-conductors driving the information age, every major step forward in human progress has been enabled by the arrival of new materials that expand the limits of human capability. Discovery of new materials has historically been achieved by diligent but expensive experimentation, but the advent of the computer changed this process. A rapid rise in computing power brings with it the possibility of simulating chemistry and physics to understand material processes at a microscopic level and to run programs that design new materials from the atoms up. In principle, such simulations are easy to formulate, as the equations of quantum mechanics that govern the constituent electrons can be written down on the back of an envelope. In practice, however, the equations become impossible to solve in all but the simplest situations, and the search for approximate models that are both accurate and efficient to compute is ongoing. Many of the most successful approximations to date fall into the class of "density-functional theory" (DFT), in which the complexity of the electronic quantum wave function is eschewed in favor of manipulating the simpler electron density function. This CAREER award supports basic research around density functional development, analyzing the fundamental quantum-mechanical nature of how electrons repel each other by interrogating the "exchange-correlation hole", a key object describing how finding an electron at one position reduces the chance of finding another electron elsewhere. The exchange-correlation hole will first be analyzed in some simple systems that challenge current DFT approximations, and this information will then be used to build more advanced DFT approximations. The resulting approximations will be tested in more complex systems relevant to technological applications. This research project will support, and be supported by, a high-school, undergraduate, and graduate education program that places importance on encouraging the participation of under-represented groups. The project's work and teaching will support outreach to community members in the New Orleans region who do not typically have access to high-quality opportunities for STEM mentorship.Technical AbstractA disconnect has emerged between applications of electronic-structure calculations and the underlying analyses that inform when and why a particular theory is successful. Of the many electronic-structure methods available, density-functional theory (DFT) has become the most popular. This project will analyse and improve approximations to the DFT exchange-correlation (XC) energy by modelling, interpreting, and visualizing the underlying XC hole, one of the most fundamental aspects of DFT. The results will be validated for a variety of molecules and solids, in particular transition-metal compounds. Whilst DFT is exact for the ground-state energy and electron density in principle, in practice the accuracy and efficiency are limited by the approximation of the XC energy, which can be formally defined by connection to the XC hole. Historically, developing an understanding of the XC hole has played a vital role in developing density-functional approximations and explaining their successes, though recent research into the XC hole has fallen behind the development of XC energy approximations. This has occurred for two reasons: 1) a practical DFT calculation needs only an XC energy approximation, resulting in developers overlooking XC holes in favor of energy densities and a gap in user understanding of XC holes, and 2) the formally defined XC hole is complicated to compute and only available for a few simple many-electron systems. This project will close the gap between users and developers as well as accelerating research in XC holes, and thus DFT generally, by i) accurately computing the formally defined XC holes for carefully chosen systems with interesting properties that are challenging to existing density-functional approximations, ii) reverse engineering holes for popular XC energy approximations and visualizing them against reference XC holes, iii) improving XC energy approximations using knowledge obtained from XC hole research, and iv) validating the existing and improved XC energy approximations on difficult systems with emphasis on transition-metal compounds.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

非技术摘要从青铜时代的冶金到推动信息时代的硅半导体，人类进步的每一步重大进步都是由于新材料的出现而扩大了人类能力的极限。 历史上，新材料的发现是通过勤奋但昂贵的实验来实现的，但计算机的出现改变了这一过程。 计算能力的快速增长带来了模拟化学和物理以在微观层面理解材料过程以及运行从原子向上设计新材料的程序的可能性。 原则上，这种模拟很容易制定，因为控制组成电子的量子力学方程可以写在信封的背面。 然而，在实践中，除了最简单的情况之外，方程在所有情况下都无法求解，并且对计算准确且高效的近似模型的搜索仍在进行中。 迄今为止，许多最成功的近似都属于“密度泛函理论”（DFT）类别，其中避开了电子量子波函数的复杂性，有利于操纵更简单的电子密度函数。 该职业奖支持围绕密度泛函发展的基础研究，通过询问“交换相关空穴”来分析电子如何相互排斥的基本量子力学性质，“交换相关空穴”是描述在一个位置找到电子如何减少在其他地方找到另一个电子的机会的关键对象。 首先将在一些挑战当前 DFT 近似的简单系统中分析交换相关空洞，然后使用该信息构建更高级的 DFT 近似。 由此产生的近似值将在与技术应用相关的更复杂的系统中进行测试。 该研究项目将支持一个高中、本科生和研究生教育计划，并得到该计划的支持，该计划重视鼓励代表性不足的群体的参与。 该项目的工作和教学将支持向新奥尔良地区的社区成员进行推广，这些成员通常无法获得高质量的 STEM 指导机会。 技术摘要 电子结构计算的应用与告知特定理论何时以及为何成功的基础分析之间出现了脱节。 在众多可用的电子结构方法中，密度泛函理论（DFT）已成为最受欢迎的。 该项目将通过建模、解释和可视化潜在的 XC 空洞（DFT 最基本的方面之一）来分析和改进 DFT 交换相关 (XC) 能量的近似值。 结果将针对各种分子和固体进行验证，特别是过渡金属化合物。 虽然 DFT 原则上对于基态能量和电子密度是精确的，但实际上，精度和效率受到 XC 能量近似值的限制，XC 能量可以通过与 XC 空穴的连接来正式定义。 从历史上看，对 XC 空穴的理解在发展密度泛函近似和解释其成功方面发挥了至关重要的作用，尽管最近对 XC 空穴的研究落后于 XC 能量近似的发展。 出现这种情况的原因有两个：1）实际的 DFT 计算只需要 XC 能量近似，导致开发人员忽视 XC 空穴而倾向于能量密度，并且用户对 XC 空穴的理解存在差距；2）正式定义的 XC 空穴计算起来很复杂，并且仅适用于一些简单的多电子系统。 该项目将缩小用户和开发人员之间的差距，并加速 XC 孔的研究，从而总体上加速 DFT，方法是：i) 为精心选择的系统准确计算形式定义的 XC 孔，这些系统具有对现有密度泛函近似提出挑战的有趣特性；ii) 对流行的 XC 能量近似值进行逆向工程孔，并根据参考 XC 孔将其可视化；iii) 使用从 XC 孔获得的知识改进 XC 能量近似值。 研究，以及 iv) 在困难系统上验证现有的和改进的 XC 能量近似，重点是过渡金属化合物。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Construction of meta-GGA functionals through restoration of exact constraint adherence to regularized SCAN functionals

• DOI: 10.1063/5.0073623
• 发表时间: 2022-01-21
• 期刊: JOURNAL OF CHEMICAL PHYSICS
• 影响因子: 4.4
• 作者: Furness, James W.;Kaplan, Aaron D.;Sun, Jianwei
• 通讯作者: Sun, Jianwei

Capturing the electron–electron cusp with the coupling-constant averaged exchange–correlation hole: A case study for Hooke’s atoms

用耦合常数平均交换相关孔捕获电子-电子尖点：胡克原子的案例研究

• DOI: 10.1063/5.0173370
• 发表时间: 2024
• 期刊: The Journal of Chemical Physics
• 作者: Hou, Lin;Irons, Tom J.;Wang, Yanyong;Furness, James W.;Wibowo-Teale, Andrew M.;Sun, Jianwei
• 通讯作者: Sun, Jianwei