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

从青铜时代的冶金到信息时代的硅半导体，人类进步的每一次重大进步都是由于新材料的出现而实现的，这些新材料拓展了人类能力的极限。历史上，新材料的发现是通过勤奋而昂贵的实验来实现的，但是计算机的出现改变了这一过程。随着计算能力的迅速提高，模拟化学和物理，从而在微观层面上理解材料过程，并运行从原子开始设计新材料的程序成为可能。原则上，这样的模拟很容易形成公式，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，除了最简单的情况外，这些方程在所有情况下都是不可能解决的，并且正在寻找既准确又有效的近似模型来计算。迄今为止，许多最成功的近似都属于“密度泛函理论”（DFT）的范畴，在这种理论中，电子量子波函数的复杂性被避免，而倾向于操纵更简单的电子密度函数。这个职业奖支持围绕密度函数发展的基础研究，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一个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。交换相关漏洞将首先在一些挑战当前DFT近似的简单系统中进行分析，然后该信息将用于构建更高级的DFT近似。所得到的近似结果将在与技术应用有关的更复杂的系统中进行检验。该研究项目将支持并得到高中、本科和研究生教育项目的支持，该项目重视鼓励弱势群体的参与。该项目的工作和教学将支持向新奥尔良地区的社区成员提供外展服务，这些社区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）已成为最受欢迎的方法。该项目将通过建模、解释和可视化潜在的XC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。该结果将用于各种分子和固体，特别是过渡金属化合物的验证。虽然DFT在原理上对基态能量和电子密度是精确的，但在实践中，精度和效率受到XC能量近似的限制，而XC能量可以通过与XC空穴的连接来正式定义。从历史上看，发展对XC洞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洞的研究已经落后于XC能量近似的发展。出现这种情况有两个原因：1)实际的DFT计算只需要XC能量近似，导致开发人员忽略了XC空穴，而倾向于能量密度和用户对XC空穴的理解存在差距；2)正式定义的XC空穴计算复杂，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，并加速对XC洞的研究，因此DFT一般是通过i)精确计算精心选择的具有有趣特性的系统的正式定义的XC洞，这些特性对现有的密度函数近似具有挑战性，ii)对流行的XC能量近似进行逆向工程洞，并将它们与参考XC洞进行可视化。iii)利用从XC空穴研究中获得的知识改进XC能量近似；iv)验证现有的和改进的XC能量近似，重点是过渡金属化合物。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.